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The Functional Configuration of the Basic Neuron
James T. Fulton
Neural Concepts
Abstract: This Chapter introduces the three-terminal Neuron based on The Electrolytic Theory of the Neuron. It
overcomes the many short-comings of two-terminal neuron based on the chemical theory of the neuron. The
Electrolytic Theory of the Neuron introduces many new concepts from Semiconductor Physics to our understanding
of the neuron, specifically the active liquid-crystalline semiconductor device, the Activa. The Activa appears in every
neuron and between each pair of neurons where it forms the synapse, a unidirectional semiconducting device when
biased electrically in-vivo. The synapse is reversible in vitro by varying the bias. The conventional synapse is a three-
teminal, PNP device. In the cerebrum, as well as the peripheral nervous system, the synapse is widely employed. There
are two different forms of neuron bearing the honorific “Purkinje neuron.” The first one in the cerebrum (also called
the giant pyramid neuron or ganglion neuron) employs the PNP synapse; the second one is used in the cerebellum and
is the key element in the storage circuit used in a large scale physical database. It is associated with a special cruciform
synapse that is of the PNPN type, also known as a four layer diode. The cruciform synapse is the key to the write
once/read multiple times characteristic of long term memory. Section 2.1 reviews the science underlying the
electrolytic Activa and three-terminal neuron. Sections 2.2 and 2.3 develop the configuration and performance of the
Activa within the electrolytic neuron. Section 2.2.3.3.5 introduces the discovery that Quantum Tunneling, may
be a key to the sensitivity in the Activa. Tunneling was only discovered by humans in 1974. Section 2.4 develops
the Activa as a three-terminal synapse. Section 2.5 addresses the neuron used in analog neural engines (making up
95% of all neurons in the CNS). Section 2.6 addresses the remaining 5% of the neurons of the CNS that operate
in the pulse mode (action potentials) leading to the definition of the phase-code used in the neural system in Section
9.3.1. Section 2.7 addresses the hybrid neurons interface the analog and pulse modes operations. Section 2.10
addresses the special modes of operations within the cerebellum and the second type of Purkinje neuron introduced
above. Section 2.11 provides a short summary of the chapter.
Keywords: neuron, three-terminal neuron, Activa, three-terminal Activa, semiconductor, liquid-crystal, EZ water
cerebrum, cerebellum, Purkinje neuron, physical database, symbolic database.
Purpose: This material is the core Chapter of this work.
This material is in draft form but leads to all of the science and conceptual framework for understanding the
physiology of the neural system of animals (including the sub-modalities of species identification and gender
identification).
This material is in draft form because I (who am now 86 yrs old) may not get the opportunity to work it into
final form and post it on ResearchGate.
The NEURONS and
NEURAL SYSTEM:
a 21st CENTURY PARADIGM
This material is excerpted from the full -version of the text. The final printed
version will be more concise due to further editing and economical constraints.
A Table of Contents and an index are located at the end of this paper.
A few citations have yet to be defined and are indicated by “xxx.”
James T. Fulton
Neural Concepts
jtfulton@neuronresearch.net
November 6, 2023
Copyright 2011-23 James T. Fulton
The Neuron 2- 3
“It seems to me that in these robot brains the transistor is the ideal nerve cell.”
William Shockley, 1949
2 The Functional Configuration of the Basic Neuron 1
Notice: The Coursera organization has recently begun offering free courses claimed to be at the college
level. The course entitled “Computational Neuroscience” by two little known instructors, Adrienne Fairhall,
Rajesh P. N. Rao2, from the University of Washington is based on the literature repeating endlessly the state
of the art in the cytology of the cell and neurons from the first half of the 20th Century–specifically prior to
the dawn of semiconductor physics, the discovery of the transistor, and the more recent discovery of the
biological transistor. The latter is now in commercial use in organic light emitting device screens in
cellphones and even television monitors. The existence of the biological transistor, a three-terminal device,
totally deprecates the two terminal device, based on the Hodgkin-Huxley conceptual explanation of their
totally empirical experiments, that is the basis of the course.
The following material is in no way compatible with that new telecourse (May 2013). No further
discussion of the telecourse except to point out that it remains possible to obtain a PhD in computational
neuroscience without having demonstrated any detailed knowledge of how the neuron actually works.
2.1 Introduction
It is a remarkable fact that the extensive neuroscience literature contains virtually no information describing the
relationship between the electrical input signal(s) applied to a neuron and the resulting electrical output signal. This
chapter will focus on this input-output relationship. It is also a fact that the neuroscience literature contains virtually
no information concerning the cytological structure internal to a neuron. This chapter will address this subject, but
a more extensive discussion of the morphology of the neuron will be presented in Chapter 5. It is also a fact that
the neuroscience community has long accepted the concept of simple heavy inorganic ions (sodium, potassium and
chlorine ions) moving freely through the liquid-crystalline bilayer cell wall of a neuron in the total absence of data
showing this to be possible and considerable data showing such passage is not possible (Section 2.1.4).
The neuron has evolved to satisfy a wide variety of applications within the neural system as suggested by the block
diagrams of Chapter 1 (Sections 1.1.2, 1.1.4 and 1.2.7).
As noted elsewhere in this work, Hodgkin & Huxley were involved in exploratory research and were grasping for
explanations as to what they observed. Their background, and that of the scientific community was relatively crude
in the 1930's and 1940's. While they were unable to demonstrate that any ions passed through their axolemma, they
assumed that ions did because of the difference in relative concentration of ions on the two sides of their axolemma.
This assumption and their assertion of an “Independence Principle” to explain their assumption has proven
unsupportable in modern science. Unfortunately, the Don’s of the natal biochemical community of the 1960's, also
relying on their limited scientific base, ordained that Hodgkin & Huxley were right and furthermore, the operation
of the neural system was fundamentally based on chemical reactions. Their position has been very difficult to
overcome because of its repeated assertion by their protégée in introductory textbooks. This situation has continued
to the present day where Purves et al3. dedicate their unit 1 (particularly chapters 2 through 4) to regurgitating the
Hodgkin & Huxley hypotheses, including their adoption of the euphemism relating the discharging of the axoplasm
potential to an inrush of sodium ions (rather than a discharging of the axoplasm by electrons exiting the space via
the internal amplifier) and the recharging of the axoplasm by an outrush of potassium ions (rather than the inrush
1Released: November 6, 2023
2https://www.coursera.org (The only current course is on Computational Neuroscience)
3Purves, D. Augustine, G. Fitzpatrick, D. et al. (2004) Neuroscience, 3rd Ed. Sunderland, MA: Sinauer
Associates.
4 Neurons & the Nervous System
of electrons from the glutamate/GABA power source) in the absence of any data to this day showing the axolemma
is permeable to these heavy ions. The fact that ions of these heavy ions do not exist alone when in solution has also
escaped the attention of these protégée (Section 8.5.4.4). That section also shows the coordinate complex of the
sodium ion and water is significantly larger in diameter (9 Angstrom) than the putative internal diameter of the pores
in the axolemma typically proposed in the literature (about 2 Angstrom).
The hypothesis that the permeability of the axolemma is a variable is also unsupported by any physical chemistry.
Such variation in permeability is not required in the context, and hypotheses, of this work, except in the fact that
modified neurolemma can form an ideal electrolytic diode. Such a semiconductor diode exhibits a deterministic and
well characterized variable impedance to electrons.
Steriade, et. al. have addressed the difficulty of interpreting neuronal oscillations in brain functions without any
understanding of the underlying mechanisms4. Their position is that the problem is the lack of a formal mathematical
base for these mechanisms. However, mathematics does not provide a base for a mechanism, it provides a
framework. A base is more fundamental and relies upon physics, electronics and chemistry. The oscillatory
mechanisms associated with neurons are based on the active element within them, the Activa. The oscillatory
performance of neurons is identical to those associated with man-made electronic circuits. The mathematical
interpretation of both type of devices is well documented in the electronics literature. This will be demonstrated in
this chapter.
Their suggestion that a set of differential equations based on phase plane analysis can describe the oscillations of
a neuron is correct. However, their supposition that the phase plane used is derivable from an autocatalytic
(chemical) mechanism where the end product further activates the enzyme creating it appears unproven5. The
resulting hypotheses, involving contorted chemistry, are not needed when the basic physics of the situation are
examines as in this and the preceding chapter. This work takes exception to the claim of Steriade, et. al. that “In
fact, chemically mediated oscillations, especially as it relates to the gK(Ca) is a most important component of the
intrinsic electrical properties of neurons.” After providing a rationale for the autocatalytic hypothesis, they conclude
“In addition, other ionic conductances are present that endow these neurons with a more complicated set of
oscillatory properties.” This is the classical solution of solving a problem based on an inadequate understanding
of the fundamentals. The investigator merely introduces more variables into the equations until a sufficient degree
of flexibility is available to meet any requirement. Rather than introducing additional ions flowing with and counter
to the local electric field, there is a need to re-examine the original chemically-based hypothesis.
2.1.1 The fundamental chemically-based neuron of biology
4Steriade, M. Jones, E. & Llinas, R. (1990) Thalamic oscillations and signaling. NY: John Wiley, pp 132-133
5Goldbeter, A. & Moran, F. (1988) Dynamics of a biochemical system with multiple oscillatory domains as a
clue for multiple modes of neuronal oscillations Eur Biophys Jour vol 15(5), pp 277-287
The Neuron 2- 5
Figure 2.1.1-1 shows the basic schematic of a neuron that will be discussed in this chapter. The expression of the
neuron in this figure is significantly modified from one by Shepherd in Byrne & Roberts (1997, page 91). This
electrolytic configuration supports a fundamental difference from the historical two-terminal neuron of Hodgkin and
Huxleys. The neuron and the biological transistor (the Activa) within it are three-terminal electrolytic devices.
These elements are developed in detail in Section 2.2 & 2.3. The small numbers shown in this figure were not
addressed in the original work except to tie that part of the neuron to simple waveforms that Shepherd related to
operation of the stage 3 signal projection neuron. These waveforms were not sufficiently precise to be included here.
The location of the Activa is shown by dashed lines in this annotated figure and is included in the region frequently
described as the hillock in stage 3A neurons.
The same neuron can be operated in two distinct modes through electrolytic biasing. In both cases, all of the signals
applied to the dendritic boutons are summed and the net sum is applied to the non-inverting input terminal of the
three-terminal internal Activa. Similarly, all of the signals applied to the poditic boutons are summed and the net
sum signal is applied to the negative (signal inverting) input terminal of the three-terminal Activa. The left version
Figure 2.1.1-1The generic schema of a biological neuron. Left; the generic
neuron biased for analog operation. Right; same generic neuron with an
extended (multi-segment axon and biased for pulse (action potential) generation.
The individual axon segments of pulse generating neurons are myelinated to
reduce signal attenuation between Nodes of Ranvier.. The combination of the
dendritic and poditic trees is frequently described as a “bi-stratified dendritic
tree.” Red elements, examples of axons of antidromic neurons. Blue; neuritic
structures of orthodromic neurons. C; signal transmission by conduction in
these regions. P; signal transmission by propagation along the myelinated axon
segments. See text. Compare to Byrne & Roberts, 2004 & 2009.
6 Neurons & the Nervous System
shows the nominal neuron amplifying the difference between the two inputs and generating an analog output signal
using an axon of less than 2 mm length (more than 95% of all neurons, see the report of Phillips (1956a) in Section
2.5). The neuron on the right is used in less than 5% of all neurons and is used where it is necessary to propagate
a signal over more than 2 mm. It described in detail in Section 2.6 & Chapter 9. It is biased to exhibit an
electrolytic threshold and is used exclusively in stage 3A neural circuits. Below this threshold, it exhibits a relatively
low amplification. When the difference between the two inputs exceeds the threshold, the amplification of the circuit
becomes very high and the Activa enters a monopulse generating mode of operation. This mode of operation is used
to propagate pulse signals over long distances (greater than 2 mm), at speeds an order of magnitude faster than
conduction allows, based on the electromagnetic equations of Maxwell. To achieve this propagation efficiently, the
axon is divided into axon segments that are myelinated. Each axon segment thereby forms a very low loss coaxial
cable. Each segment is separated from its nearest neighbor by regenerating stations known as Nodes of Ranvier.
Ramachandran6, as reproduced in Baars & Gage (2nd ed, page 66) attempts to illustrate signal projection at the
elementary level using a sine wave rather than an action potential and explaining propagation over a coaxial structure
by ionic charge transfer. These concepts are misleading and not in conformance with the facts (See Section 9.1.2).
The circulating arrows are totally misleading and based on the concept of ionic conduction. In electromagnetic
propagation, all of the circulating arrows are directed forward.
When not identified explicitly, dendrites and podites are both described as neurites. Since the two neuritic trees
provide different capabilities, either one can be absent from a given neuron. When both are present, the neuron is
frequently described as “bi-stratified.”
Earlier texts have infrequently described axosomatic synapses. These synapses in fact are associated with
the internal dendroplasm or podaplasm and should be appropriately renamed either axodendritic or
axopoditic synapses. They have occasionally proposed an axoaxonic synapse, but normally without
supporting evidence.
The neuron shown here can be compared to that of Byrne & Roberts and used in the 2nd edition of the introductory
neuroscience text by Baars & Gage (page 65). An earlier archaic but widely reproduced schematic neuron appeared
in Appendix A of their 1st edition but it conflicted with the variant in the main text and was dropped from the 2nd
edition.
The conceptual waveforms shown on the right of the neuron in Byrne & Roberts are not well developed to describe
the real situation outlined above. They do not represent the 95% of neurons that do not generate action potentials
and they do not clearly represent the other 5% of stage 3 that do. See the major discovery of Phillips in 1956
reproduced in Section 2.5. The waveforms are also foreign to the operation of the stage 3 decoding neurons so
critical to the operation of the neural system. The decoding neurons (stage 3B) recover the analog information
encoded earlier by the stage 3A neurons.
Another major difference from the highly conceptual neuron of Hodgkin and Huxley is in the role of the synapse.
Since a two-terminal neuron (frequently described as bilateral in morphology) cannot readily support voltage inputs
of opposite phase, this function has historically been assigned to excitatory and inhibitory synapses. This notation
is inappropriate for analog neurons and is unnecessary when the differential input capability of a three-terminal
device is utilized. All known synapses and Nodes of Ranvier are noninverting (or excitatory).
The individual synapse, and its close relative the Node of Ranvier, are based on the same Activa used in the neuron
and exhibit similar properties to the two forms of the basic neuron shown in the figure (sans the axon segments).
The synapse is described in detail in Section 2.4. The Node of Ranvier is described in Section 2.6.3.
2.1.1.1 An exhaustive review of neuron models –Borg-Graham,1998
Borg-Graham7 published an exhaustive paper (99 pages) in a chapter of Cerebral Cortex volume 13 that cited 294
other papers. The goal was an extensive review ending in the definition of a preferred model based on the of the
neuron. It did not contain one single figure (of 17) describing the internal organization of any neuron model they
addressed.
The chapter concludes with “some additional simulations illustrating various characteristic of the Working model.”
6Ramachandran, V. (2002) Encyclopedia of the Human Brain. San Diegeo, CA: Academic Press
7Borg_Graham, L. (1998) Interpretations of Data and Mechanisms for Hippocampal Pyramidal Cell Models
In Ulinski, P. Jones, E. & Peters, A. eds. Cerebral Cortex, Volume 13: Cortical Models. NY: Plenum Press
The Neuron 2- 7
No “Working model” was presented. He provides a one paragraph recapitulation of his working model in section
7.1.8, only listing the currents related to a long list of chemicals presumed to be critical to the operation of a neuron
(page 35 of 99 pages). He closes section 14 with “The classical basic computational characteristic of a neuron is
the transformation of a stimulus intensity into the frequency of repetitive spikes.” With this narrow interpretation
of the role of the neuron, not much can be expected of the Borg-Graham paper. The fact he only considered the
means of computational modeling a wide set of ionic currents through undefined membranes, should have appeared
in the introduction.
2.1.2 Modeling difficulties of the chemical theory of the neuron up to the current day
The present state of mathematical and computer (numerical) modeling of neurons is unsatisfactory. All modeling
found in the literature prior to 2012 has attempted to model the very early conceptual descriptions of a neuron by
Hodgkin & Huxley (H&H) based on the examination of a parametrically stimulated in-vitro and highly mutilated
neuron from a species of Mollusca8,9,10. Such modeling did not recognized the special class of the so-called giant
axon of the locomotion neuron explored by Hodgkin & Huxley.
Chapter 5 of this work will review the work of H&H and the responses of the community to that work at the time.
These actions of Hodgkin and Huxley have been noted by earlier writers. As Cole noted on page 476, “As to curve-
fitting, the procedure and the results of Hodgkin & Huxley (1952b) are entirely unorthodox and are looked at with
both amazement and admiration by trained mathematicians11.” Messenger, et. al12. have provided a discussion of
the giant axon of squid . The relevant figures are based on hand drawn sketches by Young dating from 1939 and
1973. Their opening quote is interesting. “Despite all the work on squid giant fibres since their rediscovery 60 years
ago we still know nothing about how they innervate the mantel muscles and do not really understand how they are
themselves activated. In particular we do not know the nature of the transmitters(s) at the largest synapse in the
animal kingdom: the ‘giant synapse’ between second- and third-order fibres in the squid stellate ganglion.” This
is quite a statement for a book first published in 1995!
Carnevale & Hines13 have provided an excellent discussion on “Why model?” They note, “In order to achieve the
ultimate goal of understanding how nervous systems work, it will be necessary to know many different kinds of
information” related to the anatomy, pharmacology, biochemistry and many related sciences. They develop the
complexities involved in describing the mechanisms involved and the features of signaling and one paragraph and
then go on to assert,
“Hypotheses about these signals and mechanism, and how nervous system function emerges from their
operation, cannot be evaluated by intuition alone, but require empirically based modeling.”
They use a simpler version of Figure 2.1.2-1 to address,
“ ‘Just what is involved in creating a . . . model of a physical system?’ There are several approaches
including physical circuit modeling, analytical modeling and numerical modeling. Based on a two-terminal
neuron evolving from H&H, there has not been adequate knowledge of the neuron to allow realistic physical
circuit modeling. Similarly relying on the equations developed by H&H during their exploratory
investigations of 60 years ago has not led to adequate analytical or computational models. Recent analytical
and computational models have frequently not examined whether the equations of H&H even address the
generic neuron or are only an attempt to describe a specific type of neuron. Thus the notation in the figure.
It is necessary that the modeler strain to understand what is actually known about his subject and only then
attempt to simplify his conceptual model (hopefully by stating a clear null hypothesis he intends to explore).
Once a clear null hypothesis is established, it is important to be faithful to the Scientific Method when
8Hodgkin, A. (1951) The ionic basis of electrical activity in nerve and muscle Biol Rev vol. 26 pp 339-409
9Hodgkin, A. Huxley, A. & Katz, B. (1952) Measurement of current-voltage relations in the membrane of the
giant axon of Loligo. J. Physiol. vol 116, pp. 424-448
10Hodgkin, A. & Huxley, A. (1952) A quantitative description of membrane current and its application to
conduction and excitation in nerve. J. Physiol. Vol 117, pp. 500-544
11Cole, K. (1968) Membranes, Ions and Impulses. Berkeley, CA: University of California Press
12Messenger, J. De Santis, A. & Ogden, D. (1995) Chemical transmission at the squid giant synapse Chapter
19 in Abbott, N. Williamson, R. & Maddock, L. ed. Cephalopod Neurobiology NY: Oxford University Press
13Carnevale, N. & Hines, M. (2006) The NEURON Book. NY: Cambridge Univ Press
8 Neurons & the Nervous System
evaluating the physical, analytical, computational or other model of the system.”
The underlining of the above remarks indicates the main thesis of this work; The material presented by Hodgkin
et al. in the 1950's is not adequate to support a sophisticated model of the fundamental neuron.
This chapter will focus on assembling what is known about the physical neuron after 60 years research from the time
of H&H. To put this material into a suitable context, the idea of a single conceptual model will be expanded into
a framework supporting several application specific models. Specifically, this work will develop both circuit models
and closed form analytical models for;
• Stage 1 sensory neurons (the excitation/de-excitation and the generator potentials),
• Stage 3 signal projection neurons (the action potential) and
• any other neuron subject to parametric stimulation
The chapter will then proceed to define in detail the specific characteristics and functions of these individual models.
The subject of mathematical and computer modeling will be addressed in detail in Section 2.9 after determining that
closed form analytical solutions to the equations representing neuron operation are readily available.
During the 1950's, the label action potential was not clearly defined. It was frequently applied to any pulse-like
response to almost any stimulation. This included the stimulation of a stage 1 signal generating neuron in response
to a short pulse as well as a stage 3 Node of Ranvier regenerating a pulse designed to be identical in shape to the
action potential exciting it. The former is not identified as an analog waveform describing the excitation/de-
excitation mechanism intrinsic to the sensory neurons only. The latter is now identified with the encoding and
regenerating pulse neurons of stage 3. These waveforms arise from substantially different mechanisms in
substantially differently configured neurons.
2.1.3 Roadmap and fundamental premises developed in this chapter
Section 2.2 will present the very basics of how the electrolytic portion of the neuron is formed along with its static
(first order) characteristics. Section 2.3 will show how these static characteristics lead to the dynamic (second
order) neuron. These properties represent the very core of the functional neuron that is expanded into the variety
of classes of neurons described in the following sections. Section 2.5 will address the simpler, but vastly
predominant, analog neurons. Section 2.6 will address the critically important, but less common, phasic neurons
of stage 3. Section 2.7 will address some more unique neurons found within the viscera. Section 2.4 will address
the synapse in detail. It is critically important that the inter-neuron synapse of signaling be differentiated from the
Figure 2.1.2-1 Framework for modeling the neuron. This chapter will focus on
describing the detailed mechanisms of the physical neuron as currently known
in order to develop a series of simplified conceptual models leading to multiple
detailed closed-form analytical models of the neuron. See text. Italic annotation
added, from Carnevale & Hines, 2006.
The Neuron 2- 9
neuron to other tissue synapse. The inter-neuron synapse is totally electrolytic while the neuron to other tissue
synapse can take a variety of functional forms. Section 2.8 will present some miscellaneous but important features
found within the neural system. Finally, Section 2.8 will address the state of modeling applied to the neuron prior
to this work.
This work is not compatible with the chemical theory of the neuron, emanating from the work of Hodgkin &
Huxley, HH, in the late 1930's into the 1940's and reported in the 1950's that did not recognize the semiconductor
physics of the liquid crystalline lipid membrane of cells. With the discovery of the transistor in the late 1940's, and
the first transistor radio in the 1950's, the field of semiconductor physics exploded. However the neuroscience
community has ignored the application of this new technology to the neuron and the neural system to this day.
Hodgkin14 summarized their theory in 1951, using the earlier designation of the ionic theory of the neuron and
muscle. The paper provides a good review of the state of the art in neural research as of 1951, including the
rudimentary instrumentation available, characterized by the statement on page 400 (item 3 in their summary)
indicating a reversal of the polarity of the potential across their membranes without an explanation of how this
occured. It is obviously in hind sight, that this phenomenon was due to the lack of compensation used in their probes
(Section 6.3.6 on test techniques). The reviewed material of Hodgkin predates the founding of semiconductor
physics in almost the same year at Bell Telephone Laboratories in New Jersey, and the continual developmen of that
technology to the current day.
The technology available at the end of the first half of the 20th Century, exemplified by the two-terminal
neuron of Huxley and Hodgkin (reported in1952) cannot be used to understand the individual neuron, the
synapses between neurons, the Node of Ranvier or the memory storage circuit used in the cerebellum!! The
following discussion involves a three-terminal neuron, and an active liquid-crystalline semiconductor device,
the Activa, within each of the abovementioned biological elements. These technologies were only developed
in the second half of the 20th Century; the semiconductor technology beginning with the discovery of the
transistor in 1947 and the codification of the liquid crystalline state of matter beginning in the 1980's.
In 1949 William Schockley, the most outspoken of the three inventors of the transistor, noted in a radio
interview,
“It seems to me that in these robot brains the transistor is the ideal nerve cell.”
The following material requires the reader to accept these new technologies combined under “The
Electrolytic Theory of the Neuron” and the abandonment of the previous, largely conceptual,
chemical theory of the Neuron!!
A brief, but direct, restatement of the operating principles associated with “The electrolytic theory of the
neuron” will be presented before the end of this section (Section 2.2.5.1). The electrolytic theory is not
compatible with the prior chemical theory of the neuron. It defines a three-terminal neuron and an entirely
different operating environment for the neuron, the associated synapses (and the Nodes of Ranvier). Section
2.4.1 will provide a brief recapitulation of the problems associated with the chemical theory and the virtues of
the electrolytic theory (within the context of the basic neuron). Similar recapitulations will appear at the end of
later sections and chapters after the presentation of more complex features of neurons. Understanding the
differential input structure (Section 2.2.4) provided by the three-terminal neuron is crucial and it is absolutely
mandatory for understanding the signal processing employed throughout the neural system. Understanding the
operation of the sensory neurons discussed in Chapter 8, is totally dependent on the electrolytic character of
the neural system. Similarly, understanding the operation of the action potentials by the ganglion neurons,
discussed in Chapter 9, is totally dependent on the non-linear properties of the Activa within the electrolytic
neurons of the neural system. Similarly, understanding the operation of the memory storage function by the
Purkinje neurons, discussed in Chapter 17, is totally dependent on the synapse style 2 described initially in
Section 2.4.5 and containing a modified Activa, employing a PNPN, four-layer diode.
The focus on the electrophysiological transfer characteristic, and the cytological structure of the bipolar neuron
in Section 2.5.1 will lead to a more detailed understanding of the morphology of all neurons. As usual,
terminology will be refined in this and the following chapter. The anachronism associated with the fact the
lateral neuron has a bipolar (electrophysiological) output signal while the (morphological) bipolar cell does not
will be highlighted.
The term “functional” has been used at different levels within the biological literature. In the past, it has been
used at a coarse level primarily describing the operational role of a given neuron within the anatomy of the
14Hodgin, A. (1951) The ionic basis of electrical activity in nerve and muscle Biological Reviews vol 26(4),
pp 339-409
10 Neurons & the Nervous System
specimen. The characteristics associated with this use of the term are frequently; where is it found, what is its
shape, what other neurons does it connect to and what gross activity is it related to. These are characteristics
that are associated with “traffic analysis” in the language of the cryptographer and communications specialist.
They have little to do with the detailed role of the neuron within the organism and virtually nothing to do with
how it functions in its signal processing role. This chapter will explore the function of the neuron in its
fundamental role as an electrolytic amplifier. Such an amplifier can be used for purposes of signal generation,
processing and transmission. The configuration and resulting operational functions of some of the more
complex neurons, such as signal addition and subtraction, will be introduced beginning in Section 2.5. Still
more advanced features, such as sensing and signal propagation, will be addressed in Chapter 5.
While differentiating and elaborating the membrane of a single cell, two uniquely important situations will be
discussed. The first will discuss the elaboration of the cell membrane to form more than one electrolytically
isolated chamber within the cell. Second, it will show that each of these chambers may develop a different
internal potential compared with an external reference. Next, a situation will be examined where two
membranes are brought into juxtaposition (Section 2.2). When the potentials within different plasma are
appropriate and the membranes separating the plasmas are juxtaposed appropriately, a remarkable situation
occurs. The configuration exhibits all of the electrical properties found in a man-made transistor. More
specifically and scientifically, the configuration exhibits “transistor action.” Transistor action is a quantum-
mechanical mechanism encountered in semiconductors. It is defined as an active mechanism in that it can
convert direct current (DC) input power (that does not vary substantially in amplitude with time) into an
alternating current (AC) output signal (capable of representing information in its amplitude variation with time)
at its electrical output terminal. It can accomplish this conversion under the control of an independent terminal.
The fact that the resulting circuit within a neuron is a three-terminal network instead of a two-terminal
network (as usually portrayed in the literature) makes a profound difference in (1) how the neuron operates
and (2) how it must be portrayed.
To understand the operation of the neuron at the detailed functional level will require several paradigm shifts in
the readers perspective. Justification for these changes will first appear in this chapter and reappear repeatedly
and more forcefully in the following chapters. These changes allow a detailed description of the neural system
unavailable under the previous conventional wisdom.
First, the arranging of multiple biological membrane in close proximity requires recognition of the fact that it is
the junctional properties shared by two lemma that are of critical importance and not the isolated
properties of an individual lemma.
The concept of “an excitable axolemma” will be abandoned.
Second, the quantum-mechanical mechanisms involved in the junctions created by multiple lemma are
electronic in nature. The active mechanisms within a neuron do not involve the flow of ions through the
lemma.
The concept of ionic flow as a means of charge transfer through a biological membrane will be
abandoned.
Third, the extensive database in the literature is explicitly clear, the primary neurotransmitter in neurology
is the electron, the secondary neurotransmitter is the “hole” of semiconductor physics. Other chemicals
frequently described as neurotransmitters are in fact neuro-facilitators, neuro-inhibitors or neuro-modulators
The concept of chemical neurotransmitters between neurons will be abandoned. No requirement or
situation has arisen suggesting the need for chemical neurotransmitters between neurons even though
many specific chemicals are found in the vicinity of elements of the neural system.
Fourth, Section 2.7 will redefine the character of the neuromuscular and neuroglandular interface to involve
neuro-effectors of a chemical nature, and previously grouped among the general term neurotransmitters. This
nomenclature remains consistent with the majority of the experimental data base but conflicts with a large part
of the pedagogical data base that assumes all synapses are chemical in character.
Fifth, the discussion will also continue to be based on the premise that;
the fundamental functional unit of the neural system is NOT the neuron but the neural conduit
AND the proper juxtaposition of two neural conduits to form an Activa.
The neuron is the smallest living cell associated with the neural system. However, it is not the minimal
The Neuron 2- 11
functional unit under two circumstances. As developed in Section 2.5.3, it can contain two individual
functional units. As developed in Chapter 9, it is sometimes an incomplete functional unit since the myelin
wrapping of the stage 3 axon conduit is generally supplied by a distinctly separate cell.
Sixth, the only conclusion that can be drawn at the end of this chapter is that the neuron is electrically based in
all aspects of its functional performance. Chemistry only plays a minor role in the signaling function of the
neural system. The major role of chemistry relates to maintaining the metabolic condition of the cell (which
includes maintaining the internal bias of the cell). Based on this situation, the electrophysiological
characteristics of the neuron are more important than, and determine its morphology. It becomes
apparent that every morphological feature can be interpreted electrophysiologically.
This chapter will introduce each class of neuron found in the biological system. However, the physical and
operational complexity of some of the neurons requires they be addressed in their individual chapters. Chapter
8 will address the variety of sensory neurons that all exhibit a common topology but different sensory receptor
mechanisms. Chapter 9 will address the unique neurons of the signal projection stage in detail. Chapter 16
will redefine the role of neuro-facilitators and neuro-inhibitors within neuroscience in order to bring the
nomenclature associated with those materials in line with the actual operation of the neural system. Chapter 16
will also address the neuro-effector neurons and hormones for the first time in the literature. Chapter 20 will
address the special features of the neurons and neural subsystems of the viscera.
2.1.4 Analyses of membranes in the literature
There was a great flurry of investigation of cellular membranes during the 1960's and into the 1970's within the
bio-chemistry community. The activity has been much lower recently. The early activity was primarily
exploratory research and has not provided consistent and precise information. Indicative of its exploratory
nature was the fact investigators selected tissue from their favorite organism, generally without much regard to
what type of tissue it was, kidney, heart, etc. Few seem to have given a thought to the fact that the properties of
the lemma of a cell might vary over its surface or be optimized to a specific function. Mueller has noted this
wide variation when he described the resistance (actually the resistivity) he reported versus that of others,
“which at 108 Ohm cm2 is 105 - 107 times higher than that of most cell membranes.”
Quinn noted in the same time period (1976, page 80), “Membrane models have, in the past, been
constructed from the vast amount of information obtained from plasma membranes of the myelin sheath
and retinal-rod outer segment membranes, . . . We might ask, therefore, whether a single membrane
model can be formulated to embrace all cell membranes, or whether the structure of each particular
membrane is in some way unique and distinct from all others. The answer probably lies somewhere
between these two views,” In this work, four distinct types of lemma are defined just for the lemma of
neural cells. In the case of cardiocytes, an entirely different type of cell is defined as well as different
conditions associated with the lemma of those cells (Chapter, 20, Section 20.3).
Rose provided a comprehensive discussion of the “anatomy of a mammalian cell” in 197615. It was included in
a series of five planned volumes by Jamieson & Robinson with an auspicious goal at that time.
Hidalgo edited a more advanced volume in 198816. Suwalsky, writing in that volume (Chapter 1), defined an
initial set of synthetic bilayer membrane components;
DLPE L––dilauroylphosphatidylethanolamine nominal thickness
DMPE diamystroylphosphatidylethanolamine + 5 Angstrom
DPPE dipalmitoylphosphatidylethanolamine + 10 Angstrom 1 double bond
DMPC L––dimiristoylphosphatidylcholine “lecithin” (Outer layer)
The first three materials are typically associated with the inner bilayer of a neural lemma, with DMPC generally
associated with the outer bilayer. The best estimate of the thickness of the DMPE liquid crystalline bilayer
(lemma) is 50.75 . See Section 2.2.1.3.4 for further discussion concerning these materials. The acronyms
beginning with a D for di– must be looked at carefully when attempting to understand the electronic
performance of the outer bilayer of a type 2 neural lemma. The implication is that both lipids of the molecule
15Rose, G. (1976) A current interpretation of the anatomy of the mammalian cell In Jamieson, G. & Robinson,
D . M am ma li an C e l l M e mb ra ne s N Y : B ut t e r w o r t h- He in e m a n n p p 1 - 3 0
https://doi.org/10.1016/B978-0-408-70722-0.50005-X
16Hidalgo, C. (1988) Physical Properties of Biological Membranes and Their Functional Implications. NY:
Plenum Press.
12 Neurons & the Nervous System
are the same, which normally does not occur in biological phospholipids, except possibly those of type 1
membranes acting as excellent insulators. The expanded nomenclature of McIntosh is needed when discussing
neurons (Section 2.1.4.5).
The membranes of Hidalgo were prepared over CHCl3 or CHCl3:CH3OH solutions and examined by X-ray
techniques. Their experiments were carried out at “about 18 ± 1C.” As noted in the names, the molecular films
consisted of symmetrical lipid chains of slightly varying length. They were generally observed to both be
straight chains and can be assumed to be saturated fatty acids. If true, the saturated fatty acids in both the inner
and outer bilayers of a lemma would suggest the lemma would be a very high quality insulator of quite high
resistivity (a type 1 membrane), probably in the 1013 ohm–cm–2 range.
Suwalsky noted the significance of hydration on these materials, “When oriented films of the four phospholipids
under study are introduced into excess of liquid water, DMPC and the diacylphosphatidly ethanolamines show s
remarkable difference. It is observed that the c axis (bilayer repeat) of DMPC increases from about 55
Angstrom at 92% r. h. to 63.5 Angstrom after only 1 hr of exposure to water. This value increases to 78
Angstrom after 5 hr and to 87 Angstrom after 21 hr.” “On the other hand, the c axes of
acylphosphatidylethanolamines only increase by about 1 Angstrom after 30 days of exposure to water. . .” Fatty
acids (lipids) of 16-carbons or more are generally considered insoluble in water according to Lehninger (1970).
Marsh, writing in Chapter 4 of Hidalgo, described the mobility of molecules within membranes. The material is
primarily conceptual and does not go into the interactions between adjacent phospholipids, both within the head
groups and the lipid chains, that can significantly constrain their rotational and translational freedom.
Sambrano & Rojas, writing in Hidalgo, describe the initial proposal of a conceptual “coupled Na+ and K+
transport, which serves many important physiological functions, related to controlling Na+ and K+ gradients
across membranes.” This concept evolved into the sodium pump needed by the Hodgkin & Huxley (ca. 1954)
concept incorporated into the chemical theory of the neuron. The rate of pumping defined to date does not
support the rapid transport of ions required by the chemical theory. The proposed enzyme(s) supporting the
sodium pump concept are large, molecular weight ~250,000. Only limited data supports this enzyme spanning
the bilayer, potentially in the type 3 lemma of every cell, including neurons where a much higher transport rate
is required to support electronic signaling.
In 2008, Kucerka et al17. published new data on the dimensions of other phosphatidic molecules, DPPC and
DOPC. In their Introduction, they note the liquid-crystalline character of the di-phophatidic molecules,
“Biological function is intrinsically linked to membrane structure. The structural basis of biomembranes arises
from fluid phase lipid bilayers with almost liquid-like conformational degrees of freedom, so that the structure is
best described by broad statistical distributions rather than the sharp -functions typical of crystals.”
2.1.4.1 Demonstration of impermeability of lemma to cations or water
In 1999, a new text appeared among the bio-physics community18, in honor of the “Father of membrane
permeability,” a name essentially absent from the work of the bio-chemistry community. This book reviewed
the entire history of the permeability of the cell outer membrane from a more fundamental perspective than the
largely conceptual perspective of the bio-chemistry community. The book did not enjoy good sales among the
biology community at large. Unsold copies were available for $12 in 2017. See Section 2.2.1.4 for a more
technical discussion of the Deamer et al. text.
Overton, the “Father of membrane permeability,” was a prolific investigator and author during the 1890's
and first decade of the 20th Century. Kleinzeller (page 1 of Deamer et al.) Asserted, “He is justifiably
recognized as a pioneer in the development of a comprehensive concept of the cell membrane (with
citations).”
Overton first confirmed, through laboratory experiment, that the lemma of most animal cells were
impenetrable by inorganic ions. The exception related to muscle cells where the flow of cations through
the cell wall was significant to muscle operation. Overton worked initially at the neural/muscle interface
17Kucerka, N. Nagle, J. Sachs, J. et al. (2008) Lipid Bilayer Structure Determined by the Simultaneous Analysis
of Neutron and X-Ray Scattering Data Biophysical J vol 95, pp 2356–2367
18Deamer, D. Kleinzeller, A. Fambrough, D. eds. (1999) Membrane Permeability: 100 Years since Ernest
Overton. NY: Academic Press
The Neuron 2- 13
(page 413 in Deamer et al.) Unfortunately, these papers were published in German at that time. Paula
and Deamer addressed this question again in Chapter 4 of Deamer et al. They noted initially the need to
employ the hydrated form of any ion to avoid predictions that were absurd, such as the frequently
conceptualized permeability of the H+ ion. They also noted the requirement to employ rational values of
lemma thickness in these calculations. They note the low permeability of realistic lemma to inorganic
ions initially led to the alternate assumption that the lemma must employ pores to achieve the desired
conceptual permeability. “To account for this discrepancy, transient pores in the bilayer produced by
thermal fluctuations have been suggested as an alternative pathway (page 88).” . . . “The primary
question is whether a sufficient number of pores is present in the bilayer so that the net rate of ions
permeating through pores can exceed that of ions permeating by solubility and diffusion. Intuitively, this
pathway becomes an attractive alternative as bilayers tend to become more unstable with decreasing
bilayer thickness.”
“Transient pores” appear to be a convenient way to conceptualize pores in membranes that have not been
documented by means of photography or electron microscopy as of 2017. Tredgold19, among others, has
addressed this question. “One would thus expect that thermal activation would have a very small probability of
carrying an alkali ion from water into the hydrocarbon region of a bilipid membrane and that such membranes
would thus behave as excellent insulators.”
For essentially all of the 20th Century, the bio-chemical community echoed their position that cations
could pass through bilayer membranes of biological origin and then had to define a set of conceptual
pumps to remove the ions (sometimes against the chemical and electrical gradients to maintain
homeostasis..
In 1987, Finkelstein crossed the intellectual bridge in a paper published in an important but narrowly
distributed journal. He emphatically and publicly noted the virtual impermeability of lipid bilayer
membranes to small ions such as Na+, K+ and Cl--.20 However, he did not address the subject of the
asymmetrical bilayer as a semiconductor.
After exploring potential mathematical models21,22 of the permeability of a lemma, Deamer et al. select one
model from the Hamilton & Kaler paper and assert, “This model is semiempirical and is based on a number of
assumptions, but has the advantage of being easy to approach mathematically without losing its validity.” This
assertion appears most valid over a limited temperature range. Their equation includes temperature as a
parameter in several of its (frequently exponential) terms. They present their figures 6 & 7 without citing any
temperature.
The Hamilton & Kaler paper involves very complicated terminology focused on their specialty. However, they
generally conclude,
“Phospholipids are commonly used for biological studies, since phospholipids are a major component of
animal cells, but are not suited for industrial use as they are subject to chemical and biological
degradation. The cation permeability of pure phospholipid vesicles is also difficult to measure because
the rates of transport are so small that other effects, such as vesicle fusion followed by dumping of
contents, may obscure the signal of interest. The difficulty of measurement is well shown by the
differing cation selectivity sequences reported, . . .We have thus turned to shorter tailed synthetic
surfactants in an effort to understand transport without the detractions inherent in natural systems.”
“From eq 17, the flux of ions against the bilayer is 11 ions/( 2-s). The flux of ions through the bilayer is
2 X 10–12 ions/( 2-s). This low efficiency indicates that cations are not greatly inducing the formation of
pores, a mechanism postulated for phospholipid bilayers; rather, cations take advantage of a small
population of existing pores to cross the bilayer.”
19Tredgold, R. (1977) Dielectric behiour of polypeptides: Its relationship to membrane permeability. In Roux
, E. ed. Electrical Phenomena at the Biological Membrane Level. NY: Elsevier page 83
20Finkelstein, A. (1987) Water movement through lipid bilayers, pores and plasma membranes. Volume 4 of
the Distinguished Lecture Series of the Society of General Physiologists. NY: John Wiley & Sons. Chapter 6.
21Markin, V. & Kozlov, M. (1985) Pore statistics in bilayer lipid membranes Biol Mem vol 2, 404-442
22Hamilton, R. & Kaler, E. (1990) Alkali metal ion transport through thin bilayers J Phys Chem vol 94, pp
2560-2566
14 Neurons & the Nervous System
“Thus, the reported selectivity sequences for pure bilayers are at and in fact, pure phospholipid bilayers
have been reported to be impermeable to cations23, a most reasonable conclusion.”
Hamilton & Kaler conceptualize several potential mechanisms that might contribute to a type 3 bilayer
membrane, “transient holes in the vesicle bilayer,” “so-called ‘inverted pores’,” etc.
In their section V, Deamer et al. consider hydrogen ion permeation as a special case. They note the likelihood
that the ion is probably present in a hydrated form as H9O4+. They also note a unique situation limited to
hydrogen ions, their conceptual ability to “hop” along the aliphatic chains of the lipids in a bilayer lemma by
temporarily forming hydrogen bonds between the lipids. In their summary, they note, their
“Solubility–diffusion model fails when one attempts to describe cation transport across thin lipid bilayers
such as those composed of 14 carbon phosphatidylcholines, and it becomes necessary to propose that a
second process comes into play, which is ion translocation through transient defects in the bilayer.” This is
another example of Bayesian Logic. An alternative not considered by these authors is a Type 3 bilayer
membrane supporting a protein–mediated transport of ions through the membrane.
In chapter 5 of Deamer et al., Verkman provided a very academic discussion of the potential for water transport
across membranes. Little attention was paid to actual real or synthetic membranes. He stressed the difficulty of
obtaining meaningful (precise) results. He stressed, “Many studies have demonstrated that water permeability
through lipid bilayers depends strongly on lipid composition and sterol content, which alter lipid structure and
fluid state.” There is little evidence supporting sterol content in most lipid bilayers! Verkman discussed water
movement aided by small proteins through “lens fibers” associated with the eye. No conclusions were drawn
relative to generic bilayer membranes. His summary describes several potential future discoveries but nothing
of current relevance to the study of neurons.
2.1.4.2 A short history of putative pores, carriers & gates in bilayer membranes
Noble (page 140) made a brief delineation between a carrier and a channel transporting ions but he provided no
graphic to accompany his circuitous description. He used gramicidin A, a linear polypeptide as his exemplar of
a material that could form a tube that may lie across the hydrocarbon layer of a bilayer, thereby creating a
channel. He used the term “may” multiple times and made no assertion that it did form a tube.
Armstrong, writing in Deamer et al. (chapter 9) has discussed the history of ion channels.
He noted, “Important chapters in the story were written by scientists equipped with an excellent understanding
of the physics of their time and apparently not at all in awe of the subject.”
The review of Armstrong began by highlighting the work of Hermann. “In 1872, Hermann had an accurate
understanding of the requirements for electrical transmission in nerve fibers, based on the cable equations of
Kelvin (1855).”
Hermann, room-mate of Maxwell at one point, depended on the since debunked equations of heat flow,
as they apply to signaling in cables. The equations were debunked by Lord Kelvin himself during the
late 1890's. As one of his final public pronouncements, Lord Kelvin accepted that Maxwell’s Equations
and Marconi’s experiments were applicable to cable theory and that radio and X-rays, as technologies,
did exist.
Armstrong’s assertion relating to Hermann fit his opening assertion concerning “understanding of the physics of
their time.” Hermann was wrong, Maxwell was right. The first undersea cable based on Kelvin’s calculations,
was a failure. It was replaced as soon as possible by a cable based on Maxwell’s Equations. Later, Cole
demonstrated inductance as a parameter of axons, as anticipated by Maxwell’s Equations. Armstrong’s
comments regarding Nernst (1888) should also be interpreted in terms of the “understanding of the physics of
their time.” Nernst did not contemplate membranes of the complexity of phospholipid bilayer lemma.
Armstrong encountered his own understanding of the physics of his time in his section IIA on amplification and
signal projection. The conceptual material in that section will not be discussed in this section. His figure 1,
both upper and lower frames, do not represent the actual situation. His section IIIB attempted to rationalize the
concepts of pores or carriers as the mechanism of inorganic cations through the bilayer lemma. The remainder
of his chapter is predominantly conceptual. In section 4D, concerned with the “inactivation of the conceptual
Na channels,” he defines a state diagram and concludes, “A formal solution is to draw a slanting arrow from
state I2 to C3, but the physical meaning can only be imagined.”
23Louni, L. Rigaud, J. Gary-Bobo, C. (1983) Stud Phys Theor Chem vol 24, pp 319+
The Neuron 2- 15
2.1.4.2.1 Rationalizing pores, carriers & gates discussion–types of lemma
From the literature, it is almost necessary to recognize three, or even four, types of external lemma of a neuron.
Type 1 is the generic membrane, highly impermeable to ionic materials and most polar organics. This type of
membrane is frequently modified in specific regions to serve specific function. These regions are occasionally
described as rafts in the literature, which implies the modified region is on the surface of the membrane. This is
incorrect in general. The term raft should be reserved for material, generally proteinaceous, present on the
surface of a membrane.
Type 1: It is very clear that a large part of the external lemma of a neuron (probably over 60%of its area)
consists of symmetrical bilayers exhibiting near zero electrical conductivity and near zero permeability to most
polar and non-polar molecules. This portion of the lemma appears to be well ordered at the molecular/liquid
crystal level. This work labels this type of membrane as type I.
Type 2: It is also very clear that there is a second form of membrane (probably occupying less than 10% of the
external lemma area) that is asymmetrical electrically and forms a very high quality electrical diode. It is very
well ordered at the molecular/liquid crystalline level. It remains largely impervious to most polar and non-polar
molecules. This work labels this type of lemma type 2. Type 2 membrane is the workhorse of the electrical
performance of the neurons. It is involved in the electrostenolytic process powering (internally biasing) the
plasmas of the neuron and informing internal and external electrical connections with its environment.
Type 3: There is a third form of lemma (probably limited to less than 20% of the total surface) that is
responsible for maintaining the homeostasis of the cell, a very small portion of the total lemma area that is
labeled type 3. This portion of the lemma exhibits potential voids in its molecular/liquid crystalline structure.
These voids may constitute some type of channel or by filled with a proteinaceous carrier, either of which is able
to transport a variety of polar and non-polar molecules through the lemma. The electrical performance of the
undisturbed portion of the lemma probably remains that of a very good quality insulator but may suffer some
electrical leakage at voids in the basic lattice. The voids described above support by either diffusion or some
form of complex transport still not totally understood, the transfer on a highly selective basis of a variety of
materials. In some cases, the type 3 lemma may excrete hormones in addition to its homeostatic functions. The
resulting neuron may be classified as a stage 7 neuron because of this capability. Alternately, a neuron with this
capability may be labeled a glandular cell.
Type 4: There appears to be a fourth form of neural lemma closely tied to the functions of the type 2 lemma, as
illustrated in Section 2.2.1.5. It is asymmetrical, like the type 2, but accommodates other molecule than
glutamate; it specifically accommodates dopamine and other hormones that causes changes in the sensitivity of
groups of neurons in a specific areas of the CNS (Section 16.4).
These neuro-facilitator agents may impact the operation of a neuron in either of two ways because of the
differential input structure of every neuron. The neuro-facilitator effects the Activa within the neuron. If an
investigator is exploring the signal applied to the inverting input to the neuron, the effect of the neuro-facilitator
will be generally defined as a neuro-inhibitor. If on the other hand, the investigator is exploring a signal applied
to the non-inverting input to the neuron, the effect of the same neuro-facilitator will generally be defined as a
neuro-enhancer (or just a neuro-facilitator, Section 3.5.4).
In discussing these types of hormone, this case falls between the paracrine (confined) and endocrine (ducted)
hormones (Section 23.3). In that section, they are described as Pericrine (ductless but short range) hormones.
They are found primarily within the CNS.
It makes no sense to continue any discussion of the external lemma of a neuron on a global basis. The data is
overwhelming that the external (and internal) lemma varies in its properties on a functional basis. A fully
elaborated neuron exhibiting all of the above feature is shown in Section 2.2.2.6.1. Note the ability to partition
the internal structure of the neuron to accommodate/isolate the individual functions.
2.1.4.3 Permeability of in-vivo lemma by diffusion &/or pores
A large part of the bioscience community has been led to believe that many types of molecules enter the cell
through pores in the cell wall based more on concept than data. Addressing the question of how large molecules
might pass through the combination of two bilayers that form a lemma is a difficult one from the view of
instrumentation as well as fundamental knowledge of the laws of physical chemistry that apply. As the 1999
paper24 by Paula and Deamer note, “To cross a single bilayer membrane, the permeating particle must dissolve
24Paula, S. & Deamer , D. (1999) Membrane Permeability Barriers to Ionic and Polar Solutes In Deamer, D.
Kleinzeller, A. & Farmbrough, D. eds. (1999) Membrane Permeability. NY: Academic Press Chapter 4
16 Neurons & the Nervous System
in the hydrophobic region, diffuse across, and leave by re-dissolving into the second aqueous phase.” See next
sub-section. In the real case, this process must be repeated twice. At the molecular level, the total permeation
must be achieved in a liquid crystalline environment wherein the middle aqueous phase is itself highly structured
(Section 2.4.2).
Until the work of Paula and various colleagues in the 1990's, there had been little progress in this field in several
decades. Their work was still limited to various small ions moving through a single man made bilayer of
phospholipid material.
2.1.4.3.1 Permeability of single bilayer in-vitro by diffusion and/or pores
Paula & Deamer provided a comprehensive study of the permeability of a single bilayer in 1999 based heavily
on two papers, Paula, et al. of 199625 and Paula, Volkov & Deamer of 199826, by addressing single layers of a
phospholipid surface. The surface self assembles into a liquid crystal as noted by Kucerka et al27. more recently
in 2008. In their Introduction, they note the liquid-crystalline character of the di-phophatidic molecules,
“Biological function is intrinsically linked to membrane structure. The structural basis of biomembranes arises
from fluid phase lipid bilayers with almost liquid-like conformational degrees of freedom, so that the structure is
best described by broad statistical distributions rather than the sharp -functions typical of crystals.”
It is not clear that any of the models used in the Paula et al. papers properly recognize the added constraints
imposed by the liquid crystalline state.
Paula et al. varied the molecular length of their phospholipids to provide their data points. They did not
address the length of the hydrophobic lipids in natural phospholipids of a bilayer.
Volkov & Deamer28 published a paper in 1997 providing supporting material to the above papers. It provided
the size of a long list of both ions and their hydrated forms. They did not address larger molecules the size of
most hormones. in Figure 2.1.4-1 provides their Table 2 of hard to find data, with citations. They also
provided surface tension values for the oil/water and liquid/air interfaces at 20 C for a variety of simple organic
molecules.
25Paula, S. Volkov, A. Van Hoek, A et al. (1998) Permeation of Protons, Potassium Ions, and Small Polar
Molecules Through Phospholipid Bilayers as a Function of Membrane Thickness Biophysical J vol 70, pp
339-348
26Paula, S. Volkov, A. & Deamer , D. (1998) Permeation of Halide Anions through Phospholipid Bilayers
Occurs by the Solubility-Diffusion Mechanism Biophysical J vol 74, pp 319–327
27Kucerka, N. Nagle, J. Sachs, J. et al. (2008) Lipid Bilayer Structure Determined by the Simultaneous Analysis
of Neutron and X-Ray Scattering Data Biophys J vol 95, pp 2356–2367
28Volkov, A. & Deamer, D. (1997) Two mechanisms of permeation of small neutral molecules and
hydrated ions across phospholipid bilayers Bioelectrochem Bioenergetics vol 42, pp 153-160
The Neuron 2- 17
The findings of Volkov & Deamer are worth summarizing,
“In this paper, we discuss two possibilities that in a sense represent alternative hypotheses. The first
hypothesis is that ion or dipole permeation can be understood in terms of the energy related to the
Figure 2.1.4-1 Bare and hydrated ions. Dimensions in nanometers. See text.
From Volkov & Deamer, 1997.
18 Neurons & the Nervous System
partitioning of ions into the non-polar phase of the lipid bilayer, and that electrostatic considerations,
including the Born energy, are primary concerns. The second hypothesis is that high dielectric defects
(transient pores) occur in the bilayer and allow permeating ions or dipoles to bypass the partitioning
energy barriers. The two hypotheses were tested by experimental measurements of proton and potassium
flux across lipid bilayers of varying thickness, and the results are described in detail in a paper by
Paula et al. (1996).”
Partitioning within solutions involves a parameter of Nernst’s Distribution Law of dilute solutions. The
partition coefficient, the ratio, at equilibrium, in which a solute separates into two immiscible solvents
based on the molar concentrations is typically a temperature sensitive function.
It is not clear how Nernst’s Distribution Law applies to the penetration of a 2-bilayer lemma by large
protein hormones, and when they are combined with another protein to raise their solubility in blood
serum. The potential for these materials, with molecular weights exceeding 1000 Da, to penetrate a
natural lemma appears to be marginal to infinitesimal.
“Although the partitioning model can describe the barrier properties of lipid bilayers under specified
conditions, certain assumptions regarding the hydrated radius of the permeating species are required.
We now consider an alternative hypothesis, in which fluctuations in the bilayer structure produce rare
transient defects that allow solutes to bypass the electrostatic and so|vophobic energy barriers. Two
types of pore structure in the lipid hilayer are possible, which can be roughly classified as hydrophobic
and hydrophilic defects. During the formation of a tran- sient hydrophobic defect, lipid molecules are
moved apart by thermal fluctuations so that the membrane hydrophobic core makes contact with and is
penetrated by the aqueous bulk phase. Hydrophilic defects are formed when the lipid molecules are
tilted into the transient defects, so that they are lined with lipid polar head groups. In both
hydrophobic and hydrophilic defects, pore formation results from the dynamic properties of the lipid
bilayer, and the equilibrium pore distribution is relatively constant over time.”
“In testing the two models described above, an important variable under experimental control is the
bilayer thickness, which can be changed by choosing lipids with longer or shorter hydrocarbon chains.
In the results discussed in this section, our approach was to measure the proton and potassium flux
across liposomes composed of phospholipids with fatty acid chain lengths varying from 14 to 24
carbons.” They reasoned that, in lipids with
short-chain fatty acids, non-polar forces would
not be sufficient to stabilize bilayer structures.
However, as the chain length increased, at
some point stable bilayer vesicles would be
formed providing a permeability barrier to the
ionic flux. If only the partitioning energy was
involved, the ionic flux would be reduced to a
minimum when stable bilayers were formed
and would not change significantly when
longer chain lipids were used. However, if
transient defects were the primary factor
regulating the ionic flux, shorter chain lipids
would have many more defects, leading to
much higher ionic permeability than longer
chain lipids. The results expressed as proton
and potassium permeability coefficients are
shown in Figure 2.1.4-2. In 1970, Lehninger
asserted that the hydrophobic portion of natural
bilayers usually have an even number of carbons
between 12 and 22, and that cell lemma consisting
of 2-bilayers, of different species varied
significantly between 60 and 100 Angstrom thick.
We found that the permeability decreased
logarithmically as the bilayer thickness
increased in the short chain lipids, following
the slope of the line predicted by the transient
pore mechanism. However, the permeability
tended to level off in the thicker bilayers
(C16 and C18 lipids), approaching the lines
Figure 2.1.4-2 Comparing the dependence
of K+ and H+ permeability on diametervs
length of the hydrophobic lipid chain at
30 C. See text. from Volkov & Deamer,
1997.
The Neuron 2- 19
predicted by the partitioning model. Although more data are needed to reach a conclusion, the results
suggest that the mechanism of ionic permeation may depend on the bilayer thickness: thinner bilayers
have many transient defects that allow rapid permeation of small ionic species, whereas in thicker
bilayers defects become so rare that partitioning mechanisms dominate the ionic flux.”
“Earlier work has shown that the permeability of lipid bilayers to protons is five to six orders of
magnitude greater than to other monovalent cations. This result is consistent with the partitioning model
only if every proton carries at least four waters of hydration into the bilayer phase.”
It was noted in one of the Paula papers that using the radius of an H+ ion into their equations gave absurd results.
There was no mention of whether their pore or partition models are compatible with a bilayer in the liquid-
crystalline state of matter.
2.1.4.3.2 Paula et al. papers in Bilayer Lemma Physical Chemistry
After reviewing the above papers, it should be noted Paula et al. only addressed single molecular bilayers. It
would take two bilayers back-to-back to represent a lemma. They did develop a bilayer lemma made of
phosphatidylcholine, not a phosphatidylamine, suggesting a type 1 (symmetrical and highly electrically
insulating) lemma.
The thickness of a given laboratory prepared phospholipid surface varies significantly based on the
measurement technique used, from about 50.75 Angstrom reported by Suwalsky (Section 2.1.4) to 41.3 ± 3
Angstrom using a atomic force microscope by Lind et al. (Section 2.1.4.7.1) Suwalsky provided his
measurement for DLPE, L––dilauroylphosphatidylethanolamine exhibiting 10 CH2 groups in each fatty acid
chain. He also provided higher values for two other molecules, DMPE at + 5 Angstrom greater than DLPE and
DPPE at + 10 Angstrom greater than DLPE.
The 1996 paper’s Abstact define their study,
“Two mechanisms have been proposed to account for solute permeation of lipid bilayers. Partitioning
into the hydrophobic phase of the bilayer, followed by diffusion, is accepted by many for the permeation
of water and other small neutral solutes, but transient pores have also been proposed to account for both
water and ionic solute permeation. These two mechanisms make distinctively different predictions about
the permeability coefficient as a function of bilayer thickness. Whereas the solubility-diffusion
mechanism predicts only a modest variation related to bilayer thickness, the pore model predicts an
exponential relationship. To test these models, we measured the permeability of phospholipid bilayers to
protons, potassium ions, water, urea, and glycerol. Bilayers were prepared as liposomes, and thickness
was varied systematically by using unsaturated lipids with chain lengths ranging from 14 to 24 carbon
atoms.”
The Abstract closes with,
“The results for protons and potassium ions in shorter-chain lipids are consistent with the transient pore model,
but better fit the theoretical line predicted by the solubility-diffusion model at longer chain lengths.”
There was no discussion of the length of phospholipids in natural bilayers in vivo.
The summary of their 1996 paper is informative,
“In conclusion, pores seem to be the dominant permeation mechanism for ions, but only if the membrane
is sufficiently thin. Ion permeation by partitioning and diffusion seems to become of greater importance
as membrane thickness increases, because the number of pores in the membrane produced by thermal
fluctuations certainly decreases as the bilayers become increasingly stable. This transition from one
mechanism to another is observed at chain lengths between 16 and 18 carbons for potassium ions and at
chain lengths between 20 and 22 carbons for protons. On the other hand, because of their high solubility
in a hydrocarbon phase, neutral molecules apparently cross exclusively by the solubility-diffusion
mechanism, regardless of membrane thickness.”
There was no mention of whether their pore or partition models are compatible with a bilayer in the liquid-
crystalline state of matter.
Their 1998 Abstract defines that study,
“ Two alternative mechanisms are frequently used to describe ionic permeation of lipid bilayers. In the
20 Neurons & the Nervous System
first, ionspartition into the hydrophobic phase and then diffuse across (the solubility-diffusion
mechanism). The second mechanism assumes that ions traverse the bilayer through transient hydrophilic
defects caused by thermal fluctuations (the pore mechanism). The theoretical predictions made by both
models were tested for halide anions by measuring the permeability coefficients for chloride, bromide,
and iodide as a function of bilayer thickness, ionic radius, and sign of charge. To vary the bilayer
thickness systematically, liposomes were prepared from monounsaturated phosphatidylcholines (PC)
with chain lengths between 16 and 24 carbon atoms.”
The conclusion drawn by Paula, Volkov & Deamer was quite important. They asserted,
“We conclude from our analysis that the solubility-diffusion mechanism better describes permeation of
halide ions across phospholipid bilayers than the pore mechanism. We base our argument on the
experimentally observed dependence of the permeability coefficients on the sign of the ionic charge, on
the bilayer thickness, and on the ionic size. In each case, the comparison of the experimental evidence
to theoretical predictions supported the solubility-diffusion mechanism and was inconsistent with
permeation through pores.”
This finding did not even consider the more complex back-to-back bilayers of an actual biological
lemma.
Paula & Deamer (1999) go on to discuss the case of simple ions (both hydrated and non-hydrated) passing
through a simple slab of a uniform hydrophobic material. They speak of this material as a bilayer, but is clearly
not, their figures 2 & 3.
Two figures ultimately from Paula in chapter 429 provides their estimates of permeability through a membrane
based on their measured values in related experiments is reproduced as Figure 2.1.4-3.
29Paula. S. & Deamer. D. (1999) Membrane Permeability Barriers to ionic and Polar Solutes in Deamer, D.
Kleinzeller, A. & Farmbrough, D. eds. (1999) Membrane Permeability. NY: Academic Press
Chapter 4
The Neuron 2- 21
Figure 2.1.4-4 shows the equally important graph of permeability as a function of ion radii through their
simplified membrane. [There may be a problem with the scale of the abscissa]
Figure 2.1.4-3 Permeability coefficients of potassium ions and halides
[experimental data from Paula et al. (1998)] Solid lines are solubility–diffusion
mechanism and dashed lines are pore mechanism. See text. From Paula &
Deamer, 1999.
22 Neurons & the Nervous System
When the measured permeability did not meet their expectations, they consider pores in the uniform
hydrophobic material (beginning on page88).
“Although the solubility-diffusion mechanism is satisfactory for most permeants, there are a few
instances in which it clearly fails. These mismatches are encountered in thinner bilayers if the permeants
are positively charged ions, such as potassium in liposomes made from phosphatidylcholines. In this
case, the permeability coefficients are greater than predicted by the solubility-diffusion model. To
account for this discrepancy, transient pores in the bilayer produced by thermal fluctuations have been
suggested as an alternative pathway. Parsegian (1969) showed that the energy of an ion located inside an
aqueous pore is significantly smaller than the energy of the same ion in the hydrophobic part of the
bilayer As a result of this lower diffusion barrier, the permeation rate of ions is accelerated. The primary
question here is whether a sufficient number of pores is present in the bilayer so that the net rate of ions
permeating through pores can exceed that of ions permeating by solubility and diffusion. Intuitively, this
pathway becomes an attractive alternative as bilayers tend to become more unstable with decreasing
Figure 2.1.4-4 Calculated permeability coefficient for a single bilayer of a lemma
(membrane) of a cell. See text. From Paula & Deamer, 1999.
The Neuron 2- 23
bilayer thickness.”
This quotation was followed by a theoretical discussion,
“The following paragraphs use the potassium ion as an example to illustrate permeation through transient
pores. Calculating a permeability coefficient for an ion through a bilayer of a given thickness is
mathematically challenging, although attempts have been made to achieve this goal (Markin and Kozlov,
1985). For simplicity, the approach introduced by Hamilton and Kaler (1990) will be used. This model is
semiempirical and is based on a number of assumptions, but Kas the advantage of being easy to approach
mathematically without losing its validity The model assumes that permeants pass through transient,
hydrated pores formed by thermal fluctuations in the bilayer Hydrophilic pores are assumed in the model
rather than unhydrated, hydrophobic pores because their formation is considered to be energetically less
costly and therefore more likely The rate at which permeants cross the bilayer is related to the probability
at which pores of sufficient size and depth appear in the bilayer. The probability of pore formation can
then be written as an exponential function of the energy necessary to form a pore of given area and depth.
. . . Alternatively, one could use bending constants of bilayers to calculate the energy that is required to
form a pore of given size.”
In the close of the Paula, Volkov & Deamer, paper they assert,
“We conclude from our analysis that the solubility-diffusion mechanism better describes permeation of
halide ions across phospholipid bilayers than the pore mechanism. We base our argument on the
experimentally observed dependence of the permeability coefficients on the sign of the ionic charge, on
the thickness of the [simplified] bilayer, and on the ionic size. In each case, the comparison of the
experimental evidence to theoretical predictions supported the solubility-diffusion mechanism and
was inconsistent with permeation through pores.”
In 1999, Paula, Akeson & Deamer30 provided more data on the passage of water, H2O, through “biological
membranes.” Their Introduction begins with “The bacterial toxin -hemolysin secreted by Staphylococcus
aureus damages cells by forming large pores in the cell membrane. The subsequent leakage of molecules
and ions from the cell interior leads ultimately to cell disruption.” -hemolysin channels were
incorporated into rabbit erythrocyte ghosts at varying concentrations, and water permeation was induced by
mixing the ghosts with hypertonic sucrose solutions.” Their procedure for preparing ghosts is complex and
includes centrifugation at 12000X g for 8 minutes.
They did provide useful data on the water permeability of “doped” water. Typical examples for single-channel
permeability coefficients reported in the literature for water are 9.6 x 10-- 15 cm3 /s for gramicidin A, 5.6 x
10–14 cm3/s for certain water transporters found in toad bladders, 6 x 10–14 cm3/s for the water channel
CHIP 28, 1.5 x 10–14 cm3/s for double-length nystatin, 1 x 10–13 cm3/s for single-length nystatin, and 4.5 x
10–14 cm3/s for amphotericin B. These numbers are up to two orders of magnitude smaller than the
single-channel permeability coefficient estimated for -hemolysin which is consistent with the much larger
pore size of -hemolysin.
2.1.4.3.3 A potential potassium pore in 3D--Doyle et al., 1998
An extensive paper by Doyle et al31. has described their model of a potassium ion pore. Their report is based on
the bacteria, Streptomyces lividans. Their paper open with an interesting assertion,
“Potassium ions diffuse rapidly across cell membranes through proteins called K+ channels. This
movement underlies many fundamental biological processes, including electrical signaling in the nervous
system. Potassium channels use diverse mechanisms of gating (the processes by which the pore opens
and closes), but they all exhibit very similar ion permeability characteristics (Hille, 1992). All K+
channels show a selectivity sequence of K+ Rb+ > Cs+, whereas permeability for the smallest alkali
metal ions Na+ and Li+ is immeasurably low. Potassium is at least 10,000 times more permeant than Na+
, a feature that is essential to the function of K+ channels. Potassium channels also share a constellation
of permeability characteristics that is indicative of a multi-ion conduction mechanism: The flux of ions in
one direction shows high-order coupling to flux in the opposite direction, and ionic mixtures result in
30Paula, S. Akeson, M. & Deamer, D. (1999) Water transport by the bacterial channel -hemolysin Biochim
Biophys Acta vol 1418, pp 117-126
31 Doyle, D. Cabral, J. Pfuetzner, R. et al. (1998) The Structure of the Potassium Channel: Molecular Basis of
K+ Conduction and Selectivity SCIENCE vol 280, pp 69-77 DOI: 10.1126/science.280.5360.69
24 Neurons & the Nervous System
anomalous conduction behavior (Hodgkin et al., 1955). Because of these properties, K+ channels are
classified as “long pore channels,” invoking the notion that multiple ions queue inside a long, narrow
pore in single file. In addition, the pores of all K+ channels can be blocked by tetraethylammonium
(TEA) ions (Armstrong &Binstock, 1971).” [Underline added]
This a disasterous statement, relative to the permeability of Na+, to the whole concept of the chemical theory of
the neuron and the model of Hodgkin & Huxley, if confirmed!!
The cited paper of Hodgkin & Keynes employed the Nernst Equation (1900's) and the results of Ussing (1949b)
that both assume a homogeneous material was involved, not a bilayer membrane that is fundamentally
impervious, amphiphobic ( both hydrophobic to simple ions and , lyophobic to most organics, Section 2.2.1 and
Section 2.1.4.5).
They further note,
“Two aspects of ion conduction by K+ channels have tantalized biophysicists for the past quarter
century. First, what is the chemical basis of the impressive fidelity with which the channel distinguishes
between K+ and Na+ ions, which are featureless spheres of Pauling radius 1.33 Å and 0.95 Å,
respectively? Second, how can K+ channels be so highly selective and at the same time, apparently
paradoxically, exhibit a throughput rate approaching the diffusion limit? The 104 margin by which K+ is
selected over Na+ implies strong energetic interactions between K+ ions and the pore. And yet strong
energetic interactions seem incongruent with throughput rates up to 108 ions per second. How can these
two essential features of the K+ channel pore be reconciled?”
They don’t offer any reconciliation in the following paragraph or any citations to reconciliation. They do not
offer any recociliation in their Summary!! Their use of the Pauling radii imply they are using the non-hydrated
ions in their calculations (Section 2.1.4.3.1) . They also are using a very thin bacterial lemma to associate with
their pore (their figure 3) of only 34 Angstrom instead of the generally accepted bilayer thickness of 75 ± 15
Angstrom in animal lemma (Section 2.2.1).
They recognize this disparity in lemma thickness in their following section entitled “Potassium Channel
Architecture.” The caption to their figure 1, providing aligned genetic sequences for a series of bacteria, plants
and animals.
They offer no discussion related to the much larger hydrated ions (Section 2.1.4) and how they are stripped to
the Pauling radii by that proposed configuration, other to note,
“General Properties of the Ion Conduction Pore
As might have been anticipated for a cation channel, both the intracellular and extracellular entryways
are negatively charged by acidic amino acids, an effect that would raise the local concentration of cations
while lowering the concentration of anions. The overall length of the pore is 45 Å, and its diameter
varies along its distance. From inside the cell (bottom) the pore begins as a tunnel 18 Å in length (the
internal pore) and then opens into a wide cavity (;10 Å across) near the middle of the membrane. A K+
ion could move
throughout the internal pore and cavity and still remain mostly hydrated. In contrast, the selectivity filter
separating the cavity from the extracellular solution is so narrow that a K+ ion would have to shed its
hydrating waters to enter. The chemical composition of the wall lining the internal pore and cavity is
predominantly hydrophobic. The selectivity filter, on the other hand, is lined exclusively by polar main
chain atoms belonging to the signature sequence amino acids. The distinct mechanisms operating in the
cavity and
internal pore versus the selectivity filter will be discussed below.”
“Therefore, two properties of the structure, the aqueous cavity and the oriented helices, help to solve a
fundamental physical problem in biology— how to lower the electrostatic barrier facing a cation crossing
a lipid bilayer. Thus, the diffuse electron density in the cavity center likely reflects a hydrated cation
cloud rather than an ion binding site.”
It is not clear that this paper addresses the true problem of a K+ pore in a realistic animal lemma which is
amphiphobic, thereby converting the type 1 lemma to type 3 as far as potassium is concerned. It does not
address the problem of how Na+ crosses the lemma in the opposite direction, except to dismiss the challenge due
to the low permeability of the Na+ to their configuration!!
2.1.4.4 Preparation of synthetic bilayer membranes
The Neuron 2- 25
Section 1.4.2 contains useful background information relative to the bilayers of the lemma of a natural cell.
Pearson & Pascher (1979) also provides useful background. Section 8.2 of “Processes in Biological Vision32”
also provides a broader discussion than presented below.
Quinn has provided early information on preparing synthetic bilayer membranes consisting of two different
phospholipids initially present as two separate monomolecular films33. He described the range of values he has
encountered for synthetic phospholipid bilayers and biological membranes, Figure 2.1.4-5 . His highest
resistivity value synthetic membranes reached a similar resistivity to those of Suwalsky. The thickness and
capacitance ranges appear appropriate without specifying the types of membranes encountered. Robinson34 has
provided a similar set of parameters during the same time period (1975). However, his resistivity values are
startlingly different and the ranges are reversed between the synthetic and natural membranes (page 42) without
any detailed descriptions of the types of membranes being documented. Neither Quinn or Suwalsky have
provided adequate citations to allow tracing the values in their tables.
Quinn35 also investigated a method of differential scanning calorimetry that appears to differentiate between
phospholipids exhibiting saturated and unsaturated fatty acids in their structure. He cited Phillips, Hauser &
Paltauf. Their paper will not be discussed here in detail but their data is very useful in demonstrating the change
in properties of a phospholipid as its lipid elements are changed. Their figure 1, apparently acquired via a
Langmuir trough, is particularly clear. The conclusions drawn may require updating based on more recent
knowledge concerning biological membranes. The paper also makes an interesting observation that clustering
of different phospholipids into different regions of biological membrane can occur in-vivo at temperatures
quite near 37C during gestation. This activity could account for the different types of lemma found in neurons
although it is probably not the dominant mechanism associated with differentiating the overall lemma into
Figure 2.1.4-5 Physical characteristics of synthetic and natural bilayer
membranes. A resting potential of 0 mV is probably associated with a lemma
made up of symmetrical phosphatidylcholine. It forms a near perfect electrical
insulator with no internal voltage source. Many of the other membranes may
have exhibited the characteristics of a pn junction. More sophisticated test
circuits would be needed to confirm this condition. See text. From Quinn, 1976.
32Fulton, J. (2004) Processes in Biological Vision. http://neuronresearch.net/vision/pdf/8Electrochem.pdf
33Quinn, P. (1976) The Molecular Biology of Cell Membranes. Baltimore, MD: University Park Press Chapter
2
34Robinson, G. (1975) Principles of membrane structure In Parsons, D. ed. Biological Membranes. Oxford:
Clarendon Press Chapter 2
35Phillips, M. Hauser, H. & Paltauf, F. (1972) The inter– and intra–molecular mixing of hydrocarbon chains
in lecithin/water systems Chem Phys Lipids vol 8, pp 127-133
26 Neurons & the Nervous System
distinct regions.
Phillips, Finer & Hauser have also discussed the conformational differences between lecithin and cephalin,
particularly related to the polar groups36.
Blume, writing in Hidalgo (chapter 2) recognizes distinct liquid-crystalline and gel states for the typical
individual bilayers described above using NMR techniques. Blume encounters a variety of unusual conditions,
particularly those related to non–biological temperature ranges. He also explores bilayer lemma, apparently
prepared synthetically to increase precision.
Zambrano & Rojas, writing in Hidalgo (chapter 7) provide some early information related to a putative Na+ abd
H+ pumps obtained from experiments with various animal tissue. Their conclusions include comments about the
likelihood of unsaturated fatty acids in the phospholipids forming the bilayer membranes of some species
(Walker & Wheeler, 1975).
2.1.4.5 Liquid crystalline versus gel state in phospholipids
McIntosh37, writing in chapter 2 of Deamer et al., provide very useful information, relying partly on the
information of Porohille et al. in chapter 3. Porohille et al38., writing in chapter 3 of Deamer et al., draw a
variety of conclusions as a result of their computer modeling of lipids. Together, their writings confirm many
important questions relative to bilayer lemma.
McIntosh describes the spatial regions of lemma in textual form; Porohille et al. provide compatible but more
informative graphical descriptions, Figure 2.1.4-6. They are the first set of authors who define their PC fully;
their POPC stands for the Phospholipid, 1-palmitoyl 2-oleoyl, sn-glycero 3-phosphocholine. Palmitic acid is a
saturated lipid of 16 carbons. Oleic acid is an unsaturated lipid of 18 carbons including one double bond
(assumed to be trans–. The peak–to–peak distance between the head groups is sometimes designated D and
typically is 3.68 nm. If multiple bilayers are brought together, the repeat distance is sometimes designated by
small d, and is typically reported as 5.2 nm. See figure 2.3 of Quinn (1976). The small d spacing is frequently a
function of the relative humidity or percentage of water present.
36Phillips, M. Finer, E. & Hauser, H. (1972) Differences between conformations of lecithin and
phosphatidylethanolamine polar groups and their effects on interactions of phospholipid bilayer membranes
Biochim Biophys Acta, vol 290, pp 397–402
37McIntosh, T.(1999) Structure and Physical properties of the lipid membrane In Deamer, D. Kleinzeller, A.
Fambrough, D. eds. Membrane Permeability: 100 Years since Ernest Overton. NY: Academic Press Chapter
2
38Porohille, A. New, M. Schweighofer, K. & Wilson, M. (1999) Insights from computer simulations into the
interaction of small molecules with lipid bilayers In Deamer, D. Kleinzeller, A. Fambrough, D. eds. Membrane
Permeability: 100 Years since Ernest Overton. NY: Academic Press Chapter 3
The Neuron 2- 27
A more detailed version of the above figure is provided by Huber et al39. in Figure 2.1.4-7.
Figure 2.1.4-6 Free energies of small anesthetics across the water–POPC
interface at 310K: CH4 (solid line), CH2F2 (dotted line), CF4 (dashed line), and Xe
(long–dashed line). From Pohorille et al., 1999.
39Huber, T. Rajamoorthi, K. Kurze, V. et al. (2002) Structure of Docosahexaenoic Acid-Containing
Phospholipid Bilayers as Studied by 2H NMR and Molecular Dynamics Simulations J AM CHEM SOC vol
124(2), pp 298-309, 2002 10.1021/ja011383j
28 Neurons & the Nervous System
Figure 2.1.4-7 “Electron density profiles and segmental group distribution
functions. (a) Simulated electron density profile for the POPC bilayer at 27 °C;
(b) simulated profile for the PDPC bilayer at 37 °C. The contributions of the lipid
segments and water are designated as follows: total corresponds to lipids and
water; H2O, water; CHO, choline group; PO4, phosphate; GLYC, glycerol; COO,
ester carbonyl; CH2, methylene; CH, vinyl; and CH3, methyl groups.” From Huber
et al., 2002.
The Neuron 2- 29
McIntosh also described the “unit membrane” concept that now requires further definition into various regions
of the lemma with different detailed parameters. He also introduced the “fluid mosaic” model of the lemma for
purposes of discussions related to the temperature of the lemma. McIntosh describe both PE and PC as
Zwitterions.
A zwitterion (from German, hybrid or hermaphrodite) is a chemical compound that carries a total net
charge of 0, thus electrically neutral but carries formal positive and negative charges on different atoms.
Zwitterions are polar and are usually very water-soluble, but poorly soluble in most organic solvents.
All of the phosphatidic acid derivatives are also amphipathic.
Amphiphile– A compound having a polar head (ionic) which tends to dissolve in water (hydrophilic)
and a water insoluble (hydrophobic) organic tail.
Amphipathic– These materials exhibit a capability to self organize themselves into liquid crystalline
monolayers and to further organize themselves into bilayer lemma.
He also introduced the fact that the number of double bonds associated with the aliphatic lipid portions of the
phospholipids lead to different transition temperatures between the liquid crystalline and gel states of the
bilayers and quantified these temperatures. After presenting a list of citations, McIntosh noted, “both synthetic
phospholipids and lipids isolated from membranes exhibit polymorphism. That is, depending on the lipid head
group, hydrocarbon composition, temperature, pH, and water content, phospholipids can form lamellar phases
(bilayers) with their hydrocarbon chains in either a partly ordered (gel) conformation, of a highly disordered
(liquid-crystalline) conformation or else form non lamellar (non bilayer) phases.” After citing additional
references, he went on to note, “The phase transition temperature and enthalpy of lamellar depend on a number
of factors, including lipid head group, hydrocarbon chain length, number of double bonds, and amount of
cholesterol present.” He asserted the following critically important conclusion, “most lipids found in biological
membranes have melting temperatures well below physiological temperatures, meaning that the lipids are in
the liquid–crystalline phase at 37C.” It can be presumed they remain in that state from below 0C and up to at
least 65C or higher, the recognized biological range. These are difficult experiments and it is difficult to draw
conclusions (Section 2.1.4.7.2).
Ziblat et a40l. have defined three distinct states of matter for purposes of membrane research;
“Liquid disordered phases, Ld, are characterized by high diffusion states.
Solid ordered phases, So, or gel phases have a veery low diffusion rate and are generally composed of lipids
with saturated alkyl chains.
Liquid ordered states, Lo, phases are characterized by an intermediate diffusion coefficient. This phase may
contain high levels of cholesterol.
The Lo and So phases include crystalline domain detectable by X-ray diffraction. Their coherence lengths are
typically nanometers in the Lo and tens of nanometers in the So phase.”
Ziblat et al. also noted several properties of interest to the medical field. “When accumulated by cells in excess,
cholesterol was found to participate in several pathological phenomena such as cataracts and atheoscleorsis.
They noted that cholesterol could crystalline within lipid structures ane eventually expand to create larger
cholesterol crystals spanning multiple membranes (as in cataracts).
As McIntosh also notes, in an aside, “because some membrane lipids, such as sphingomyelin and uncharged
glycolipids, melt at much higher temperature, the isolated lipids form gel or ordered phases at 37C.” He goes
on, “lipids that have the capacity to hydrogen bond with neighboring lipids (such as PE and glycolipids) tend to
have higher phase transition temperatures than lipids that do not hydrogen bond with neighbors (such as PC).”
The last statement may require reviewing his citations more closely. On page 27, McIntosh also notes, “PCs and
PEs with saturated hydrocarbon chains (which are approximately cylindrical in shape) form bilayers, whereas
PEs with unsaturated chains (which are cone shaped because of their relatively small head group and bulky
hydrocarbon chain regions) tend to form hexagonal phases.” The PEs he is discussing here obviously involve
cis–double bonds. As shown in section 2.2.1.3.3, PEs incorporating trans–double bonds do not deviate
significantly from the cylindrical shape. Finally, he notes, “Gruner (1985, 1989) has pointed out that in addition
to molecular shape, other factors, such as electrostatic interactions and hydrogen bond formation may be
40Ziblat, R Leiserowitz, L Addadi L. (2011) Crystalline Lipid Domains: Characterization by X-Ray
Diffraction and their Relation to Biology Chemie vol l50(16), pp 3620-3629
https://doi.org/10.1002/anie.201004470
30 Neurons & the Nervous System
involved in determining the aggregation properties of phospholipids.” McIntosh repeats some of these
properties in his section IIC. His sections III and IV provide more details than needed in this study.
Section VI of McIntosh presents a key question, “a fundamental question of membrane biology has been the
reason for the presence of such a vast variety of membrane lipids, . . .” This question is answered to a large
degree in Chapter 8 of this work, where selections of phospholipids are the critical receptor molecules of
gustation, olfaction and oskonation (sensing of other members of the same species, and their sex. McIntosh
describes, in concept, the second messenger role of some phospholipids. When reinterpreted on a more
fundamental plane, it is this property of the phospholipid sensory receptors that generates a electrical potential
bio–physically that causes a chemical change that is frequently sensed as a second messenger by bio-chemists.
McIntosh also notes the propensity of PE in aiding the fusion of lemma when brought into close juxtaposition.
This may be an important factor in the formation of active semiconductor devices within neurons, at synapses
and as Nodes of Ranvier. The section asks a number of other important questions unrelated to the themes of this
work.
2.1.4.6 Electrostatic properties of charged lipids
Quinn (section 2.2.6) has provided data on the electrostatic properties of several phospholipids that are directly
involved in the sensory receptors of neurons. The material is in the language of a physical chemist. It does not
relate directly to the potential dipole of the various molecules. It appears to be the change in this potential
dipole that is sensed by the first Activa of the sensory neuron (Chapter 8 of this work). Figure 2.1.4-8
presents his data. The figures are only partial formulations as indicated in the caption. Several structures fail to
show a positive charge, suggesting it occurs elsewhere in the complete molecule.
The majority of the discussion in Quinn relates to the phospholipids identified when present in individual
phospholipid bilayers not related to the total complex of the outer bilayer of type 2 lemma of a neuron.
Thus, he speaks of the swelling of a layer due to electrostatic charges on adjacent molecules when
arranged in a monolayer. The situation is significantly different in the proposed sensory receptors of
biology where the potential dipole of each phospholipid molecule is associated with an active sensing
element. Quinn does note, “When charged phospholipids are oriented, as for example in a mono-
molecular film or a bilayer structure, the charged groups will reside in a plane near the junction of the
aqueous and hydrophobic regions (his figure 2.17 shows this plane as external to the lemma and
associated with a boundary layer). He designates this plane as 0 and its value in millivolts as “The
electrical potential at the plane of shear is referred to as the zeta ( ) potential.” Quinn provides a simple
equation for the zeta potential that may be used to calculate the dipole potential between the two surfaces
of the bilayer. He notes, “Another feature of the negatively–charged surface of phospholipid structures is
that protons derived from the dissociation of water molecules are attracted to the surface layer, causing a
decrease in pH of the surface phase (pHs) relative to the bulk aqueous phase (pHb).
The Neuron 2- 31
Adamson41 discussed this subject briefly in a Special Topics section referring to it as within the field of
“electroosmosis,” a field closely related to but separate from electrophoresis. Both of these fields are focused
on motion and charged elements. The mechanisms frequently induce additional moving charges. In the case of
sensory modalities, the interest is on stationary charged elements and how the associated potentials change when
participating on coordinate bonding. Zeta potentials associated with phospholipids are typically within the ±100
mV range.
Figure 2.1.4-8 Electrostatic properties & structure of selected phospholipid
charged groups. The R to the left of each chemical diagram relates to the
glyceride portion of the molecule. The R to the right in item 2 is the inositol
moiety that actually is the active receptor portion of the phospholipid associated
with GR 3, the “hydrated sodium ion” sensing channel of the gustatory modality.
Item 5 is the receptor associated with OR 1 and GR 1, the organic acid sensing
channel of of both olfaction and gustation. See text. From Quinn, 1976
41Adamson, A. (1973) A Textbook of Physical Chemistry. NY: Academic Press Page 1015
32 Neurons & the Nervous System
2.1.4.7 Expanding the lemma nomenclature
Recently, it has become necessary to expand the nomenclature used to describe the lemma of all cells in general
and neurons specifically. The following sections, by different authors, employ slightly different terminology
with respect to the liquid crystalline state (that is critically important in biology). The terminology follows that
of EZ Water (deverloped in 1969) in Section 1.3.2.2 and in Section 2.2.3.4
The L, used below, oorresponds to “Liquid ordered states, Lo, phases are characterized by an intermediate
diffusion coefficient.” of Ziblat, above. The diffusion coefficient may be due to “hole” transport through the
liquid crystalline material acting as a semiconductor..
2.1.4.7.1 Membranes of Escherichia coli–Lind
Lind et al42. has presented material on the lemma of Escherichia coli,E. Coli, in 2015. E. coli is a gram
negative bacteria. The paper illustrates the considerable difference between bacterial and animal membranes.
Their description of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine (POPE) and
(1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) are detailed. They also explore
1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoglycerol (POPG), a molecule not commonly found in the animal
literature. Their figure 1 shows POPE with a trans–double bond at position C9. However, their measurements of
the thickness of the bilayer membrane, using Atomic Force Microscopy, AFM, are considerably thinner than
that of animal measurements, 41.3 ± 3 Angstrom compared to ~50.75 Angstrom. They also explored, surface
sensitive techniques including dissipation enhanced quartz crystal microbalance (QCM-D) and , neutron
reflection (NR) techniques.
It is likely their value of 41.3 ± 3 Angstrom refers to the center-to=center distance between the centroids
of the head group, whereas the value of ~50.75 Angstrom may refer to the overall width of the bilayer.
Lind et al. do provide surface roughness data for their membranes that is probably new and useful. The values
range from 4 ± 1 to 10 ± 5 Angstrom depending on how the membrane was formed. Their Table 1 also provides
other useful dimensional data. The challenge is to extend the AFM technique to natural lemma of type 2, 3 & 4
(Section 2.1.5.1).
The none overlapping roughness ranges provided above suggest significantly different lemma thicknesses
for the two measurement sequences. All samples related to the limited types of lemma associated with
bacteria.
The Lind et al. paper was meticulously documented but was clearly exploratory in nature. No statistical
values (number of samples or number of AFM traces) per test sequence (two) were provided. No
explanation was offered to account for the difference in interfacial roughness between their hydrogenated
and their deuterated E coli supported lipid bilayers. This difference suggests an uncontrolled variable in
their very complicated sample preparation protocol.
Seelig et al43,44. have discussed the relevance and effect on the critical temperature of a phospholipid, of double
bonds in the unsaturated lipid. In the first paper, focused on cis–double bonds , they note, “Monounsaturated
phospholipids are predominant but lipids containing more than one double bond also occur quite commonly.”
The second paper explored both cis– and trans–double bonds using deuterated nuclear magnetic resonance.
“The labeled fatty acids are used to prepare l-palmitoyl-2-oleoyl-, 1 -palmitoyl-2-elaidoyl-, and
1,2-dielaidoyl-sn-glycero-3-phosphocholine.” Their first conclusion was, “This suggests that to a good
approximation the hydrocarbon interior of a POPC bilayer may be divided into strata running parallel to the
bilayer surface. Segments which are located in the same stratum are then characterized by the same segmental
order parameter Sm0|. This certainly simplifies the statistical-mechanical analysis of the POPC bilayer.”
42Lind T, Wacklin H, Schiller J, Moulin M, Haertlein M, Pomorski T, et al. (2015) Formation and
Characterization of Supported Lipid Bilayers Composed of Hydrogenated and Deuterated Escherichia coli
Lipids. PLoS ONE 10(12): e0144671. doi:10.1371/journal.pone.0144671
43Seelig, A. & Seelig, J. (1977) Effect of a Single Cis Double Bond on the Structure of a Phospholipid
Bilayer1 Biochem vol. 16(1), pp 45–50
44Seelig, J. & Waespe-Sarcevic, N. (1978) Molecular Order in Cis and Trans Unsaturated Phospholipid Bilayers
Biochem vol 17(16), pp 3310–3315
The Neuron 2- 33
Johnson and Johnson45 recently note,
“Glycerophospholipids, comprising half of the brain's lipids, consist of a polar head group attached to a
glycerol backbone and up to two fatty acyl chains. Glycerophospholipids are dominant in cell membranes
providing stability, fluidity, and permeability. Moreover, they are required for the proper function of
membrane proteins, receptors, and ion channels and act as reservoirs for second messengers and their
precursors. Glycerophospholipids are broadly categorized based on their head group into
phosphatidylcholine, phosphatidylethanolamine, phosphatidylserine, phosphatidylinositol,
phosphatidylglycerol, and cardiolipin. The different combinations of glycerophospholipid head groups
and fatty acyl chains give rise to thousands of molecular species. DHA and ARA [both multi-
unsaturateed lipids] are the most prominent fatty acyl chains within neuronal glycerophospholipids,
accounting for approximately 60% of esterified fatty acids in the plasma membrane.”
A contradiction exists between the last two papers. I accept the latter as more current research..
2.1.4.7.2 Expanding the outer bilayer nomenclature
When accounting for the variation in amino acid content and dopant level of the outer bilayer of a neural lemma,
it is necessary to expand the nomenclature beyond the four letter groups of the above paragraph. Note, bacteria
do not exhibit neural systems and do not require the additional complexity of the lemma of a cell that is needed
by a neural system. In the case of the sensory receptor neurons, it is necessary to recognize that the amino acids
attached to the phospholipid moiety may vary among a wide group to accommodate the gustatory (Section 8.5),
olfactory (Section 8.6) and oskonatory (Section 8.6.11) modalities. It is also useful to expand the descriptor
related to the individual lipids, when speaking of their electrical properties, to indicate their dopant level. This
is most directly indicated by the number of double bonds in each lipid, on the assumption that the outer layer
exhibits only one type of phospholipid in a local area. If the local area is not populated uniformly by a
phospholipid of a specific number of double bonds in a specific lipid, an even more density specific
nomenclature may be needed.
For the present, it is recommended that the nature of a given outer layer be described using the following
nomenclature; AnBmPX where the following labels apply,
A = The name of the lipid at position sn = 1 along the glyceride moiety, and 0 > n > 9, the number of double
bonds it contains.
B = The name of the lipid at position sn = 2 along the glyceride moiety, and 0 > m > 9 the number of double
bonds it contains.
P = The abbreviation for the phospholipid structure in toto.
X = The one letter descriptor for the amino acid associated with that phospholipid if available.
If no single letter abbreviation for the amino acid or an amino acid derivative is involved, a longer label
can be used in this position; such as Caa for Cinnamyl amino acid for the OR 6 channel receptor in
olfaction (Section 8.6.2).
The need for a more complex description of the inner bilayer of a lemma is not obvious at this time.
2.1.4.7.3 Features of membranes & junctions–Pappas, 1975
Pappas46 has defined a variety of terms that are difficult to find elsewhere. The problem remains that the
foundation of these definitions does not include the Electrolytic Theory of the Neuron, The following
definitions and quotations refer to his work.
Desmosome– an area between two cells that is strongly adhesive. “The function of the desmosomes seems t be
purely mechanical; that of holding together surface cells, . . .” “The junctions can be more accurately compared
to rivets or spot wlde–discrete points holding together two otherwise unconnected. A less common type of
desmosome, . . ., it can be compared to a seam weld rather than a spot weld.”
Syncytium– a single, muoltinucleated giant cell with continuous cytoplasm. “This view is consistent with what
could be seen with a light microscope. More recent, electron microscopic studies have established that this view
45Johnson, Jennifer L. &Johnson, Lance A. (2022) Glycerophospholipids In Encyclopedia of Behavioral
Neuroscience, 2nd edition, vol 1 of 3, pp 439-470
46Pappas, G. (1975) Junction between cells. In Weissmann, G. & Claiborne, R. ed. Cell Membranes:
Biochemistry, Cell Biology & Pathology. NY: HP Publishing Co. Chap 9, pp 87-94
34 Neurons & the Nervous System
is incorrect.”
Tight junction–An area of tight connection between two adjacent cell membranes–so tight, in fact, that the
junction is essentally impermeable.”
Blood-brain-barrier– consisting of the lining of the cerebral blood vessels, the cell of which, unlike those of
vascular endothelium elsewhere in the body, are joined by tight junctions. “Of course the blood-brain-barrier is
not, and cannot be, copletely impermeable: molucules such as glucose and some neuro-humors routinely pass
through it as does carbon dioxide in the opposite direction.”
Gap junction–“In one sense intermediate between the desmosome and the tight junction. Like the former, it
bridges the space between two cells but that space is considerably narrowed, from its normal 200 Angstrom or
so to a width of 20 to 40 Angstrom. In another since, however, the gap junction differs markedly from both the
other types in that it does not merely connect the exterior membranes of cells but also their cytoplasms.” See his
additional discussion, page 89.” His illustration on page 91 is informative.
These definitions by Pappas are subject to further specification based on the Electrolytic Theory of the Neuron
(Section 1 through Section 1.2.6 &, Section 2.2.5 through Section 2.5). Specifically, these definitions do not
reflect the fact that different types of lemma exhibit different electrolytic characteristics.
2.1.4.7.4 Bilayers as studied by 2H NMR & molecular dynamics–Huber, 2002
Huber et al47. made an early and sophisticated contribution to understanding of the role of DHA in the neuron.
The paper relies on molecular dynamics (MD). The paper is one of the fact-filled papers in the academic
literature
Huber et al. recognize the phospholipids exist in a liquid crystalline state when they are
incorporated into the bilayers of lemma of neurons at endothermic temperatures,
They recognized the role of DHA played in the neural lemma,
“Here we have employed two complementary structural methods for the study of polyunsaturated bilayer
lipids, viz. deuterium (2H) NMR spectroscopy and molecular dynamics (MD) computer simulations. Our
research constitutes one of the first applications of all-atom MD simulations to polyunsaturated
lipids containing docosahexaenoic acid (DHA; 22:6 cis-¢4,7,10,13,16,19). Structural features of the
highly unsaturated, mixed chain phospholipid,
1-palmitoyl-2-docosahexaenoyl-sn-glycero-3-phosphocholine (PDPC), have been studied in the
liquid-crystalline (L) state and compared to the less unsaturated homolog,
1-palmitoyl-2-oleoyl-snglycero-3-phosphocholine (POPC). The 2H NMR spectra of polyunsaturated
bilayers are dramatically different from those of less unsaturated phospholipid bilayers.”
“Structural features of the highly unsaturated, mixed chain phospholipid, 1-palmitoyl-2-
docosahexaenoyl-sn-glycero-3-phosphocholine (PDPC), have been studied in the liquid-crystalline (LR)
state and compared to the less unsaturated homolog, 1-palmitoyl-2-oleoyl-snglycero-3-phosphocholine
(POPC). The 2H NMR spectra of polyunsaturated bilayers are dramatically different from those of less
unsaturated phospholipid bilayers.”
POPC is generally recognized as composing at least part of the outer bilayer of the lemma of neurons (see
Section 2.1.4 for an earlier interpretation by Blume in Hidalgo using synthetic membranes).
The data of Huber et al. in general notes the limit of >30 C to insure the sample is in the liquid
crystalline state (Section 2.1.4.8.7).
Huber et al. calculate 400,000 conformational “snapshots” available to DHA when present in PDPC (page 30•5)
47Huber, T. Rajamoorthi, K. Kurze, V. et al. (2002) Structure of Docosahexaenoic Acid-Containing
Phospholipid Bilayers as Studied by 2H NMR and Molecular Dynamics Simulations J AM CHEM SOC vol
124(2), pp 298-309, 2002 10.1021/ja011383j
The Neuron 2- 35
Figure 2.1.4-9 Ramachandran Plots for PDPC. Left: “Definition of the dihedral
angles 1 and 2 for a methylene group in a -CH=CH-CH2-CH=CH- acyl fragment.
The conformation of the structure shown is 1 = 2 = 120° (skew+, skew+). Right:
Dihedral angle distribution function, presented in terms of mean force potential,
where 1 and 2 are the two adjacent dihedral angles for the methylene group of
a -CH=CH-CH2-CH=CH- fragment. The data are averaged over the trajectories for
all five inequivalent positions of the docosahexaenoic acyl chain of PDPC. (a)
Contour plot of the potential of mean force calculated from the probability
distribution, spanning the ( 1, 2) plane, with a linear spacing of 1 kJ mol-1
between contour levels. The levels are labeled by the free energy in kJ mol-1
relative to the most probable conformation, which is assigned to the zero level.”
From Huber et al., 2002.
using the method of Ramachandran et al48. Figure 2.1.4-9 shows their Ramachandran Plots. The Right frame
shows the capability of all snapshots at equal probability. Many of these correspond to the normal Brownian
motion associated with a molecule. The analysis in Huber et al. is outside the realm of this author. For the
DHA for all cis-double bonds in PDPC is not clearly annotated.
Wikipedia has an introduction to this technique on the page labeled “Ramachandran Plots.” The angles shown
are defined differently from Huber et al.
Saiz and Klein49 continue the investigation of the model membrane, a 1-stearoyl- 2-docosahexaenoyl-sn-
glycero-3-phosphocholine (SDPC, 18:0/22:6 PC) lipid bilayer. They develop the skewness criteria
further and discuss the increased water permeability in the liquid crystalline state of the SDPC. They
speak of hydrogen bonding, N–P•••N, in an interesting way. The hydrogen bonding may contribute to the
electrical conductivity of the SDPC.
A second paper by Saiz and Klien50 develops, using a very large computer, a snapshot of SDPC, 18:0/22:6 PC,
showing the details of each SDPC molecule in a liquid crystalline bilayer,. Figure 2.1.4-10. They also define the
helical, angle-iron & hairpin conformations of the DHA molecule. Compare to an earlier representation by Quinn
((1976) in Section 2.1.4.8.3.
They also, for the first time include the olfactory sensors in the group, CNS and retina, of high concentrations of
DHA. This would suggest that, at least, all external sensory neurons would be sites of high DHA content upon
48Ramachandran, G.N.; Ramakrishnan, C.; Sasisekharan, V. (1963) Stereochemistry of polypeptide chain
configurations J Molec Biol vol 7, pp 95–99. doi:10.1016/S0022-2836(63)80023-6
49Saiz, L. & Klein, M. (2001a) Structural Properties of a Highly Polyunsaturated Lipid Bilayer from
Molecular Dynamics Simulations Biophysical J vol 81, pp 204–216
50Saiz, L. & Klien, M. (2001b) Influence of Highly Polyunsaturated Lipid Acyl Chains of Biomembranes on
the NMR Order Parameters J Am Chem Soc vol 123, pp 7381-7387
36 Neurons & the Nervous System
further research.
The Neuron 2- 37
Figure 2.1.4-10 “Instantaneous configuration of the SDPC lipid bilayer. For
the sake of clarity, water molecules, which are located between the
headgroups of two opposite leaflets, i.e., the void region, are not shown.
The headgroup region is indicated by the positions of the nitrogen atoms
(colored blue) and the phosphorus atoms (colored yellow). The rest of
the lipid atoms are displayed as balls and sticks. By the use of periodic
boundary conditions, images of the simulation cell are replicated at
every face of the orthorhombic central cell (colored red).” The snapshot was
modeled at a temperature of 303 K (30 C) that may be marginal for insuring the
sample represents the liquid crystalline state of matter. From Saiz & Klein,
2001b.
Saiz and Klein discuss their findings related to,
38 Neurons & the Nervous System
“Orientational Order of the Saturated Chains.
The effects of the specific conformations of the molecular fragments of the polyunsaturated chain on the
order of the saturated chain are evidenced in Figure 3a,b, where we plot the partial order parameter
profiles.”
The Figure 3 is largely unreadable; they expand the individual traces in following figures to develop their
conclusions.
The paragraphs are followed by their findings related to,
“ Orientational Order of the Polyunsaturated Chains”
Both of these headings are followed by discussions that do not include inputs suggested by the ETN, such as
inter-phospholipid molecule cooperation to support hole transport through the bilayer..
Weizenmann et al51. provided similar NMR data for POPC using 1H MAS NMR where MAS is “magic-angle
spinning.” Figure 2.1.4-11 shows a composite of frames from their figures 1 &2.
51Weizenmann, N. Huster, D. & Scheidt, H. (2012) Interaction of local anesthetics with lipid bilayers
investigated by 1H MAS NMR spectroscopy Biochimica Biophysica Acta vol1818, pp 3010–3018
The Neuron 2- 39
Figure 2.1.4-11 Composite frames showing NMR of POPC. Lower frame shows
the NMR. Single letter above peaks refer to procaine HCL. Multiple letter labels
are defined in upper frame showing POPC. From Weizenmann et al., 2012.
Sterratt and Mason52 carried out different experiment than Huber et al. They did not prepare PDPC but merely a
52Sterratt, S. & Mason, R. (2018) Eicosapentaenoic acid and docosahexaenoic acid have distinct membrane
locations and lipid interactions as determined by X-ray diffraction Chem Physics Lipids vol 212, pp 73-79
40 Neurons & the Nervous System
solution of POPCmixed with either EPA or DHA (1:10 mol ratio to POPC) and then went through a
centrification protocol. Their results show that the EPA and DHA were impregnated into the POPC to different
locations intracellular to the POPC molecular array. Their results do not apply to the PDPC in the liquid
crystalline state, where the DHA is expected to be present in the sn-2 position and therefore make up ~50% of
the PDPC’s molecular weight.
2.1.4.7.5 Potential lipids in type 2 lemma and the photoreceptors–Crawford, 2013
Crawford et al53. has presented a thought provoking paper that combines many numerical values along with
many concepts in an obscure journal that are poorly referenced. It addresses the tunneling possible in long chain
lipids as a function of the number of double bonds. It focuses on a highly conjugated lipid, docosahexaenoic
acid, DHA. The following material also appears in Section 5.4.5.1 of “Processes in Biological Vision.” This
material is closely tied to Section 2.2.1.3 in this work. See also Section 2.2.3.4.4 for a list of lipids with double
bonds.
Crawford et al. assert,
“we calculate that the bond has a dissociation energy of about 65 kcal/mole.”
docosahexaenoic acid, DHA (-cis-docosa-4,7,10,13,16,19-hexaenoic acid or C22:6n-3)
“As far as our knowledge goes, DHA has been the dominant fatty acid in the membrane
phosphoglycerides of the photoreceptors, neurons and synapses for all 600 million years of animal
evolution.”
“DHA is present in greater than 50% of the outer rod segment membrane phosphoglycerides, with some
phosphoglycerides containing two DHA molecules (no reference, see Section2.1.4.7.6).”
“The brain can contain numerous proteins but is absolutely dysfunctional without DHA and arachidonic
acid (20:4n-6, AA) (no reference).”
“The likely scenario is that instead of converting photonic energy to carbohydrates or proteins, DHA
converted it to electricity and hence the evolution of the nervous system and ultimately the brain (no
reference).”
“ The conjugated double bond sequence of retinal is capable of transporting electrons like a copper wire
as the-electron clouds are in close proximity and can overlap (no reference).”
These quotations are generally compatible with the ETN and are the first quotations from the literature
describing the lipids of the type 2 lemma of the neurons in detail.
Crawford and various members of his team have been quite prolific in researching the evolution of the human
brain over the eons of time. There won’t be time forme to review all of the teams work .Crawford et al54.
prepared another paper where they asserted their frustration in seeking a purpose for the preponderance of DHA,
in the human brain,
“DHA is the most prominent essential fatty acid used for the structures and functions of the
photoreceptor and synaptic junction. So the question addressed in this paper is why, and what are the
evolutionary implications of the abundance of DHA in the marine food chain compared the relatively
paucity in land ecosystems.”
“The question which arises from this discussion is what is so special about DHA? Why has DHA been
chosen so overwhelmingly for photoreceptor and synaptic membranes, despite the availability of similar
molecules which would be less difficult to obtain, and are less vulnerable to oxidative damage? In
53Crawford, M. Broadhurst, C. Guest, M. et al. (2013) A quantum theory for the irreplaceable role of
docosahexaenoic acid in neural cell signalling throughout evolution Prostaglandins, Leukotrienes and Essential
Fatty Acids vol 88, pp 5–13
54Crawford, M. Bloom, M., Leigh Broadhurst C. (2000) Evidence for the Unique Function of Docosahexaenoic
Acid (DHA) During the Evolution of the Modern Hominid Brain Lipids vol 34, pp S39-S47
The Neuron 2- 41
particular, what advantage does it convey relative to the very closely related ω3 and ω6 DPAs, each of
which differs from DHA only in the absence of one double bond (between carbons 4 -5, and 19-20,
respectively)?”
“What is the cause of such specificity in membrane composition? It is understood that biological
membranes, while always having the form of a fluid lipid bilayer, have detailed distributions of lipid and
protein molecules that reflect the interactions between lipids and integral membrane proteins (40). It
seems that the one missing double bond in DPA species renders them unsuitable for whatever
lipid-protein interaction favours DHA’s inclusion in membranes of the brain.”
“In summary, a number of studies have been conducted on the physical effects of polyunsaturation on
membranes, in which DHA has been compared to a range of other unsaturated chains having from one to
five double bonds. Thus far, however, all differences that have been measured have been matters of
degree, and none provide a compelling explanation for the striking specificity with which DHA is
selected for membranes of the eye and brain.”
The answer, based on the Electrolytic Theory of the Neuron, ETN, is the need to pass electrical charges along
the axis of phospholipids when forming a liquid crystalline outer bilayer of the type 2 lemma of a neuron.
(Section 2.2.1.3). This process is aided by the maximum number of consecutive double bonds of the -cis- form.
Section 2.1.4.7.6 will address the utility of a high number of double bonds in one or more lipids of the
phospholipids.
Crawford et al., 2000, continue their search using structural models of “3D energy-minimized structure of
docosahexaenoic acid (DHA). These models are not compatible with the phospholipid forming the bilayer of a
lemma of a neuron.
Figure 2.1.4-12 shows their model. Unfolding the two lipids to their full length will achieve their configuration.
This makes them compatible with the liquid crystalline structure of Section 2.2.1.3.
42 Neurons & the Nervous System
Figure 2.1.4-12 “Phospholipids in 3D energy-minimized configuration. a: 3D
energy-minimized structure of phospholipid with ethanolamine, DHA, DHA. Side
view. b: Ethanolamine, DHA, DHA. End view, note position of phosphate group.”
Unfolding both the Ethanolamine, DHA and DHA groups to their full lengths will
give the configuration used in the bilayers of type 2 lemma. Using a molecular
drawing that shows the double bonds more prominently would be useful. From
Crawford et al., 2000.
Crawford et al55. provided another paper in 2018 addressing the same questions as quoted above. but a different
perspective. Their subtitle was “The six methylene-interrupted double bonds and the precision of neural
signaling.” Their figure 3 has a subtitle associated with the 3D energy-minimizing configuration of DHA,
“DHA - Neural Signaling Molecule” The text provides no justification for this assertion.
Crawford appears to have introduced the term, interrupted double bonds, for those chains that are
otherwise conjugated.
Crawford & colleagues frequently refer to DHA as a resistor without quantifying the value. Figure 2.1.4-13
clarifies their use of the term. The upper part of the figure shows DHA using various nomenclatures. It stresses
55Crawford, M.Thabet, M. Wang, Y. et al. (2018) A theory on the role of π-electrons of docosahexaenoic acid
in brain function EDP Sciences https://doi.org/10.1051/ocl/2018011
The Neuron 2- 43
Figure 2.1.4-13 Clarification of Crawfords use of “Double bonds: A depiction of
the comparison between potential for electron conductivity in conjugated double
bonds compared to the methylene interrupted double bonds of DHA. The
overlapping π-electrons clouds in the conjugated set (e.g. in retinal) overlap
allowing the electrons to flow freely in response to a potential difference. The
methylene groups separating the double bonds in DHA localise the electrons.”
See text. From Crawford et al.,2018.
the fact that DHA is not conjugated but the double bonds are separated by a methylene group. This makes them
resistive compared to the conjugated form shown in the lower part of the figure. Both the conjugated molecule
and those separated by methylene groups are highly resistive compared to a single copper strand of equal
diameter (see Section 2.2.1.3.2). However, that is not the criteria.
Note the equivalence of C22:6n-3 and C22:63 in line two fo the figure. The “O”is apparently a typographic
error for “=.”
Neurons are high impedance devices, with the resistive component of the impedance frequently in the hundreds
of megohms range. The important value in type 2 lemma is the total resistivity in Ohms-centimeters, where the
thickness of each bilayer divided by the area is multiplied by its resistivity to obtain the resistance of an area of
type 2 lemma This value may be in series with a diode depending on the applied of the applied voltage.
Figure 2.1.4-14 shows the actual configuration of the lemma of a neuron. The work in this field is addressed in
Section 2.2.1.3.
44 Neurons & the Nervous System
Figure 2.1.4-14 Single layer plasma lemma
showing the two bilayers in a liquid
crystalline form. The pairs of outlined
molecules represent type 1 lemma,
forming a perfect insulator. The pairs of
one filled and one outlined molecule
represent type 2 lemma. The type 2
lemma may be thicker if the filled
molecules represent DHA. The important
feature is that both bilayers form liquid
crystalline structures. The double bonds
of the filled molecules are free to share
their bonds and contribute to the total
current through the bilayer. See text.
From Pannese, 1994.
The work of Crawford & colleagues suffers form a
lack of any detailed model of both the nature of
the bilayer and neural signaling they want to
address. This is a serious shortcoming!
In 2018, Crawford et al56 , 57. wrote two papers on
the same general subject but they appear to be
more philosophical than conceptual!
56Crawford, M. Thabet, M. & Wang, Y. (2018) An introduction to a theory on the role of π-electrons of
docosahexaenoic acid in brain function OCL vol 25(4), paper A402 https://doi.org/10.1051/ocl/2018010
57Crawford, M. Thabet M., Wang, Y., Broadhurst, C. & Schmidt, W. (2018) A theory on the role of -
electrons of docosahexaenoic acid in brain function OCL vol 25(4), paper A403
https://doi.org/10.1051/ocl/2018011
The Neuron 2- 45
Figure 2.1.4-15 Calder (2016) nomenclature used for DHA discussion.
2.1.4.7.6 Concentration of DHA in the Human brain & its nutrition–Calder, 2016
Calder58 has provided more data & more precisely worded data on DHA than did Crawford in the first part of
Section 2.1.4.7.5. The data reviews the structural data of the molecule and provides a caricature in figure 7 of
the possible uses of DHA. It also provides the nutritional value and sources of DHA throughout life, beginning
with the fetus.
He also provides an Appendix with his nomenclature, shown in Figure 2.1.4-15.
Calder presented figure 1, reproduced as Figure 2.1.4-16, showing multiple depictions of DHA.
58Calder, P. (2016) Docosahexaenoic Acid Ann Nutr Metab vol 69(suppl 1), pp 8–21
DOI: 10.1159/000448262
46 Neurons & the Nervous System
Figure 2.1.4-16 Four configurational representations of DHA. Note the form used
in lemma is believed to be the all-Cis- version of DHA. “DHA has 22 carbons and
6 cis double bonds in its hydrocarbon (acyl) chain. The α-carbon is the carbon
of the terminal carboxyl group (COOH) and the ω-carbon is the carbon of the
terminal methyl (CH3) group.” The distance between two CH2 groups is 3.01
Angstrom. Adapted from Calder, 2016.
Calder presented figure 2, reproduced as Figure 2.1.4-17 to explain the complex conversion of a linolenic
acid, ALA, to DHA, The enzyme, elongase, adds (Ch3-CH3)) from an unknown source in two places??
In a section of the paper, Calder asserts,
“
DHA is Highly Concentrated in the Human Brain and Eyes
More than 50% of the dry weight of the human brain is lipid, particularly structural lipid (i.e.
phospholipids). The most abundant fatty acids in the brain are DHA, arachidonic acid and adrenic acid
[O’Brien et al, 1965, Crawford et al., 1976] . The human brain and retina contain an especially high
proportion of DHA relative to other tissues and little EPA [[O’Brien et al, 1965, Crawford et al., 1976,
Anderson, 1970] ( table 3 ). For example, DHA was reported to contribute an average of 18% of fatty
acids to adult human brain grey matter [Skinner et al., 1993].
“ In the latter study [Makrides et al.], the contributions of EPA were <0.05 and 0.1%, respectively.
Within cell membranes, EPA and DHA are distributed differently among the different phospholipid
components and in the brain and eye specific phospholipids are especially rich in DHA. For example,
DHA was reported to contribute an average of 36% of fatty acids in mammalian brain grey matter
The Neuron 2- 47
phosphatidylserine [ Crawford et al., 1976] and an average of 22% of fatty acids in retina
phosphatidylcholine [Anderson, 1970] . DHA contributes 50–70% of the fatty acids present in the rod
outer segments of the retina [ Anderson, 1970] . These rod outer segments contain the eyes’
photoreceptors.”
The sentences in the above quote differs significantly from Crawford et al. in Section 2.1.4.7.5. Crawford
appears to have condensed his remarks concerning the brain and retinas, thereby introducing ambiguity
Crawford et al., 2016, presented a figure 7, in caricature, of the uses of DHA at the lemma of a neuron. This
caricature does not recognize the role of phospholipids as triglycerides, instead of simple DHA molecules and
many other unproven DHA participations that are not supported by the ETN.
2.1.4.7.7 Raman Spectroscopy of DHA and related lipids–Broadhurst,2018
Raman spectroscopy can provide good information concerning the precise state of many individual atoms in a
molecule. While not critically important to the development of this work, the early work of Lewis & Wilkins59
have provided information concerning many atoms within amino acid complexes. They cite the many studies of
Bellamy and associates during 1952 to 1959, particularly Part 3 of 1959, for further information.
Broadhurst et al60. provides data on six relatives of DHA having double bonds. Their Abstract contains the
Goal of the paper,
“ We present systematic analysis of oleic (18:1n-9), linoleic (18:2n-6), alpha-linolenic (18:3n-3),
arachidonic (20:4n-6), docosapentaenoic (22:5n-3), and docosahexaenoic (22:6n-3) acids. Continuous
gradient temperature Raman spectroscopy (GTRS) applies the temperature gradients utilized in
differential scanning calorimetry to Raman spectroscopy. GTRS can identify and differentiate specific
carbon chain sites, finally allowing Raman analysis to explain why the long-chain polyunsaturated
fatty acids (LC-PUFA) exhibit such extreme functional differences despite minimal changes in
chemical structure. Detailed vibrational analysis of the important frequency ranges 1450 - 1200 cm 1
(includes CH2 bending and twisting) and 1750 - 1425 cm 1 (includes C=C stretching and C-C stretching
plus H-C in-plane rocking) shows for the first time that each molecule has its own characteristic set of
modes with only some redundancy/commonality. The number and frequency of modes correlates with
three-dimensional molecular structure, not the degree of unsaturation. The high degree of specificity of
lipoxygenase and cyclooxygenase enzymes should be reconsidered in light of the fact that individual sites
on the polyunsaturated fatty acid chain are nonequivalent, and each long-chain polyunsaturated fatty acid
(LC-PUFA) molecule has an individual, specific three dimensional structure incorporating torsion.”
[Emphasis added]
“ Herein we present a detailed, comprehensive vibrational analysis of six fatty acids with 1, 2, 3, 4, 5, and
6 double bonds (OA, LA, alpha-linolenic acid (ALA, 18:3n-3), AA, N-3DPA, and DHA. With the
improved GTRS spectroscopic technique, second derivatives can be utilized to resolve and identify
vibrational modes which previously were not completely assigned. We show that individual sites on the
LC-PUFA chain are nonequivalent although they are technically identical moieties.”
This is more data than required here, but it should be mentioned, Broadhurst et al. utilizes the “3D
energy-minimized structure” as did Crawford et al. This fact is illustrated in their figure 3 and at a more
definitive level in figure 4 using Fisher Projections. This is not the configuration believed to be used in the
bilayer of the neural lemma (Section 2.2.1 & Section 2.2.2.7). The discussion of symmetry and redundancy
surrounding their figure 5 only applies to the 3D energy-minimized configuration (see caption of fig. 5). This
discussion and the relevant experiments need to be repeated for the linearized configuration. Further useful
information may be found in the list of references. The temperature limits for DHA listed in Reference 3 might
not apply when DHA is incorporated in a liquid crystal.
See Section 2.2.3.4.4 for a tabulation of the Broadhurst samples.
The work of Broadhurst & colleagues suffers form a lack of any detailed model of the nature of the bilayer
59Lewis, J. & Wilkins, R. (1960) Modern Coordination Chemistry. NY: Interscience Publishers page 387
60Broadhurst, C. Schmidt, W. Nguyen, J. et al.(2018) Gradient Temperature Raman Spectroscopy of Fatty Acids
with One to Six Double Bonds Identifies Specific Carbons and Provides Systematic Three Dimensional
Structures J Biophys Chem vol 9, pp 1-14. https://doi.org/10.4236/jbpc.2018.91001
48 Neurons & the Nervous System
lemma of the neuron, that appears to be a goal of their paper. In the absence of any detailed model, their paper
can only be considered basic research and not applied research.
2.1.4.7.8 Expanded properties of DHA –Crawford, 2020
Crawford et al. continued their fascination with DHA in their opening thought,
“One of the great unanswered biological questions is the absolute necessity of the polyunsaturated
lipid docosahexaenoic acid (DHA; 22:6n-3) in retinal and neural tissues? Everything from the
simple eye spot of dinoflagellates to cephalopods to every class of vertebrates uses DHA, yet it is
abundant only in cold water marine food chains.”
The answer to their question appears to be at hand in the Electrolytic Theory of the Neuron. ETN. And their
paper contributes to this understanding.
2.1.4.8 Apparatus for creating & evaluating bilayer lemma
The apparatus described in this section are rarely familiar to physiologists. However, they are well known to
investigators in their specific fields.
2.1.4.8.1 Creating symmetrical & asymmetrical membranes
Quinn (Section 2.3) has discussed the creation of arbitrary bilayer membranes. His generic method is illustrated
in Figure 2.1.4-17. A Langmuir trough can be modified by introducing a septum down the middle of the
trough. Once identical or different phospholipids have been allowed to self assemble into known monolayers on
each side of the septum, the septum can be lowered into the trough. As the septum is lowered, a bilayer
membrane is formed across the orific of the septum. The physical characteristics of the membranes are quite
similar to membranes of biology as documented by Quinn in Section 2.1.4.4 The notable exception is the range
of resistivities encountered. This is undoubtedly due to inadequate labeling of the phospholipids employed as
discussed in Section 2.1.4.5.
Figure 2.1.4-17 Schematic of a method for producing asymmetrical lipid bilayers.
It may be useful to combine the schematic with certain aspects of the Langmuir
trough to insure each film is in fact monomolecular. See text. From Quinn, 1976.
The Neuron 2- 49
2.1.4.8.2 The Langmuir trough– –lipid strength & thickness
Robinson has discussed the test apparatus used to evaluate synthetic organic films61. He describes an apparatus
known as the Langmuir trough and accompanies it with a stylized force-area diagram showing how multiple
molecular layer films can be identified and evaluated. He accompanies the figure by a table comparing the
parameters of biological bilayer membranes and artificial bilayer membranes without describing either in detail.
His values typically represent a range in each category. In general, the ranges of his biological bilayers suggest
they represent a range of different bilayer materials rather than statistical ranges associated with a single
molecular type. Robinson does not provide a temperature for his data. However, he does note, “Inclusions in
artificial bilayers can move laterally in the plane of the membrane; most of us will have observed this
phenomenon in bubbles. Cooling the membranes prevents this movement, the lipid structure becomes rigid
(freezes) over a narrow temperature range.” This quotation reflects the conventional wisdom of the 1970's. As
discussed above, this quotation needs to be rewritten to include gel, liquid crystalline, and liquid states of matter.
The rest of his paper is similarly dated.
Ziblat, et al62. have provided more recent data using a more sophisticated Langmuir trough approach to bilayer
formation than that suggested above. Their main focus after membrane fabrication was grazing angle X-ray
crystallography (Section 2.1.4.7.7)
2.1.4.8.3 Scanning calorimetry–evaluating TC in lipid chains-Quinn,1976
Attempting to isolate specific forms of a phospholipid molecule from biological sources is a complex, and
difficult, experimental challenge. A technique known as “differential scanning calorimetry” has been used to
determine the difference in transition temperature, TC, between different phospholipids (and different states of
matter related to a specific phospholipid.
Quinn provides useful data on the critical temperature, TC, of various phospholipids, including those with
different levels of unsaturation in Figure 2.1.4-18. Quinn only discussed frames a and b after citing his source
as Philllips et al63. He transposed frames c and d totally omitted frame e showing the response of a mixture of
1–stearoyl-2--elaidoyl.. Elaidic acid, IUPAC name (E)-octadec-9-enoic acid, exhibits one trans–double bond
between C9 & C10. Unfortunately, the investigations suffer from two shortcomings; The work of Phillips et al.
was very early exploratory and lacked any signs of statistical precision. Second, Quinn retraced the data of
Phillips et al. free-hand and significantly changed the baseline level of each of the frames in Figure 2 of Phillips
et al. The major peak near 0C went off scale in each frame of the original figure.
No recognizable trend can be perceived from this figure. Without more statistically relevant data, few
conclusions can be drawn from these investigations, particularly in comparing frames a, b and d.
Quinn64 also provided a simpler figure 2.5, showing the orderly change in temperature of the transition point as
the number of carbons in the 1,2–diacylphosphatidylcholines dispersed in an equal mass of water (not
necessarily a relevant condition for material formed into a bilayer). No laboratory temperature can be specified
for these measurements as the temperature is the independent variable in the measurements.
61Robinson, G. (1975) Principles of Membrane Structure In Parsons, D. ed. Biological Membranes:Twelve
Essays on their Organization, Properties and Function. Oxford: Clarendon Press
62Ziblat, R. Leiserowitz, L. Addadi, L. (2010) Crystalline Domain Structure and Cholesterol Crystal Nucleation
in Single Hydrated DPPC:Cholesterol:POPC Bilayers JACS vol 132, pp 9920-9927
63Phillips, M. Hauser, H. & Paltauf, F. (1972) The inter- and intra-molecular mixing of hydrocarbon chains in
lecithin/water systems Chem Phys Lipids vol 8, pp 127-133
64Quinn, P. (1976) The Molecular Biology of Cell Membranes. Baltimore, MD: University Park Press Chapter
2
50 Neurons & the Nervous System
Quinn also provided his interpretation of the difference between two bilayer cases in Figure 2.1.4-19. The work
during that period was based on soaps and not lemma.
Figure 2.1.4-18 Differences between different levels of unsaturation in PC
measured by differential scanning calorimetry. Graphs were truncated in original
figure. Note frame a contains one double bond in each lipid. Frame b contains
no double bonds. Frame c contains one double bond in only one lipid. Frame d
An equimolar mix of distearoylPC and dioleoylPC. The left end of the two lipids
shown in insets should not be shown ending at the same vertical line. See text.
From Quinn,1976.
The Neuron 2- 51
Figure 2.1.4-19 Diagrammatic representation of the structure of two phospholipid
bilayers. a; crystal phase, b; liquid crystal phase. Circles represent phospholipid
polar groups and lines indicate the hydrocarbon chains. From Quinn, 1976,
credited to Luzzati & Tardieu, 1974.
Blume (Chapter 3 in Hidalgo) has provided additional data on calorimetry applied to several additional
phospholipid membranes. The material includes both pedagogy associated with the technique and also useful
results. Unfortunately, Blume does not define his many acronyms in one place so careful reading is required just
to identify his phospholipids. The data is more extensive and precise than that of Quinn. His material related to
the gel phase of the phospholipids is separated from that for the liquid crystalline phase.
2.1.4.8.4 2H & 13C spectroscopy
Blume (Chapter 2 in Hidalgo) has provided a discussion of both 13C and 2H NMR spectroscopy and noted,
“Besides phospholipid bilayers consisting of only a single species, the study of mixed systems is particularly
fruitful as the different components of the mixed membrane can be observed separately since only one of the
different species can be labeled by 13C or 2H at a time.
Preparing reliable samples of asymmetrical phospholipids appears to be a laborious undertaking with the purity
needed being a criteria. After quantifying the number of double bonds along one of the lipid chains, it is then
necessary to prepare adequately mixed quantities of the asymmetrical and similar symmetrical phospholipids in
order to determine the resistivity of the mix. The change in resistivity can be much larger than the change in
double bond density.
2.1.4.8.5 Low-Temperature 2H NMR Spectroscopy of Phospholipid Bilayers- Barry, 1991
Barry et al65. reported on an extensive study, including the hysteresis in the state change, of phospholipids.
They note in their Summary,
“When compared to the phase transition temperatures of the corresponding disaturated
phosphatidylcholines, the presence of docosahexaenoic acid (22:6) was found to (1) significantly
decrease the main phase transition temperatures; (2) cause a substantial hysteresis between the warming
and cooling transition temperatures; and (3) remove the approximately linear dependence of the
transition temperature on chain length.”
“To test the applicability of reduced temperature for normalizing the moment data with respect to
temperature, an alternate empirical method was used in which the lipids were compared by examining the
order in the La and gel phases at the phase transition temperature. For the lipids in this study, a
65Barry, J. Trouard, T. Salmon, A. & Brown, M. (1991) Low-Temperature 2HNMR Spectroscopy of
Phospholipid Bilayers Containing Docosahexaenoyl (22:63 ) Chains Biochem vol 30(34), pp 8386-8394
52 Neurons & the Nervous System
Figure 2.1.4-20 “The first moment (M,)of
the 2H NMR spectra for the
(pr-2H-n:0)(226)PC and di(per-2H-n:0) PC
series plotted on a reduced temperature
scale . Decreasing temperature (open
symbols) and increasing temperature
( f i l l e d s y m b o l s ) f o r t h e
(per~2H-n:0)(22:6)PC series (circles) and
di(per-2H-n:O)PC series (triangles). The
number of carbons (n) in the saturated
(n:0) acyl chain is (a) 12, (b) 14, (c) 16, or
(d) 18. The reduced temperature is
defined as (T - Tm)/Tm. From Barry et al.,
1991.
comparison of these two methods of normalization suggested that any residual effects of temperature left
by the reduced temperature method were insignificant when the effects of acyl chain length and
docosahexaenoic acid substitution on bilayer order were evaluated. The simple empirical method
described here to remove the effects of temperature can also be applied to comparative studies of other
lipid systems close to a phase transition, as a prudent check on the applicability of reduced temperature
for the system or systems being studied.”
Figure 2.1.4-20 shows their fig. 8, showing the hysteresis as a function of number of carbons.
2.1.4.8.6 X-ray crystallography
Ziblat et al. have explored the properties of a
variety of synthetic membranes and their
association with cholesterol. They presented
considerable data. However, it is ot totally clear
how much would relate directly to natural
membranes, because of the number of individual
interactions between adjacent molecules in various
states of matter and larger ensembles.
2.1.4.8.7 X-Ray crystallography and
DHA-Lor, 2015
Lor and Hirst66 have recently provided data on
DHA under an expanded name, DHA-PE, but also
identified the other lipid. Thus suggesting even a
more specific identifier, palmitoyl, DHA-PE, or
(16.0)(22.6)PE, indicating palmitic acid occupying
sn-1, DHA occupying sn-2 and ethanolamine as
the amino acid occupying sn-2, both attached to
the phosphate group of PE via the glycerol group.
Their specific interest was in binary mixtures of
diPALM-PE, (22.6)(22.6)PE, and (16.0)(22.6)PE
at low concentrations, below 5mol%, according to
the nomenclature in Huber et al.
Their Abstract concludes, using this new
terminology,
“Our results show that PALM, DHA-PE
induces phase separation into a DHA rich
liquid crystalline (L(α)) phase and a DHA
poor gel (L(β’) ) phase at overall PALM,
DHA-PE concentrations as low as 0.1 mol%.
In addition, we find that the structure of the
L(β’) phase, from which the PALM, DHA-PE
molecules are largely excluded, is modified in
the phase-separated state at low PALM,
DHA-PE concentrations, with a decrease in
bilayer thickness of 1.34 nm for 0.1 mol% at
room temperature, compared to pure DPPC
bilayers. This result is contrary to that seen in
similar studies on mono-unsaturated lipids
where an increase in bilayer thickness is
observed. The surprising effect of such low
PALM, DHA-PE concentrations on membrane structure may be important in understanding the role of
66 Lor, C. & Hirst, L. (2015) Effects of Low Concentrations of Docosahexaenoic Acid on the Structure and
Phase Behavior of Model Lipid Membranes Membranes vol 5, pp 857-874 doi:10.3390/membranes5040857
The Neuron 2- 53
Figure 2.1.4-21 Structural models of diPALM-PC & PALM, DHA-PE used in Martin
et al. paper. A; diPALM-PC (a.k.a. DPPC), note the three CH3 groups attached to
the N+, B; PALM, DHA-PE. From Lor & Hirst, 2015.
highly polyunsaturated lipids in biological membrane-based structures and similar artificial surfactant
systems.”
Additional assertion in the paper include,
“Certain classes of biological cells contain high concentrations of polyunsaturated lipids in the
membrane. For example, DHA-lipids are particularly enriched in the synapses of neural membranes and
in the rod-cell outer segment in the retina (Martin et al.). In these special cases, the amount of DHA
present can approach almost 50% of the total membrane fatty acids and di-DHA phospholipids are
present [2 ref.]; in which both phospholipid chains on the same molecule have the characteristic 22:6
(ω3) DHA composition (alkyl chains 22 carbons long with 6 unsaturated bonds). DHA-lipid levels in
other biological membranes can vary and are typically about 5%.”
“Despite significant nutritional and biomedical research, the fundamental physical significance of DHA-
lipids in the plasma membrane and their interactions with other membrane lipids are still not fully
understood.”
“This article presents a detailed look at the low concentration regime of 1-palmitoyl-2-docohexaenoyl-sn-
glycero-3-phosphoethanolamine (PALM,DHA-PE) in the PALM, DHA-PE/DPPC binary system using
X-ray diffraction.” “In this work we focus on the lower concentration limit of DHA membrane content
and the effects of this molecule on membrane phase behavior in this regime.
“In general, DHA is a challenging lipid molecule to work with due to its high susceptibility to
peroxidation. DHA has a total of 6 double bonds that lie in between methylene bridges, therefore the
hydrogens [holes, editor] in the fatty acid chain are very reactive. Free radicals in the environment can
strip these hydrogens from the lipid thus turning that particular region into a radical itself until it becomes
stable.”
“DHA-lipids are extremely prevalent in biological systems; however their interactions with membrane
lipids, in the dynamic cell are not well understood.
Their structural models of diPALM-PE and PALM, DHA-PE, figure 1, reproduced as Figure 2.1.4-21 are quite
similar to those in frame B in Section2.1.4.7.8
Their figure 2 suggests a significant change in the binary configuration with temperature effecting warm-
blooded mammals and room temperature laboratories, Figure 2.1.4-22 . Usually a discontinuity encountered
with temperature, in 2H NMR spectroscopy implies a change of state in a sample under test.
The result of these temperature measurements is a significant change of state for temperatures above 30 C for
DPPC/DHA-PE. IT CAN BE ASSUMED , THE LIQUID CRYSTALLINE STATE IS ONLY ACHIEVED
54 Neurons & the Nervous System
FOR TEMPERATURES ABOVE THIS VALUE FOR ANY PC OR PE CONTAINING DHA IN THE
PAPERS DISCUSSED IN SECTIONS 2.1.4.7 & 2.1.4.8 UNTIL SHOWN OTHERWISE.
The Neuron 2- 55
Figure 2.1.4-22 “Transmission solution small angle X-ray scattering (SAXS) data
for DPPC/DHA-PE mixed with DHA-PE 0.1 mol%. At 25 °C, phase coexistence can
be observed as two sets of Bragg peaks are present. The first order peaks for
each phase are indicated by arrow 1 (fluid phase—Lα ) and arrow 2 (gel
phase—Lβ ).” From Lor & Hirst, 2015
Neither Lor & Hirst, or the following paper by Martin et al., included any figure relating to the physical neuron
they were discussing. This is particularly important in the Martin et al. paper where they are discussing various
parts of the outer segment of a photoreceptor as well as the protein, opsin.
Martin et al67. wrote a paper at the conceptual level containing some mumerics. Their purpose was stated as,
“In recent years, detergent-resistant membranes (DRMs) have been isolated in in-vitro models of lipid
rafts, from photoreceptor outer segments (ROS), and the localization of a specific complement of
photoreceptor proteins has been demonstrated. However, surprisingly little is known about the lipid
composition of these important membrane domains. The present study provides the first characterization
of phospholipids and fatty acids from ROS-derived DRMs."
67
Martin, R. Elliott, M. Brush, R. & Anderson, R. (2005) Detailed Characterization of the Lipid Composition
of Detergent-Resistant Membranes from Photoreceptor Rod Outer Segment Membranes (Invest Ophthalmol
Vis Sci. vol46, pp1147–1154 DOI:10.1167/iovs.04-1207
56 Neurons & the Nervous System
Figure 2.1.4-23 Electron micrograph of the photoreceptor and nuclear laminates
of the bullfrog. Chosen for clarity and believed similar to that of all chordates,
including human. The labeling of rods and cones is not supported in this work;
all of the Outer Segments of photoreceptors are cylindrical. From Steinberg
(1973 ).
The focus on rafts in the above paragraph calls out for a graphic model, there are no micrographs that would
explain where these purported rafts would be found. Figure 2.1.4-23 shows a typical group of photoreceptors
of a bullfrog. The limited resolution of the micrograph does not identify any outer membrane surrounding an
individual disk stack.
If the rafts (or DRM) are integral to the ROS components, they might qualify as type 2 or type 3 lemma/
(Section 2.1.4.1)
LorMartin et al. make a series of assertions,
The Neuron 2- 57
“Klausner et al. were among the first to recognize the significance of lipid microdomains within the cell
membrane. One type of membrane domain is characteristically insoluble in cold Triton X-100 and can be
isolated by flotation on sucrose density gradients. These preparations are perhaps more appropriately
called detergent-resistant membranes (DRMs), but Brown and Rose (1992) were the first to call them
“lipid rafts.”
“ Many significant biological activities are ascribed to the DRM micro-domain, but there is still much debate regarding
their relevance, or even existence, in living cells..”
“Twenty-five years ago, Andrews and Cohen observed membrane micro-domains in amphibian and
rodent photoreceptors, which they termed “particle-free patches” (PFPs).”
“We also determined the fatty acid profiles of individual lipid classes separated by HPTLC (Fig. 5). As
shown in Figure 2, phosphatidyl choline,PC. was resolved into three spots: PC1, -2, and -3. The PC1 spot
of DRMs had only trace amounts of polyunsaturated fatty acids, PUFA, (<2% 18:1n-9, 10% 18:0), and
the remainder was 16:0 (87%). With the exception of 8% more 18:1n-9 and 4% more 18:0 (14%), the
PC1 of ROS was little different from DRMs. The principal n-3 fatty acid of the retina, 22:6n-3, was the
same in phosphatidyl ethanolamine, PE, of ROS and DRMs (34%–36%), but was relatively enriched in
ROS over DRMs in all other lipid classes. Posphatidyl serine, PS, and PC3 of ROS contained 34% and
59% more 22:6n-3 than DRMs, respectively. The PC2 of ROS also appeared to have more 22:6n-3 than
DRMs, but this difference was not significant.” [See Section 2.2.3.4.4 for codes of different PUFAs]
Martin et al. did present several statistically precise histograms of the contents of different PUFAs under
different conditions.
“All data are expressed as the mean +/- SD (n =3). Multivariate analysis of variance with post hoc
Newman-Keuls tests determined significant differences between ROS and DRMs (P < 0.05).
“Three independent [bovine] retina homogenates containing 18 to 29 fresh retinas were used to generate
the ROS fractions.”
Figure 6 shows a HPLTC showing Opsin as a separate entity of 33 kiloDaltons. The paper notes the rarity of
opsin within the DRM.
2.1.4.9 Evaluating the individual lemma found in neurons
The first task under this heading is to select the most effective class of neurons. The stage 2 signal processing
and stage 4 information extraction neurons as a group are by far the dominant form of neuron in the neural
system. The signal processing neurons of the retina are reasonably easy to isolate. Figure 2.1.4-15, reproduced
from Section 3.2.3.5 from “Processes in Biological Vision”, suggests the ease of physically isolating the signal
processing neurons of stage 2, prior to further chemical isolation.
58 Neurons & the Nervous System
Figure 2.1.4-24 Expanded cross section through a human retina to show circuitry.
The overlay shows the nominal bipolar circuit on the left, the nominal bistratified
midget ganglion in the middle, and the nominal horizontal circuit on the right.
The left side shows the bipolar circuit (yellow) forming the R-channel (brightness)
signal by collecting the signals from four spectrally different types of
photoreceptors (upper green axons). The analog output signal synapses with a
“parasol” ganglion neuron (lower green element) that encodes the monopolarity
sum signal into a series of Action Potentials. The middle frame shows a
frequently discussed circuit where the signals from groups of spectrally similar
PCs are relayed through the INL to a bistratified midget ganglion that has a
differential input and generates action potentials at its output. The right side
shows a horizontal neuron (yellow) with distinct ON and OFF inputs, marked plus
and minus respectively. The two axons synapsing with the plus terminal are
from photoreceptors of the same spectral type, and the two axons synapsing with
the minus terminal are from photoreceptors of a different spectral type. The
result at the pedicle of the horizontal neuron is a bipolarity signal at the pedicle
of the horizontal neuron that synapses with a “midget” ganglion neuron that
encodes the difference signal into a series of Action Potential. The middle and
right circuit configurations support formation of any of the chrominance
channels, O–, P– or Q–. See text. Micrograph from Boycott & Dowling, 1969.
The Neuron 2- 59
2.1.4.9.1 Test apparatus for evaluating whole individual neurons
Stampfi68 have described an early method of exploring the electrical performance of simple neurons, particularly
those not exhibiting an extensive poditic tree as part of a bi-stratified neuron and only a single Node of Ranvier.
They made little effort to isolate the hillock region of the neuron. In the bistratifed tree case, much greater care
is required to establish the cytological location of the Activa, within the hillock of the neuron, and to interpret
the performance related to the polarity of the dendritic and poditic trees. Stampfli recommends the method of
Nonner & Stampfli for more precise measurements. The graphs in Stampfli provide excellent early responses
for stage 3 neurons generating true action potentials.
Nonner & Stampfli69 extended the double air gap method to multiple air gaps to allow analyses of more complex
neurons incorporating one or more Nodes of Ranvier. The paper boasts of an early all-transistorized, and
chopper stabilized, feedback amplifier while still referring to a “grid current of less than 10–13 amps,” This is a
respectable uncompensated input amplifier current and may suggest use of an early Field Effect Transistor, FET.
An input impedance of 470 Megohms is also excellent. However, the input capacitance of 7pF is excessive
when you are measuring cell features exhibiting less than 5 pF. The circuit needs modification to compensate
for this level of input capacitance. It is particularly interesting that their all electronic test equipment expresses
the axon (collector) current in terms of the euphemistic sodium ion current density. They did not indicate how
they ascertained that any sodium ions flowed into or out of their neuron.
The combination of one of the multiple air gap techniques described above combined with a vintage Tektronix
Model 576 Curve Tracer can evaluate the electrolytic performance of any Activa in the neural system, whether
in a neuron, a synapse or a Node of Ranvier. All of the Activa are of the PNP bipolar junction transistor, BJT,
type. If tests are to be performed over an extended period, a flowing Ringer’s solution containing controlled
amounts of glutamic acid and CO2 should be used. Since the maximum frequency of any neuron is less than a
megahertz, simpler portable curve tracers can also be used effectively. There are a variety of videos on
YouTube demonstrating the use of the Model 576 Curve Tracer and various adapter accessories. It provides a
0.5 mV and 1 nA measurement resolutions (in magnified modes). A more modern curve tracer is the Tektronix
Model 370A. It is fully programmable and incorporates a 3.5" disc drive.
2.1.4.7.7 Concentration of DHA in the retina-Jeffrey, 2001
Jeffrey et al70., while interpreting their data using the chemical theory of the neuron (including the concept of
rods & cones) and an archaic figure 1, may provide useful data related to the mammalian retina,
“DHA is particularly concentrated within the disk membranes of the receptor outer segment, ROS, where
it accounts for up to 30% of total fatty acids and 54% of phosphatidylethanolamine (PE) fatty acids (4
references). The retina is unique in that it contains phospholipids with polyunsaturates at both the sn-1
and sn-2 positions (dipolyenes). In the monkey, dipolyenes with long-chain polyunsaturated fatty acids
(LC-PUFA) in both the sn-1 and sn-2 positions constitute 16% of the diacyl ethanolamine
phosphoglycerides, and 15% of these have DHA in both positions (Lin et al., 1994).”
2.1.4.7.7 Percent content of DHA in neural tissue
Lin et al. and Bazan et al. have written extensively on the percent of DHA in the brain.
68Stampfli, R. (1969) Dissection of single nerve fibres and measurement of membrane potential changes of
Ranvier Nodes by means of the double air gap method In Passow, H. & Stampfli, R. eds, Laboratory
Techniques in Membrane Biophysics. NY: Springer pp 157-166
69Nonner, W. & Stampfli, R. (1969) A new voltage clamp method In Passow, H. & Stampfli, R. eds, Laboratory
Techniques in Membrane Biophysics. NY: Springer pp 171-175
70Jeffrey, B. Weisinger, H. Neuringer, M. & Mitchell, D. (2001) The Role of Docosahexaenoic Acid in Retinal
Function Lipids vol 36(9), pp 859-871
60 Neurons & the Nervous System
The Lin et al71. source provides considerable data. Their Purpose was,
“To characterize the molecular species composition of ethanolamine glycerophospholipids (EGP) in the primate
retina and to examine the effects of different dietary fats, the authors fed rhesus monkeys diets containing widely
ranging amounts of n-3 fatty acids.”
On page 795, lin et al. don”t say DHA in both sn-1 and sn-2. They only say polyunsaturated fatty acid in both
positions.. Also on page 795, they assert,
“Docosahexaenoic acid [DHA, 22:6(n-3)] is the major polyunsaturated fatty acid of retinal lipids and is
preferentially taken up by photoreceptor cells.10 This fatty acid is most concentrated in the ethanolamine
and serine glycerophospholipids but is also present in the choline and inositol glycerophospholipids. No
previous data are available on the phospholipid molecular species composition of the primate retina.”
Because of their gross approach to the retina, and the lack of a model of the photoreceptors (Section4.3.1 of
“Processes in Biological Vision”), PBV, they are unable to assign these glycerophospholipids to particular
functions within the photoreceptors, Figure 2.1.4-25 reproduced from Section 4.3.2 of PBV . These
glycerophospholipids also play substantive roles in the olfactory modality (Section 8.6.2.9).
71 Lin, D. Anderson, G. Connor, W. & Neuringer, M. (1994) Effect of Dietary N-3 Fatty Acids Upon the
Phospholipid Molecular Species of the Monkey Retina Invest Ophthalmol Vis Sci vol 35, pp 794-803
The Neuron 2- 61
Figure 2.1.4-25 An exploded view of the baseline photoreceptor cell
configuration. An RPE cell is shown at upper right. The central image is the
extracellular Outer Segment, i.e., the disc stack immersed in the IPM
(foreshortened for convenience). The typical disc stack consists of 2000 discs,
formed into a “spaceframe” structure and immersed in the IPM. The lower left
shows all of the neural elements of the photoreceptor cell as a group (including
both the distal and proximal axon segments). The distribution Activa is shown
explicitly. The microtubules relate to the Activa associated with the adaptation
amplifiers. The adaptation amplifier Activa cannot be shown at this scale. The
lower right image shows all of the glandular portion of the photoreceptor cell
(exemplified by the inner segment) as well as the other housekeeping functions
(exemplified by the nucleus).
62 Neurons & the Nervous System
Their Results are,
“. Twenty-eight molecular species were identified in the retina of control monkeys. Ether phospholipids
comprised 36% of the retinal ethanolamine glycerophospholipids. Species containing polyunsaturated
fatty acids in both the sn-1 and sn-2 positions (dipolyenes) were present only in the diacyl subclass and
comprised 16% of the total species. Species having n-3 fatty acids in the sn-2 position contributed 59%,
36%, and 70% of total species in the diacyl, alkeny-lacyl, and alkylacyl subclasses, respectively. In the
molecular species of the n-3 fatty acid deficient monkeys, the major change was the loss of most of the
18:0-22:6(n-3) species and its partial replacement with 18:0-22:5(n-6). In contrast, the species
18:l-22:6(n-3) decreased only slightly, from 6.2% to 4.8% of total diacyl species. Although the total
concentration of dipolyenes (15% to 20% of the total species) was not affected by diet, their fatty acid
compositions were changed drastically. The dipolyene species 22:6(n-3)-22:6(n-3) nearly disappeared in
the n-3 deficient monkeys. Concomitantly, two new species, 22:5(n-6)-22:6(n-3) and 2:5(n-6)-22:5(n-6),
appeared at 2.6% and 2.0%, respectively. Deficient monkeys given the ethyl ester of 22:6(n-3) in the diet
recovered to a near-normal molecular species composition, except in the ether lipids, in which 16:0-20:4
remained low.”
Bazan and colleagues have also written extensively on DHA in the context of the brain, the retina as well as
other tissue. (2003-2011). Search "NG Bazan". Most of his work has been on biological methods to protect
DHA
.
Niemoller & Bazan72 have written,
“Omega-3 fatty acids have beneficial effects for vision, brain function, cardiovascular function, and
immune-inflammatory responses. Docosahexaenoic acid [DHA; 22:6(n-3)], the most abundant essential
omega-3 fatty acid in the human body, is selectively enriched and avidly retained in the central nervous
system as an acyl chain of phospholipids. Brain-ischemia reperfusion and seizures trigger rapid release of
DHA and of arachidonic acid (AA) as free, unesterified fatty acids. AA in turn generates eicosanoids,
and DHA forms docosanoids.”
“Omega-3 essential fatty acid family members, DHA (22:6, n-3)] and linolenic acid (18:3, n-3) after
dietary intake, are actively incorporated in the liver prior to distribution to various organs. Then linolenic
acid is elongated and desaturated by liver hepatocytes to DHA, which in turn is activated (22:6-CoA) and
acylated into phospholipids and eventually released as lipoproteins into the bloodstream. DHA accretion
in the CNS after liver release correlates with photoreceptor membrane biogenesis and synaptogenesis
during the postnatal development. DHA is involved in aging, memory formation, synaptic membrane
function, photoreceptor biogenesis and function, and neuroprotection. Epidemiologic studies indicate that
diets enriched with DHA are associated with reduced risk of cognitive impairment]. Certain diets, such as
those of vegans, vegetarians, and the elderly, contain relatively low DHA]. While low dietary DHA leads
to progressive loss of DHA in the CNS, both the brain and retina display a striking ability to retain and
actively conserve DHA even after prolonged omega-3 fatty acid dietary deficiencies]. Extended
deficiencies result in decreased amounts of DHA in neuronal membranes, altering membrane fluidity and
signaling properties].”
“A membrane phospholipid containing a docosahexanoyl chain of sn-2 is hydrolyzed by a phospholipase
A2 generating a free (unesterified) DHA.”
“In the nervous system, DHA accumulates as an acyl chain in the aminophospholipids, phosphatidyl
ethanolamine, and phosphatidyl serine (PS).”
“Phosphatidyl serine, which is rich in DHA, increases the translocation/activation of Akt, but DHA's
action/s downstream messengers of the Akt cascade are NOT well defined.”
Akt is a title mainly used in genetics [Wikipedia]. The name Akt does not refer to its function. The "Ak" in Akt
refers to the AKR mouse strain that develops spontaneous thymic lymphomas. The "t" stands for 'thymoma'; the
letter was added when a transforming retrovirus was isolated from the Ak mouse strain, which was termed
72Niemoller, T. & Bazan, N. (2010) Docosahexaenoic Acid Neurolipidomics Prostaglandins Other Lipid
Mediat vol 91(3-4), pp 85–89
The Neuron 2- 63
"Akt-8". Protein kinase B (PKB), also known as Akt, is the collective name of a set of three
serine/threonine-specific protein kinases that play key roles in multiple cellular processes such as glucose
metabolism, apoptosis, cell proliferation, transcription, and cell migration.
Their Conclusion, in its entirety, was,
“Diets of differing n-3 fatty acid content had profound qualitative and quantitative effects on the
molecular species of retinal phospholipids, and the replacement of 22:6(n-3) by 22:5(n-6) in the retinas
of n-3 deficient monkeys was asymmetric and functionally incomplete.”
Bazan73 has also co-authored a paper on the role of DHA in ageing.
Svennerholm74, who provides large tables by age and gender, notes,
“Phosphatidyl serine (PS) is the major acidic phospholipid class that accounts for 13–15% of the
phospholipids in the human cerebral cortex.”
He does include or even define DHA in his early work in PtdSer.
The task of determining the amount of DHA in the type 2 lemma that might be the source of the lemma’s high
conductivity in the light of too much data in Section 2.1.4.7, is awkward. The authors found there do not
describe their concept of a neuron either graphically, or in text. The name of long chain lipids are not
specified in a name, such as “phosphatidyl serine”, by nutritionists. It may require more research in this
area. LipidWeb 75 says,
“Analysis of phosphatidyl ethanolamine and related lipids is straightforward, as they are readily isolated
by thin-layer or high-performance liquid chromatography methods for further analysis, for example by
modern mass spectrometric methods. Analysis of phosphatidyl ethanolamine adducts is much more
challenging.”
These are indirect methods and require significant experience to read them precisely. Lipidweb. org also notes,
“The O-alkyl and O-alkenyl groups at the sn-1 position of the analogous ether lipids generally have 16:0,
18:0 or 18:1 chains, whereas arachidonic and docosahexaenoic acids are the most abundant components
at the sn-2 position.”
The credentials of LipidWeb follow,
“ My personal interests in lipid science are represented in these pages, which began life in 1999. In this
website, the various topics are updated on almost a daily basis as new information becomes available -
one of the virtues of the web as opposed to more formal publications. The downside is that there is no
peer review, and I am always grateful when errors, inconsistencies or omissions are drawn to my
attention.
The LipidWeb was created by William (Bill) W. Christie and is maintained by LipidMaps”
The LipidMaps.org is run by a consortium of universities and supported by the Welcome Trust. It has a large
database, the Lipid Maps Structured Database, LMSD
73Walter, L. & Bazan, N. (2008) Docosahexaenoic Acid and the Aging Brain J Nutrition vol 138(12), pp
2510-2514 https://doi.org/10.3945/jn.108.096016
74Svennerholm, L. (1968) Distribution and fatty acid composition of phosphoglycerides in normal human brain
J LIPID RESEARCH vol 9, pp 570-579
75LipidWeb (Christie, W. online)
www.lipidmaps.org/resources/lipidweb/lipidweb_html/lipids/complex/pe/index.htm
64 Neurons & the Nervous System
Lipid Category Curated Computationally-generated All
Fatty Acyls [FA] 8794 1878 10672
Glycerolipids [GL] 355 7379 7734
Glycerophospholipids [GP] 1763 8328 10091
Sphingolipids [SP] 1809 3168 4977
Sterol Lipids [ST] 3777 0 3777
Prenol Lipids [PR] 2674 0 2674
Saccharolipids [SL] 51 1294 1345
Polyketides [PK] 7164 0 7164
TOTAL ` 26387 22047 48434
Number of structures per lipid category
The Glycerophospholipids are further broken down into numerous classifications (Browse Classification Tab &
click on + signs to expand a classification). As of October,2023, the Glycerophosphoethanolamines [GP02]
does not appear to contain any name incorporating docosahexaenoic acid, DHA, or Arachidonic acid, ARA.
According to Lin et al. (1994),
“Docosahexaenoic acid [DHA, 22:6(n-3)] is the major polyunsaturated fatty acid of retinal lipids and is
preferentially taken up by photoreceptor cells. This fatty acid is most concentrated in the ethanolamine
and serine glycerophospholipids but is also present in the choline and inositol glycerophospholipids. No
previous data are available on the phospholipid molecular species composition of the primate retina.”
The Neuron 2- 65
Figure 2.1.4-26 “The metabolic pathway of conversion of α-linolenic acid to DHA
showing the enzymes involved. The details are provided in the original text.
From Calder, 2016.
66 Neurons & the Nervous System
Figure 2.1.4-27 shows the complexity of the phospholipids. The figure shows dual palmitic acid as the fatty
acids in both sn-1 and sn-2.
The Neuron 2- 67
Figure 2.1.4-27 Phosphoglycerides, before condensation with the suffix to form
a phosphotidyl(suffix amino acid). The phosphoglyceride is formed of three
components, a, b & c. LEFT: a; the basic glyceride, b; the basic polar group, c;
the general formula, with X being an amino acid, FA being fatty acids. As
indicated. the fatty acid in column, sn-1, is usually saturated and that in sn-2 is
usually unsaturated--to a degree. On the RIGHT is shown a typical
phosphoglyceride as shown on the left after condensation (except for
condensation with the amino acid labeled X). The typical phosphoglyceride is
shown with dual palmitic acids as the fatty acids. From Weissmann, 1975.
68 Neurons & the Nervous System
Figure 2.1.4-28 Full name of phosphatidyl ethanolamine according to LipidWeb.
It is important to note the two double bonds of octadecadienoyl are not
conjugated. The two double bonds are separated by a CH2 group. The distance
between the CH2 groups separate by a double bond is 3.01 Angstrom. The
distance two adjacent CH2 groups is 1.27 Angstrom and the angle between the
single bonds of an isolated CH2 is 111 degrees. From Christie, 2023, LipidWeb.
The actual chemical occupants of sn-1 and sn-2 are the subject of interest here. Historically, the neural
community has considered the inner bilayer of the external lemma to be phosphatidyl ethanolamine and the outer
bilayer to be phosphatidyl choline (without providing much information concerning the contents of sn-1 and sn-
2 according to the Lipid WEB, “Phosphatidylethanolamine or 1,2-diacyl-sn-glycero-3-phosphoethanolamine
(once given the trivial name 'cephalin') is usually the second most abundant phospholipid in animal and plant
lipids, after phosphatidylcholine, and it is frequently the main lipid component of microbial membranes.” The
term “diacyl” refers to two unspecified fatty acids.
The above discussion by the nutritionists have taken a CONTRARY VIEW. They specify the contents of sn-2
as DHA at least since the 1980's and assert this molecule is the dominant fatty acid in the mammalian and human
brain.
Figure 2.1.4-28 shows the full name of phosphatidyl ethanolamine according to LipidWeb. Note
spelling of top label (phospha- - -) and blue label (phospho - - -).
The dimensions between atoms of the lipid chains are taken from Section 2.2.1.3.3.
The Neuron 2- 69
Figure 2.1.4-29 Comparison between PtdEth, or EPG, of two schools,
neuroscience and nutrition. A; PtdEth according to LipidWeb, associated with
the neuroscience school. B; PtdEth according to the nutrition community. The
molecule is more completely described as PALM, DHA-PE. The sn-2 (lower
branch in B) is a much more complex molecule with six cis-double bonds. These
double bonds, when in a liquid crystalline state may contribute to a significant
conductivity through the material. Also in B, the length of sn-2 is significantly
longer than in A, leading a overall thicker type 2 lemma. The axial distance
between two CH2 groups, separated by a double bond is 3.01 Angstrom. In the
absence of the double bond, the distance between two CH2 groups is 1.27
Angstrom and the angle between adjacent bonds is 111 degrees.
The saturated lipid is in stereo-specific number, sn, position sn-1 and the unsaturated lipid is in position sn-2
Novir et al76. made the following assertion.
“Notwithstanding considerable similarities between DHA/DPA/EPA, 22–22-20 carbons and 6–5-5
double bonds respectively, DHA is the most important one. It forms almost 97 of the omega-3 fatty acid
in the brain and about 93% of the total omega-3 fatty acid in the retina. Also, DHA constitutes around
half of the neuronal membranes.”
2.1.4.7.8 Comparison between PtdEth of the two schools
The two schools of neuroscience and nutrition have greatly different view concerning the lipids associated with
phosphatidyl ethanolamine, PtdEth (also known as ethanolamine glycerophospholipids, EGP.) Figure 2.1.4-29
illustrates these differences.
The dimensions between atoms of the lipid chains are taken from Section 2.2.1.3.3.
76Novir, S. Tirandaz, A. & Lotfipour, H. (2021) Quantum study of DHA, DPA and EPA anticancer fatty acids
for microscopic explanation of their biological functions J Mole Liquids vol 325, Article 114646
https://doi.org/10.1016/j.molliq.2020.114646
70 Neurons & the Nervous System
Based on the groups portrayed by Weissmann in Section 2.1.4.7.7, the molecular weight , etc., of the principal
players are,
Name Molecular Weight Formula # Carbon in acyl lipids Attch.
DHA 328 g/mol C22H32O2 22 sn-2
Hexadecanoyl 172 C14H28O2 14 sn-1
Polar Group 80 PO3 0 sn-3
Glycerol w/o 2 oxygens 45 C3H5O 0 frame
----
631
The loss of oxygens in glycerol is to avoid double counting after the condensation process(s).
PtdEtn when incorporating DHA, has a molecular wt. of 625 g/mol, with 53% due to DHA
In the case of a second DHA replacing the Hexadecanoyl, the phospholipid has a molecular wt. 781 g/mol with
84% due to DHA. There is no known functional role for the dual DHA version of the phospholipid.
The estimate of 50% DHA in the literature for PtdEtn compares favorably with the calculated 53% value for the
case of both bilayers of the lemma being the same. If the inner layer of the type 2 lemma employs DHA in
position sn-2, in order to achieve the high conductivity, the total presence of DHA per area of type 2 lemma
would equal 50-53% regardless of the name of the phospholipid, whether the old name for the inner bilayer is
cephalin or the most recent name PtdEtn.
2.1.4.7.9 Dry weight of a typical neuron vs types of lemma present
There are many physical variants of the neurons. It is best to discuss a fully functional neuron with a compact
physical form. It is also best to recognize the internal nucleus of a compact neuron contribute minimally to the
dry weight compared to the total weight of the lemma of the neuron . Based on these criteria, the choice leads to
a most common neuron. The stage 2 signal processing neurons, along with the stage 4 information processing
neurons and the stage 5 cognition neurons fits the specification. Many of these are spherical, with short
appendages that can be ignored initially.
The signal processing neuron tends to have spherical soma with areas dedicated to each type of lemma. The
types of lemma with higher numbers appear at multiple locations on the surface of the type 1 lemma. The type
1 lemma is generally an excellent electrical insulator. The type 2 lemma is made up of one diode, with excellent
conductivity in one direction. The type 3 lemma has the ability to move physical molecules from one fluid
environment on one side of the lemma to the other, in very small amounts per hour (Section 2.1.4.1). The
quantities are to small to support neural signaling at rates measured in hundredths of second..
The question is how much, as a percentage, of each type of lemma is present in the baseline neuron?
The ETN has identified multiple types of distinct lemma of the typical neuron while the chemical theory has not
identified any types of lemma. Section 2.2.4.4 offers a block Diagram of a typical signal processing/information
extraction neuron. The figure shows two input structures and one output structure that most certainly involve
areas of type 2 lemma. At least two additional inputs are shown on the upper part of the symbology showing the
electrolytic power supply input (shown by the symbol e) and one or more chemical modulators (relatively slow
hormone inputs) and and one common output on the bottom of the symbology serving both the electrolytic and
chemical terminals. The sum of these areas of type 2 lemma are not known. Additionally, there may be a
separate type 3 lemma area supporting additional homeostatic functions. The remainder of the external lemma
is assumed to be type 1 lemma, a nearly perfect electrical insulator and impervious to chemical penetration
(Section 2.2.4.2.1).
Lin et al. made an extensive study of this subject in monkey retina. Their Introduction asserted,
“The phospholipids of cell membranes represent a heterogeneous population of molecular species that
occur in characteristic proportions. Different molecular species have different metabolic and physical
properties and thereby influence membrane fluidity and the function and activity of membrane-bound
proteins (2 references). Analysis of the molecular species of retinal phospholipids, which gives
information about the pairing of fatty acids in membrane lipids, can provide the foundation for studies on
the biosynthesis of retinal membrane lipids and their relationship to membrane function.
The Neuron 2- 71
The phospholipid molecular species of the retinas of rainbow trout (1 ref.), frog(2 refs.), cow (2 refs.),
and rat (1 ref.) have been studied by several investigators.”
This has led investigators to only research the molecular contents of the lemma at gross Levels.. Svennerholm
investigated the lipids of the human brain in 1968 and Lin et al. investigated the lipids of the monkey brain in
1990 (although they asserted they were the first). Svennerholm reviewed the earlier work of at least 10
investigators of the human brain. Svennerholm identified 19 lipids (in Table2) and noted,
“Abbreviations: Fatty acids are deisgnated by chain length : number of double bonds; n-6 denotes that the first
double bond from the methyl group occurs after the sixth carbon atom, the methyl group being counted as number 1. EPG,
ethanolamine phosphoglycerides; SPG, serine phosphoglycerides; IPG, inositol phosphoglycerides; CPG, choline
phosphoglycerides; Sph, sphingomyelins; CC, cerebral cortex; \YM, white matter; TLC, thin layer chromatography; GLC, gas-
liquid chromatography; C, chloroform; M, methanol ; DEGS, diethylene glycol succinate polyester”
“ The most striking finding was the small individual variations found in the phospholipid distribution of
mature brain. In fetal brain, CPG constituted about 50%, EPG nearly 30%, and the remaining three
phospholipids only a little more than 20%. With increasing age the phospholipids of cerebral gray matter
underwent some changes: a decrease of CPG to 35-40%, and an increase of EPG to 35-40% and of Sph
from 5 to 10%. Otherwise there was no change. Cerebral white matter differed from gray matter by a
relatively smaller proportion of CPG (about 25%) and larger portions of SPG and Sph. EPG constituted
the same percentage as in gray matter.”
Lin et al. identified 24 lipids and noted in their Abstract,
“Fatty acids in the sn-2 position differed markedly among the diet groups, but the sn-1 position always
contained only 16:0, 18:0, or 18:1. In the diacyl subclass of the control brain, the n-3 molecular species
represented 41% of total and the n-6 species 45%, whereas in the deficient brain the n-3 molecular
species decreased to 9% and n-6 molecular species increased to 77%. The fatty acid 22:5n-6 did not
replace 22:6n-3 in a symmetrical fashion in the molecular species of the deficient brain. In the brains of
the fish oil-fed monkeys, the n-3 molecular species amounted to 61% and n-6 molecular species were
reduced to 25%. The species 18:1–22:6, 16:0–22:6, and 18:0–22:6 generally changed proportionally in
response to diet. However, 18:1–20:4, 16:0–20: 4, and 18:0–20:4 responded differently. The fish oil diet
led to an increase in the proportion of 18:1–20:4 in the alkenylacyl subclass, whereas 16:0–20:4 and
18:0–20:4 decreased. Thus, total species containing sn-1 18:1 increased at the expense of sn-1 16:0 in the
fish oil animals. Regardless of diet, each subclass of ethanolamine glycerophospholipid showed a
strikingly different ratio of sn-1 16:0 to 18:0 to 18:1 for a given sn-2 fatty acid. In conclusion, the
different diets had profound qualitative and quantitative effects on the molecular species of brain
phospholipids, and these changes have implications for possible functional changes.”
Lin et al77. proceeded to examine the monkey retina using similar techniques with similar results. They
recognized 28 molecular species of fatty acid in the control monkeys. They used the method of Folch, 1957,
with caveat described on Folch, page 498. Their Results included,
“Ether phospholipids comprised 36% of the retinal ethanolamine glycerophospholipids. Species
containing polyunsaturated fatty acids in both the sn-1 and sn-2 positions (dipolyenes) were present only
in the diacyl subclass and comprised 16% of the total species. Species having n-3 fatty
acids in the sn-2 position contributed 59%, 36%, and 70% of total species in the diacyl, alkenylacyl, and
alkylacyl subclasses, respectively. In the molecular species of the n-3 fatty acid deficient monkeys, the
major change was the loss of most of the 18:0-22:6(n-3) species and its partial replacement with
18:0-22:5(n-6). In contrast, the species 18:l-22:6(n-3) decreased only slightly, from 6.2% to 4.8% of total
diacyl species. Although the total concentration of dipolyenes (15% to 20% of the total species) was not
affected by diet, their fatty acid compositions were changed drastically. The dipolyene species
22:6(n-3)-22:6(n-3) nearly disappeared in the n-3 deficient monkeys. Concomitantly, two new species,
22:5(n-6)-22:6(n-3) and 22:5(n-6)- 22:5(n-6), appeared at 2.6% and 2.0%, respectively. Deficient
monkeys given the ethyl ester of 22:6(n-3) in the diet recovered to a near-normal molecular species
composition, except in the ether lipids, in which 16:0-20:4 remained low.”
Their Conclusions were,
77Lin, D. Anderson, G. Connor, W. & Neuringe, M. (1994) Effect of Dietary N-3 Fatty Acids Upon the
Phospholipid Molecular Species of the Monkey Retina Invest Ophthalmol Vis Sci vol 35, pp794-803
72 Neurons & the Nervous System
“Diets of differing n-3 fatty acid content had profound qualitative and quantitative effects on the
molecular species of retinal phospholipids, and the replacement of 22:6(n-3) by 22:5(n-6) in the retinas
of n-3 deficient monkeys was asymmetric and functionally incomplete."
In their text, they confirmed a finding in Section 4.5 and Section 4.6.1.4 of “Processes in Biological Vision,”
“Retinal membranes are dynamic structures whose components are constantly being renewed. Primate
retinal outer segment membranes are completely replaced every 10 to 14 days. Renewal of outer segment
membrane lipids proceeds by two mechanisms: membrane replacement and molecular replacement.
Despite the rapid replacement of outer segment membranes, however, 22:6(n-3) is retained in the retinas
of adult animals even when they are fed an n-3 fatty acid deficient diet for several months. This retention
apparently results from mechanisms for the recycling of 22:6(n-3) back to the photoreceptors from the
retinal pigment epithelium. Thus, the degree of alteration in retinal phospholipid molecular species seen
in these deficient monkeys is found only when deprivation occurs during development.”
The wording in this quotation from Lin et al. is archaic and leans on Young’s description of two photoreceptor
classes, rods & cones, with outer segments of different shapes (from the early 1970's). The ETN shows there are
only one physical shape to outer segments, and the fact all outer segments are extruded, their cross sectional area
remains constant All outer segments lack a surrounding membrane so as to allow chromophores to access the
substrates, disks, of the newly extruded opsin via the Inter Photoreceptor Matrix, IPM (see Section 2.1.4.7.7).
2.1.5 Formation of islands and plates of lemma
After developing Section 2.1.4, it appears that the nature of the lemma of animal neurons share a close analogy
to the physiography of the earth (the study of the earth’s crust), and particularly the study of the (non–volcanic)
elements of the earth’s tectonic structure. The analogy is illustrated in Figure 2.1.5-1; the scale is greatly
different but the features appear analogous,
The inner bilayer of the lemma The earth’s mantle (separate from the crust)
The outer bilayer The crust and oceanic basins
The inactive portion The oceanic basins & large lakes
The active portion The islands and continents
Electrostenographic areas Local (small) islands
Pedicles and boutons Local (small) islands
Epithelium (taste & smell) Continents & large islands
The formation of individual pedicles associated with axons, and boutons associated with neurites exhibit
relatively rapid growth as a function of time, and in that respect they might be concerned with volcanic activity.
However, their close coupling with the simultaneous growth of the reticular lemma inside the axon or neurite is
more suggestive of deep mantle disruption accompanied by crustal dislocation.
Besides the boutons and surface areas associated with synapses, there are also similar type 2 areas associated
with the electrostenolytic process providing electrical power to the neurons. When in the surface form, these
areas may be indistinguishable from synaptic terminals in the absence of molecules of glutamic acid, or various
associated energy sources, or GABA and other waste products associated with electrostenolytics.
In the case of taste and smell, the finer dendrites, sometimes labeled cilia or even micro-cillia, may be formed
as continuous chemical receptor surfaces. In those cases, the analogous geographic areas are the continents and
large islands shown on the right in the left frame of the figure. The roughness of the outer surface of the outer
bilayer of the right frame may sometimes be important in relation to stereographic features. The roughness may
be sufficient to prevent some molecules from forming a coordinate bond with various receptor sites (Section
2.1.5.1). These features may be considered analogous to escarpments and other asymmetric geographic
features.
The Neuron 2- 73
Frequently, a lap joint is observed in neural cells. This arrangement is a stationary feature that is the analog of a
subduction zone in physiography. Their may be lap joints involving only one of the bilayers of a lemma but
these have not been documented clearly in the literature.
The above tabulation and analogy can be used to describe any type 1, type 2 or type 4 lemma. These membranes
remain uniformly amphipathic while exhibiting different electronic characteristics. It does not relate directly to
type 3 lemma that may incorporate other features. An example might be a fissure (pore) in a type 3 membrane
that would be analogous to a deep canyon caused by erosion (such as the Grand Canyon of the Colorado River).
This feature might support the transport of ionic and/or molecular material through the lemma for purposes of
homeostasis.
The method of implementation of individual active portions of the outer bilayer remains unknown as the
analogous elements of physiography also remain a mystery.
2.1.5.1 Applying AFM to natural type 2, 3 & 4 lemma roughness
The AFM technique is presently limited to very local areas, on the order of a few hundred Angstrom or less.
This is a minuscule area even when exploring the lemma of a neuron. The active area of individual type 1
regions on the surface of a neuron may be on the order of a few hundred to a few thousand square Angstrom out
of a much larger area, on the order of 1-5 million square Angstrom. In the electrostenolytic process, the relevant
area may be at the smaller end of this range. An exception may occur in the gustatory and olfactory modalities
where most of the surface of an individual dendrite may consist of type 1 lemma. The situation is so complex
that it is necessary to carefully develop individual exploration protocols.
Section 3.2.2 discuss the stereochemistry of the electrostenolytic process associated with type 2 lemma. Figure
3.2.2–3 shows the fundamental mechanism and Figure 3.2.4–1 shows the more subtle stereo-chemical selection
process that might be identifiable using AFM techniques. In this case, the surface of the lemma may support a
mediating molecule, potentially a protein (at least conceptually defined in the literature), that prevents some
molecules from interfering with glutamic acid from coordinate bonding with the receptors of the lemma.
The simpler gustatory and olfactory situations described in Chapter 8 are similar but involve coordinate
chemistry, rather than valence chemistry at the sensory neuron surface. Coordinate chemistry involves
forming a low energy coordinate bond (a hydrogen bond) between the stimulant and the sensory nerve.
Actually two hydrogen bonds are employed in the formation of a hetrodimer (which is a very low energy
relationship.
If AFM techniques are able to locate, recognize and describe the surface roughness in the above cases, it will
Figure 2.1.5-1 Analogy between the dendritic outer wall and the earth’s crust.
Left; typical physiography of the earth’s crust showing the oceanic area
containing non-volcanic protrusions with significant height as well as at sea
level. Right, typical structure of the dendrites showing type 1 regions with a
outer bilayer in blue. Type 2 regions are shown with the outer layer (above the
dashed lline) the same color as the inner layer. The paired layers form a
semiconducting diode. The reticulum bilayer also forms a semiconducting diode.
The high peaked region of type 2 lemma surrounded by type 1 material
constitutes a bouton (with its peak forming part of a synapse. The lower
elevation type 2 lemma surrounded by type 1 material constitutes part of a
surface synapse. The combination of the lemma and reticular layer form an
active semiconducting device, an Activa, when properly biased electrically. See
text.
74 Neurons & the Nervous System
have provided a major step forward in neuroscience!!
2.2 The structural and electrical characteristics of the static (first order) neuron
The neuron and the neural system are very special in that their electrical performance is determined by the
repetitive use of a single circuit group. At the heart of this group is an electrical conduit formed by the
enclosure of an electrically conductive electrolyte within an insulator formed of a BLM that is itself surrounded
by an electrolyte. Morphologically, the result is a series of conduits connecting a source of information to a
consumer of that information. Each of these conduits exhibit a variety of surface characteristics associated with
their chemical composition at the molecular level. Chemically, the result is a series of regions formed of
bilayers of various phospholipid molecules. Electrically, the result is a set of circuit elements representative of
the electrical characteristics of each region of the membrane. These sets of circuit elements form the electrical
barriers between the various plasmas inside and outside the cell. With one crucial exception to be discussed
below, the values of the circuit elements of a given region are fixed. No variable elements controlled by
external or unspecified forces are involved.
The crucial exception involves the following fact. Under conditions where the cathodes of two semiconductor
diodes are formed on a common crystalline substrate, the two diodes can exhibit “transistor action.” Transistor
action causes a current to flow in the second diode under the control of the current through the first diode. It
does this in spite of the second diode being reverse biased. This activity will be introduced in Section 2.2.2 and
be explored extensively in Section 2.3.
The operation of the fundamental neuron is best understood by proceeding to examine a generic biological cell
before it becomes a neuron. This will be done in steps. In the following sections, three degrees of complexity
will be explored. Initially, only the fundamental cell membrane will be examined. A basic, or first order,
fundamental cell will then be examined as an operating entity without regard to the physical arrangement
providing electrical bias to the circuit. Finally, a second order fundamental cell will be considered as a
complete operational entity. This second order cell consists of multiple individual membrane isolated conduits
within a single external membrane. The surface of the membrane surrounding each of these compartments is
usually differentiated into regions at the molecular level. At this point, the importance of the electrolytic and
metabolic matrix surrounding the cell is found to be critically important to its static characteristics. In-vitro
experiments must observe these requirements placed on the surrounding interneural matrix if the results are to be
meaningful.
2.2.1 The fundamental cell membrane
An expression frequently encountered in discussing cell membranes is “black lipid membrane. Tien et al78. have
defined this material,
”The so-called bimolecular lipid leaflet, postulated as a basic structural component of natural
membranes, has only recently become available for direct experimental investigation. The formation and
properties of bilayer lipid and proteolipid membranes, separating two aqueous phases, have been
investigated. The thickness of these membranes in aqueous solution is of the order of 70 Å, and they
appear “black” when viewed by reflected light. For this reason they are called “black” lipid membranes
(or films) to distinguish them from the well known black soap films in air.” In fact, the membranes
appear as largely transparent optical pellicles. When of uniform thickness and devoid of interference
patterns, they reflect virtually no light and were therefore described erroneously as “black.”
Unfortunately, the prefix, “black” has stuck to the membranes ever since 1969.
Danielli has provided a brief overview of the evolution of the bilayer hypothesis of membrane structure79. It is
based on his long involvement in the field, includes many of the early caricatures of cell walls, and stresses the
conceptual nature of these early ideas.
Steed & Atwood have provided the clearest caricature, Figure 2.2.1-1, of how amphiphilic molecules self-
78Tien, H. Carbone, S. & Dawidowicz, E. (1966) Formation of “Black” Lipid Membranes by Oxidation
Products of Cholesterol Nature vol 212, pp 718-719 doi:10.1038/212718a0
79Danielli, J. (1975) The bilayer hypothesis of membrane structure. In Weissmann, G. & Claiborne, R. ed. Cell
Membranes; Biochemistry, Cell Biology & Pathology. NY: HP Publishing Co. Chapter 1
The Neuron 2- 75
organize into one of several configurations80. However, two conditions need to be noted. First, the vesicle is
shown with alternating molecular alignments between inner and outer films. The figure employs an “artist’s
license.” At the actual scale of the vesicle versus the individual molecules, the alignment between the molecules
of inner and outer films exhibits a one-to-one alignment. Second, the fluid background should appear outside of
all of the molecular structures shown, and inside the vesicle, but should not appear between the inner and outer
polar elements of the vesicle wall, or between the polar elements of the bilayer. The monolayer shown at the
fluid/air interface is an important configuration used to measure the dipole potential of an amphiphilic film
(Section 2.2.1.5).
The fundamental cell membrane is defined here as
a bilayer lipid membrane (BLM) where each layer
is a continuous liquid crystalline film of
phospholipid material. The BLM is nominally 75
± 15 Angstrom in thickness. There are no
inclusions within the BLM and no disruption of
either film above the molecular level.
From an electro-chemical perspective, a BLM is a
surface of finite thickness composed of a highly
structured material exhibiting a characteristic
electrical impedance and a characteristic voltage
potential between its two surfaces. The electrical
equivalent circuit of the BLM may contain both a
variable resistive component (characteristic of a
diode) and a battery in series with the combination
shunted by a capacitive component. These
properties are directly related to the molecular
structure, the thickness, the temperature, and to
other properties of the membrane to be defined
below. These electrical properties are independent
of the properties of any more complex regions of a
membrane separating two electrolytes that are used
for genesis or metastasis.
Both the intrinsic voltage of the internal battery and the impedance of the BLM are highly dependent on the
degree of symmetry between the two bilayers of the membrane. For a symmetrical membrane, the impedance is
exceedingly high and the material acts as an insulator. For more asymmetrical arrangements, the impedance per
unit surface area is also asymmetrical. It can be defined by the reverse cutoff current of the diode. For these
asymmetrical BLMs, the intrinsic voltage of the battery is usually in the range of 0.00 +/– 50 mV.
The properties of the phospholipids found in neural lemmas (Section 1.4.2) suggest the electrical nature of the
conduits defined above. The highly structured nature of the phospholipids in the membrane supports the
assertion that the materials are in the form of a “liquid crystal” when at biological temperatures. The polar
groups of the phospholipids are structurally complex and contain a large amount of oxygen. These
characteristics suggest the electrical properties of the liquid crystalline layers may be quite complex and the
structural arrangements may support unusual stereographic associations with other molecules. These
possibilities will be found important in the discussion to follow.
There have been many caricatures of the fundamental membrane. Pannese discusses the history of this
research81. Discounting his comments concerning excitability of the membrane, he points out that “The study of
neuronal plasma membrane is beset with particular problems.” He also points out that most of the common
wisdom concerning neural membranes has been obtained by inference from data on non-neural cells and by
inference from experiments prior to the development of the electron microscope. Most of the resulting
caricatures, including those of Danielli & Davson (1935) and of Robertson (1959) assemble the various
constituents known to be associated with a membrane into a single structure. In the above two cases, protein
“skins” are shown on each side of the bilayer. Although such protein layers are undoubtedly present in some
situations, and may be key to the electrostenolytic support to the operation of the neuron, they are not believed
to be intrinsic to the membrane.
Figure 2.2.1-1 Ordered amphiphilic
materials in aqueous solution. The
monolayer extends into the gaseous
space above the fluid. The solvent should
not be shown between the polar heads on
each side of the bilayer. See text.
Modified from Steed & Atwood, 2000.
80Steed, J. & Atwood, J. (2000) Supramolecular Chemistry. NY: Wiley
81Pannese, E. (1994) Neurocytology. NY: Thieme Medical Pulbishers. Pg. 74
76 Neurons & the Nervous System
There has been no way for the above investigators to know when they were dealing with a fundamental
membrane or a highly differentiated segment of neural membrane. Pannese also addresses this problem due to
the fact that a neural membrane does not show uniform properties over its whole surface.
There have only been a few attempts to create a synthetic BLM (Section 1.4.2). The attempts have generally
sought to create a BLM where the two layers were symmetrical. The result has generally produced high quality
electrical insulators. While these have been descriptive of the bulk of the BLM’s in neurons, they have not
described the functionally critical type 2 membrane of the neuron. More experiments are needed based on this
theory to quantify the characteristics of type 2 membranes.
Slater & Huang82 have published an extensive study of “interdigitated bilayer membranes. The paper includes a
review of virtually all of the technologies of value in evaluating bilayer membranes. The study addresses both
symmetrical bilayer membranes (insulating) and asymmetrical membranes that offer the features of a
semiconducting membrane. They note a wide range of disparate facts without providing any apparent road map
to their overall impact. The paper includes very few figures. Many may be only anecdotal and without citation.
Their paper requires significant study to interpret their data in a modern context. Their concluding remarks are
surprisingly short for a 33 page paper. Figure 2.2.1-2 illustrates their use of the concept of interdigitation. Note
all of the molecules illustrated are fully saturated and labeled as PC (phosphatidylcholine) even when the
molecules in A and B exhibit distinctly different lipid components and are thus clearly different molecules. All
of the lipid portions are shown as straight chain aliphatic moieties, although they may contain kinks in the case
they are not fully saturated. Although Slater & Huang did not provide dimensions, Mueller & Rudin (1969)
suggest most natural bilayers are 75 ± 15 Angstrom thick. More recent numbers extend down to 50 Angstrom in
important cases.
82Slater, J. & Huang, C.-H. (1988) Interdigitated bilayer membranes Prog Lipid Res vol 27, pp 325-359
The Neuron 2- 77
See Section 2.2.1.3.3 for nominal values for calculating CL and C. Moderm molcular drawing programs do
these calculation automatically.
Slater & Huang address both X-Ray and Neutron Diffraction techniques. “The diffraction methods are
unequivocally the most direct methods available for determining bilayer interdigitation, since they are capable of
determining the bilayer thickness. All other methods used for determining the presence of interdigitation,
although extremely useful and insightful, do not have the ability to directly monitor the bilayer thickness.” “As
a water-free lipid sample is progressively hydrated, initially a single homogeneous phase exists as water
gradually permeates the interbilayer space and associates with the lipid head groups. At a particular
concentration of water within the sample, the bilayers are maximally hydrated, and a separate phase consisting
of excess water appears in the sample. If the X-ray diffraction pattern is measured as a function of bilayer
hydration, the water concentration at which the bilayers are maximally hydrated may be ascertained. At this
concentration, a single homogeneous phase still exists without the appearance of a separate excess water phase.
This information regarding the point of maximal hydration is used in the determination of the bilayer thickness.”
Slater & Huang also address several spectroscopic techniques useful in determining the detailed parameters of
phospholipids. They also discuss Nuclear Magnetic Resonance as a useful technique for defining the parameters
of phospholipids. They note that phosphorus NMR is particularly useful in studying the head group of the
phospholipids. They also address Electron Microscopy, Electron Spin Resonance, and Fluorescence techniques.
Use of all of these techniques has provided a wealth of new information at a quite detailed level. Comments on
Figure 2.2.1-2 Options in interdigitation of bilayer membranes. Frames A and B
are assumed to be of primary interest to this work, although further analysis may
change this view. Note, all of the molecules illustrated are fully saturated. A;
C(16):C(16) PC non–interdigitated lilayer. B; C(16):C(10)PC partially interdigitated
bilayer. C; C(16):C(10)PC mixed–interdigitaated bilayer. D; C(16):C(16)PC fully
interdigitated bilayer and E; diagrammatic representation of the quantities used
to calculate the chain inequivalence parameter shown for C(16):C(10)PC. From
Slater & Huang, 1988.
78 Neurons & the Nervous System
page 349 related to the alignment of two bilayers brought into juxtaposition. This may be critical to the further
understanding of the formation of an Activa within a neuron, a Node of Ranvier, and/or a synapse. Page 351
addresses unsaturated phosopholipids superficially. No data on the electrolytic performance of these different
conformations was provided in the paper.
Although, it may be significant in the packing arrangement, the criteria in frame E, C/CL, does not appear to
be relevant to the electrolytic performance of the molecule when present in a liquid crystalline bilayer. The
presence of double bonds and other means of doping the bilayer are apparently more significant.
Quinn (Chapter 2) has provided an extensive discussion of the use of X-ray crystallography to characterize
bilayer lemma. He notes the amphipathic character of these materials contributes greatly to their ability to self
assemble into liquid crystalline monolayers and to further assemble into bilayer lemma. He quotes the same
parameters as McIntosh, 3.68 nm for the center-to-center spacing of the head groups of phospholipids when
present in a bilayer lemma. He also discusses the variation of this and similar parameters in the face of varying
amounts of water in the matrix. His equation 2.3 provides a means of calculating the surface area of the lemma
occupied by the head group of a single phosphoditic molecule, varying with the presence of water. Using the
values of Levine and Wilkins for Phosphotidylcholine, he calculates an area of 0.627 nm2 when hydrated to 21%
water. The same calculation gives 0.589 nm2 when the water content is reduced to 14%.
Quinn opens a discussion on the state of matter involving the phospholipids of a lemma and introduces one
method of distinguishing the state based on the critical temperature separating these states (Section 2.1.4.7.2).
The Neuron 2- 79
Quinn goes on to discuss many other properties of the bilayer lemma, including some of its hydrophobic and
electrostatic properties.
De Levie et al. has provided the electrolytic performance of laminar (as opposed to vesicle) bilayers83,84 by
building on the work of Mueller and Rudin85 of 1969. They provide both the real part (resistive) and the
imaginary part (capacitive) of the impedance for a variety of specific phospholipids. They use a faster method of
collecting data than Cole did during the 1940's and attribute it to, and cite, Smith. De Levie et al. did not
demonstrate that there were no diode elements in their membranes. The technique only applies to linear circuits
as originally defined. In the first paper, their circuit diagram does not include any diode element and their
choice of phosphatidylcholine, PC, would be consistent with this diagram. On page 104, they discuss several
problems with their protocol, including the following, “The values found for the capacitance, C, vary between
0.34 and 0.45/Fcm-2. Such a variation of single, unaveraged measurements on different membranes is not
uncommon with membranes containing hydrocarbon solvent, and is mostly due to the unavoidable presence of
microlenses (? probably spheres in their solutions). Clearly, the reproducibility of our membranes is not up to
the level of our data analysis procedure, and we are at present trying to improve the former by using fused
monolayers instead.” They go on to make the important statement, “Our model calculations indicate that it will
often be impossible to distinguish experimentally, on the basis of small-amplitude electrical measurements,
between ion transport across the membrane and that across the water-membrane interface, because the two
processes behave, in electrical terms, as series resistances.” The italics were added. This last observation is
compatible with this work and the following assertions of Finkelstein.
Finkelstein (1987) crossed the intellectual bridge in a paper published in an important but narrowly
distributed journal. He emphatically and publicly noted the virtual impermeability of lipid bilayer
membranes to small ions such as Na+, K+ and Cl--.86 However, he did not address the subject of the
asymmetrical bilayer as a semiconductor. Wanting to accept the transport of ions through a membrane,
he assigned this capability to proteinaceous pathways inserted into and through the membrane. In this
position, he appears to be supporting the complex caricature of a BLM presented by Mackowski87. This
caricature does not assign any quantum-mechanical properties to the membrane. Such gate structures are
not seen at the molecular level in electron micrographs (or from x-ray scatter analyses) of conduit
membranes. See Section 2.2.2.6.1 for delineations of the three types of lipid bilayer membranes.
In the second paper, de Levie et al. show how they can convert from simple bridge-based measurements of
admittances and impedances to a faster technique employing computer-controlled step-function pulse
stimulation, small signal circuit modeling and Fourier Transform analysis, where the amplitude of the individual
frequency components are indicative of the admittance of the artificial black lipid membranes at that frequency.
Their protocol is quite complex is based on an early desktop computer, PDP-11/20, of limited capability and the
use of the Fast Fourier Transform. They do provide a Table 1 comparing their bridge and computer-aided
results. They note their approach is able to recognize non linearities when present in the artificial black lipid
membranes under test, as illustrated in their figures 13 and 14. Little data relating to such membranes were
included in the paper.
The article by Mueller & Rudin, while still valuable, contains many overly broad statements drawn from very
83De Levie, R. & Vukadin, D. (1975) Dipicrylamine transport across an ultrathin phosphatidylethanolamine
membrane Electroanalytical Chem Interfacial Electrochem vol 62. pp 95-109
84De Levie, R. Thomas, J. & Abbey, K. (1975) Membrane admittance measurements under computer control
Electroanalytical Chem Interfacial Electrochem vol 62. pp 111-125
85Mueller, P. & Rudin, D. (1969) Bimolecular Lipid Membranes: Techniques of Formation, Study of Electrical
Properties, and Induction of Ionic Gating Phenomena In Passow, H. & Stampfli, R. eds, Laboratory Techniques
in Membrane Biophysics. NY: Springer pp 141-156
86Finkelstein, A. (1987) Water movement through lipid bilayers, pores and plasma membranes. Volume 4 of
the Distinguished Lecture Series of the Society of General Physiologists. NY: John Wiley & Sons. Chapter 6.
87Mackowski, L. Casper, L. Phillips, W. & Goodenough, D. (1977) Gap junction structure II: Analysis of x-ray
diffraction data J. Cell Biol. vol. 74, pp 629-645
80 Neurons & the Nervous System
Figure 2.2.1-3 En face view of a gap
junction in a neuron found in the liver of a
rat. Negative stain was used. The central
region of each “particle” is penetrated by
the stain to produce a 15-20 Angstrom
electron dense spot. Lattice spacing is
approximately 80-85 Angstrom. From
Gilula (1975)
early exploratory laboratory research. “Bimolecular membranes formed from cellular lipids have many
properties of cell membranes. They have the same values for thickness (75 ± 15 Å), electrical capacitance (0.4 –
1.2 μF depending on lipid type), dielectric strength (5 × 105V cm-1) [, water permeability (1 μ min-1 atm-1 by
osmometry) and surface tension (between 0 and 5 dynes cm-1).” They provided no details as to what type of
bilayer membrane they were referring. They note without significant discussion (page 141), “One outstanding
difference is their high electrical resistance which at 108 Ohm cm2 is 105 - 107 times higher than that of most cell
membranes.” This assertion has not been supported based on later research under better laboratory conditions
(the units indicate the term should be resistivity, not resistance). Note is taken of the words “Induction of Ionic
Gating Phenomena” in the title of their article. These phenomena and the low natural membrane values cited
above have not been properly interpreted in the past.
2.2.1.1 Local (cytological) uniformity of the neuron membranes.
Many authors invoke caricatures of neural membranes containing a variety of inclusions and/or voids in the
membranes. The voids are frequently described as gates for the passage of (simple or complex) ions through the
membrane under controlled or controllable conditions. Proposals for such gates are especially common when
describing the synaptic region between two neurons. Some authors become quite fanciful and indicate a
separate void (gate) for each ion participating in the proposed process along with a wide variety of other
inclusions in the membrane surface. These caricatures are usually proposed based on interpretations of electron
micrographs made at around 50,000x. Shepherd reviews a number of these concepts88.
The description of the membrane face as containing a large number of “gates” seems highly unlikely since a
great many different tailored holes would be needed per unit surface. Figure 2.2.1-3 from Gilula89, supports
this position. It shows an en face view of a gap junction at 360,000x. There are no signs of either inclusions or
physical holes in the area shown (about 6000 x 3000 Angstrom or 0.6 x 0.3 microns). On the contrary, the
uniformity of the para-crystalline lattice strongly supports the idea that the cell wall is a continuous liquid
crystalline structure devoid of gates. The staining of the individual phospholipid end groups is not unexpected
based on their complex molecular structure.
At the molecular scale, the change of molecular
species within one or both bilayers with position
along the surface of the BLM is well accepted.
This may be represented in the upper right corner
of the figure. Although such changes would not
support a major change in the permeability of the
membrane to large particles and ions, it can have a
significant impact on the permeability of the
membrane to fundamental electrical charges.
2.2.1.2 Molecular level uniformity of
the fundamental membrane
As explored earlier, the fundamental membrane is
typically subdivided into a series of application
oriented regions. These regions of material differ
primarily at the molecular level. Section 1.4.2
has introduced the molecular characteristics of
these regions. Their electronic properties have yet
to be codified completely. However, Seanor has
discussed their properties generically90. He
addresses the self-assembly of supramolecules of fatty acids, such as the phospholypids, into micelles and
membranes. These materials can exhibit either n-type or p-type semiconductor performance. Wikipedia91 (as of
December 2015) listed more recent publications relating to the properties of these materials with a focus on the
88Shepherd, G. (1991) Foundations of Neuron Doctrine. Pg. 277
89Gilula, N. (1975) Junctional membrane structure. in The Nervous System, Tower, D. ed. vol. 1, The basic
neurosciences. NY: Raven Press pg. 6
90Seanor, D. (1982) Electrical properties of polymers. NY: Academic Press
91https://en.wikipedia.org/wiki/Polythiophene
The Neuron 2- 81
polythiophenes (Pts). The PTs are currently of great interest in the electronic display area for consumer
television sets.
A number of comprehensive reviews have been published on PTs, the earliest dating from 1981.[1]
Schopf and Koßmehl published a comprehensive review of the literature published between 1990 and
1994.[2] Roncali surveyed electrochemical synthesis in 1992,[3] and the electronic properties of
substituted PTs in 1997.[4] McCullough's 1998 review focussed on chemical synthesis of conducting
PTs.[5] A general review of conjugated polymers from the 1990s was conducted by Reddinger and
Reynolds in 1999.[6] Finally, Swager et al. examined conjugated-polymer-based chemical sensors in
2000.[7] These reviews are an excellent guide to the highlights of the primary PT literature from the last
two decades.
Ziblat et al. have described the two lipids of the typical phospholipid molecule as each having a cross section of
~20 Angstrom. When formed into a monolayer, these molecules frequently exhibit a tilt relative to a
perpendicular to the planar surface of up to 27 degrees. However, when transformed into a bilayer, the
molecules generally reorient themselves to exhibit negligible tilt relative to this perpendicular (Table 1 and
figure 5).
2.2.1.3 Charge transfer through the bilayer membrane– by “holes”
The question of charge transfer through the lemma of a neuron has not been addressed in a concerted manner in
the biological literature. The concept of charge transfer has remained within the pedagogy of solution
chemistry. Treating the lemma as a liquid-crystalline structure with the electrical properties of a crystalline
material has yet to become common. The problem is exemplified by the statements of Gennis when discussing
the permeability of lipid bilayer membranes as recently as 1989. “Experimentally, it is not possible to
distinguish proton permeability from hydroxide permeability, so this is usually indicated as (H+/OH–). We will
refer to this simply as proton permeability.” After introducing the subject of the permeability of membranes to
small ions, he notes, “Nevertheless, it is clear that proton permeability is at least 106 greater than for other
simple ions.” He cites Gutknecht as a reference92. Gutknecht begins a mini-review with the statement, “The
proton/hydroxide (H+/OH–) permeability of phospholipid bilayer membranes at neutral pH is at least five orders
of magnitude higher than the alkali or halide ion permeability, but the mechanism(s) of H+/OH– transport are
unknown.” He reiterates this in his opening paragraph,
“During the past six years, about twenty laboratories have studied the H+/OH– transport properties of
phospholipid bilayers. In general, the original observations of Nichols and Deamer have been confirmed.
However, the mechanism(s) of H+/OH– permeability remain unknown.”
If Figure 2 of Gutknecht is modified to incorporate the hole/electron concept described below, reinterpretation
of his data becomes very valuable. Writing in the same journal, Deamer also presented a much longer mini-
review. Unfortunately, he plows the same ground,
“Proton permeation of the lipid bilayer barrier has two unique features. First, permeability coefficients
measured at neutral pH ranges are six to seven orders of magnitude greater than expected from
knowledge of other monovalent cations. Second, proton conductance across planar lipid bilayers varies at
most by a factor of 10 when pH is varied from near 1 to near 11. Two mechanisms have been proposed to
account for this anomalous behavior: proton conductance related to contaminants of lipid bilayers, and
proton translocation along transient hydrogen-bonded chains (tHBC) of associated water molecules in the
membrane.”
He concludes his work with,
“Although these results are suggestive that trace contaminants may contribute to proton conductance in
planar lipid membranes, they do not provide a complete explanation of the proton permeability
anomaly.”
The Agmon team93 has pursued the physical movement of positive nuclei through the aqueous environment in
recent times without clear success (Section 1.3.2.2). They define it as the Grotthuss mechanism honoring a
German of the early 19th Century who speculated on the movement of positive hydrogen ions before the formula
92Gutknecht, J. (1987) Proton conductance through phospholipid bilayers: Water, wires or weak acids? J
Bioenerg Biomemb vol 19(5), pp 427-442
93Markovitch, Omer; et al. (2008). Special Pair Dance and Partner Selection: Elementary Steps in Proton
Transport in Liquid Water. J. Phys. Chem. B 112 (31): 9456–9466
82 Neurons & the Nervous System
for water was known. They focus on the grouping of liquid water molecules into multiple shell complexes.
Their more recent work on hydrated sodium ion clusters, Fifen & Agmon, appears in Section 1.4.2.7.
The problem is the limited perspective of the cited investigators. They are unaware that the currents moving
through liquid-crystalline lipid bilayer membranes are subject to the laws of quantum physics and not
electrolysis of solutions. The currents in liquid crystalline membranes consist primarily of electrons and the
absence of electrons (holes). No protons transit the typical membrane any faster than their sibling ions. The
movement of positive charge through a membrane is accounted for by the concept of hole transport. Hole
transport involves the lack of an electron at a given atomic site in a liquid-crystalline or solid crystalline lattice
and the replacement of this lack by another electron from an adjacent lattice location in accordance with the
electrical field present. The result is the apparent slow motion of a positive charge across the lattice within the
ground electrical state of the material. Simultaneously, a much faster electron transport can occur within the
valence band of the material in accordance with the same electrical field and the impedance of the valence band.
These two currents are easily separated using the Hall Effect. The result is typically a hole transport velocity
that is many orders of magnitude lower than that of the electron current. This hole current is, however, many
orders of magnitude (106 as noted by Gennis) greater than any physical transport of ions (including protons)
through the membrane. Table 7.1 of Gennis should be corrected by changing the “compound” label under item
8 to read, “Hole current” in Egg Phosphatidylcholine. As noted above, the fact that this was a hole current can
be confirmed by Hall Effect measurements.
Dowben described the motion of “holes” in water conceptually, using the language of chemistry, in 196994 as did
Lehninger in 1970. Lehninger95 noted the mobility of the charge associated with the water lattice (semi-metallic
water) is stable up to 100 centigrade and six times the mobility of either sodium or potassium ions.
The above currents are independent of any pores, channels or other voids in the overall lipid membranes of
neural cells. These currents can be even larger when the lipid bilayers are tailored to specific purposes, as in
type 4 lemma (Section 2.2.1).
In 2015, the question of conductivity through biological lemma was becoming a subject of greater interest. The
work of Geim & Novoselov96 relating to a single layer film of carbon atoms in a film labeled graphene exhibits a
structure similar to the cross-section of a phospholipid film forming the exterior bilayer of a neural lemma.
They note a single layer of graphene can conduct what they describe as protons. However, they note the cloud-
like swarm of unbound electrons surrounding the monolayer of carbon atoms in a hexagonal honeycomb array.
Neto, et al. developed these properties in greater detail97.
A conceptual challenge for the reader unfamiliar with the hole/electron concept is the fact that the neural system
is built using pnp type electrolytic devices. The hole currents are the dominant currents in such devices, as
opposed to electron currents. Thus, the hole current can be associated directly with the previously presumed H+
current through a membrane. However, no physical ions pass through the membrane. Only holes (in fact
electrons in the ground state and in the opposite direction to the electrical field) pass through the membrane.
2.2.1.3.1 The long chain molecules of the lemma as nematics
The long nominally electrically neutral tails of the molecules forming the inner and outer layers of the neural
lemma are liquid crystalline, they are nematic in structure. The potential movement of charge along these
structures has not been extensively studied.
Turiv et al. have provided a generic discussion of spherical entities along nematic molecules98. Their
conclusion, “Our work demonstrates that the orientational order in a nematic liquid crystal causes a profound
effect on Brownian motion of a small spherical particle and results in anisotropic subdiffusion and
94Dowben, R.(1969) General Physiology: a molecular approach. NY: Harper & Row
95Lehninger, A. (1970) Biochemistry. NY: Worth Publishing pp 39-44
96Geim, A. & Novoselov, K. (2007) http://arxiv.org/ftp/cond-mat/papers/0702/0702595.pdf
97Neto, A. Guinea, F. Peres, N. Novoselov, K. & Geim, A. (2009) The electronic properties of graphene Rev
Mod Phys vol 81(109) http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.81.109
98Turiv, T.Lazo, I. Brodin, A. et al. (2013) Effect of Collective Molecular Reorientations on Brownian Motion
of Colloids in Nematic Liquid Crystal Science 342, 1351-1353
The Neuron 2- 83
superdiffusion.” Extension of their work to charged particles in an electrically biased regime will require further
study.
2.2.1.3.2 The Nobel Prize in Chemistry for 2000–semi-conductive lipids
A critical element in understanding the operation of neurons, and particularly the sensory neurons involves the
transport of electrical charges (not ions, like sodium calcium or potassium) through the lemma of a neuron.
The documentation of this capability was presented during the last decade of the 20th Century by three research
scientists99. The cited paper provides a significant bibliography relevant to polymer conductivity. Figure
2.2.1-4 illustrates the range of conductivities achieved in doped conjugates carbon chains. This range has been
exploited in the development of man-made organic light emitting diodes and other applications in flat screen
imaging devices. It is also key to the operation of the semiconducting lemma of neurons that is presented below.
The scale in the lower part of the figure has long been available in the literature100.
In the neurons, the conjugated carbon chains are commonly found in small areas of the external lemma of
neurons and in internal areas of the lemma separating the fluid chambers of the neuron (Section 2.2.2.6). These
areas are described as type 2 membranes in the following sections. These areas will be described further in
Section 2.2.2..
2.2.1.3.3 The role of double bonds in semi-conductive lipids
To the extent that the fatty acid chains of phospholipids are saturated, they constitute very good insulators even
in the liquid crystalline state. The intrinsic number of free electrons per unit volume in such material is not
readily obtained. However, it is clear that the level of non-saturation in these chains is significant. A carbon-
carbon double bond exhibits a –bond that is an electron donor in the language of semiconductor physics. Even
one such donor in 108 molecules101 can change the resistivity of the material by a factor of 10. In phospholipid
bilayers, the dominant molecules are present at a surface density of ~1014 molecules/cm2.
Figure 2.2.1-4 The conductivity range achieved in conjugated carbon molecules
compared to that of solid state materials. The range is clearly as broad as that
used in solid state semiconductor devices. See text. From Heeger, MacDiarmid,
& Shirakawa, 2000.
99Heeger, A. MacDiarmid, A. & Shirakawa, H. (2000) Conductive polymers. Nobel Prize Lecture
http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2000/advanced-chemistryprize2000.pdf
100Nssau, K. (1983) The Physics and Chemistry of Color. NY: John Wiley & Sons
101Millman, J. & Halkias, C. (1972) Integrated electronics, NY: Mc Graw-Hill, page 30
84 Neurons & the Nervous System
Figure 2.2.1-5 shows a figure from Quinn cataloging some of the most important lipids in membranes. Note
carefully the distribution of the double bonds along the aliphatic chain of the lower three lipids. Each of these
lipids contains 18 carbon atoms. Linolenic acid is shown with a single double bond at the lower right that is
continued at lower left. The double bonds of the lower three lipids are not conjugated. Conjugation would
introduce an entirely different electronic environment to these molecules. In the form illustrated, each of these
lipids can introduce only discrete levels of “dopant” into the liquid crystalline bilayer. At this time, by
combining different isomers of these lipids into a localized area of a bilayer membrane, a nearly continuous
level of dopant could be achieved on a volumetric basis. A 20–carbon unsaturated lipid is arachidonic acid; it
exhibits four non-conjugated double bonds. See Section 2.2.3.4.4 for a continuation of this figure.
The Neuron 2- 85
Note that Lauric and palmitic acids are most often associated with the vast amount of type 1 lemma found
throughout the tissue of an animal. However, most of these discussion occur in text books or in the introductory
sections of papers (where the authors are frequently repeating common wisdom as a means of establishing their
credibility) rather than in the more substantive part of the paper. A common problem dating from the 1960's, is
the suggestion, in both graphics and comments that both of the aliphatic lipids fo the phospholipids are are
identical, or at least contain the same number of carbon atoms. See the next section.
In a conventional conjugated, wherever the double bonds are of the cis–type, the lipid will exhibit a kink in its
aliphatic chain. If the double bonds are of the trans–type, the lipid will remain straight and support a more
orderly liquid crystalline packing arrangement. Lehninger has shown that the packing density is not affected
significantly by trans– double bonds, Figure 2.2.1-6 . Due to a slight change in angles and bond length, the
introduction of a trans– double bond has negligible affect on the overall aliphatic chain length for the fatty acids.
Figure 2.2.1-5 Fatty acyl residues ( R) commonly found in membrane lipids. Note
specifically that the double bonds in the lower three lipids are not conjugated.
The presence of the (CH2)7 chain suggests two additional double bonds could be
introduced into linolenic acid. See text. From Quinn, 1976.
86 Neurons & the Nervous System
In the case of docosahexaenoic acid, DHA, (see next section) because the double bonds are separated by a CH2
group, the opposite relationship is applicable. The cis-double bonds leads to the linear axis, and the trans-
double bonds lead to kinks in the axis.
A Google search uncovers numerous papers relating to cephalin (phosphatidylethanolamine) and the
value of 18.2ac Megohms–centimeter2. This value appears to represent the catalog value of the
resistivity of the filtered water used in many experiments. The source of this resistivity is found
explicitly in Xia et al, (2017).
As reported in Hills102, Makarova et al103. and Lidorenko et al104. have studied polymer structures containing
finely dispersed silver. They reported, their “Type 1 membranes with Ag concentrations up to 9% (w/w) were
non-conducting (electrical resistivity 1016 ohm-cm) while membranes containing Ag concentrations greater than
9% had a resistivity of 1 ohm-cm.”
Suarez-German et al105. have studied bilayers common to lemma. Their Abstract outlines their program,
“Phosphatidylethanolamine (PE) and phosphatidylglycerol (PG) are the two main components of the
inner membrane of Escherichia coli. It is well-known that inner membrane contains phospholipids with a
nearly constant polar headgroup composition. However, bacteria can regulate the degree of unsaturation
of the acyl chains in order to adapt to different external stimuli. Studies on model membranes of mixtures
Figure 2.2.1-6 Spatial dimensions related to double bonds in lipid tail. Lehninger
asserted that the cis– double bond was predominant on a global basis (not even
restricting it to neurons, or kigneys, etc.) but did not differentiate between type
1 and type 2 neural lemma. This work proposes the trans– double bond is the
more prevalent in the outer bilyaer of type 2 neural lemma. From Lehninger, 1971
102Hills, G. (1972) Electrochemistry, vol 2, London: Royal Society of Chemistry
103Makarova, V. Pevnitskaya, M. & Grebeuyuk. (1970) Akad Nauk, U.S.S.R. No. 3, pg 151
104Lidorenko, N. Gindin, L. Egorov, B. et al. (1969) Dolady Chem vol 187, p 570
105Suarez, C. Montero, M. Mullol, J. et al. (2011) Acyl Chain Differences in Phosphatidylethanolamine
Determine Domain Formation and LacY Distribution in Biomimetic Model Membranes J Phys Chem B vol
115(44), pp 12778-12784
The Neuron 2- 87
of PE and PG,
mimicking the proportions found in E. coli, can provide essential information on the phospholipid
organization in biological membranes. . . In this work we have studied how different
phosphatidylethanolamines differing in acyl chain saturation influence the formation of laterally
segregated domains. Three different phospholipid systems were studied: DOPE:POPG, POPE:POPG,
and DPPE:POPG at molar ratios of 3:1. Lipid mixtures were analyzed at 24 and 37 C through three
different model membranes: monolayers, liposomes, and supported lipid bilayers (SLBs).”
However, their basic research program was to study the connection between proteins and the basic
phospholipids forming the inner bilayer phospholipids identified above. It did not provide any obvious
information useful in this work.
Meynaq106 began a systematic study of phospholipids during his PhD program but did not report significant
impedance data. He did show that most ions did not penetrate his membranes, although they did associate with
the various head groups of the phospholipids to different degrees. He designed a 4–electrode test chamber
reminiscent of a Ussing apparatus in his Paper I, but reverted to a 2–electrode configuration to avoid what he
described as large measurement errors. No absolute resistance or resistivity measurements were provided.
2.2.1.3.4 An alternate family of potential phospholipids
Calder presented figure 1 in Section2.1.4.7.5, reproduced as Figure 2.2.1-7, showing multiple depictions of
docosahexaenoic acid, DHA or C22:6n-3. The nutrition community has identified DHA as a large component in
neural lemma, and the photoreceptors of vision. The figure includes a variety of representations of this
molecule. Note, DHA is not conjugated, but has a methylene group in line between each pair of double bond.
This lipid when incorporated into a liquid crystalline phospholipid of a type lemma may provide the necessary
conductivity. See Section 2.1.4.7 more details.
106Meynaq, M. (2017) Electrochemical investigations on Lipid Cubic Phases PhD Thesis, Sweden: Umea Univ
56 pages
88 Neurons & the Nervous System
Figure 2.2.1-7 Four configurational representations of DHA. Note the form used
in lemma is believed to be the all-Cis- version of DHA. “DHA has 22 carbons and
6 cis double bonds in its hydrocarbon (acyl) chain. The α-carbon is the carbon
of the terminal carboxyl group (COOH) and the ω-carbon is the carbon of the
terminal methyl (CH3) group.” Adapted from Calder, 2016.
2.2.1.3.5 Spacial parameters of the neural phospholipids ADD
Suwalsky, provided a thorough review of the phospholipids found in biological membranes in 1988. He also
provided a considerable list of citations to the work of others.
A caution; in discussing the phospholipids, they are often described as di-acyl . . . . This term generally
refers to the 1st and 2nd groups of the glycerol moiety of the phosphoglycerides and not to the lipids
present. While the two acyl groups are identical, the aliphatic backbone of the lipids may differ. Space
filled models of phospholipids found in textbook frequently suggest the two lipids are identical in a given
molecule, with a frequent comment in the text that the lipid associated with position 2 is unsaturated
(frequently suggesting only a single double bond along the aliphatic chain. As noted above, it is
conceivable for the lipid at position 2 to provide as many as five double bonds within an 18-carbon
chain. The ability of each of these double bonds to provide an electron to the lattice structure of the
liquid crystalline state of the phospholipids of a lemma leads to their representing a donor dopant within
the crystalline lattice. Acting as a dopant, these bonds can change the resistivity of these molecules, and
the associated lattice, significantly. It is proposed in this work that the di-acyl’s of a given molecule in
type 2 membrane are not attached to identical lipid structures (at least in a significant fraction of the
The Neuron 2- 89
phospholipids present). As a result, it is necessary to describe the molecules in the type 2 membrane
using longer labels than exemplified by DMPE, DMPC etc. defined in Section 2.1.4.
A quick primer on crystallography can be found at http://web.pdx.edu/~pmoeck/phy381/lecture3.pdf by
Portland State University staff.
Suwalsky et al107. described the structural arrangement of the liquid crystalline bilayers in the language of
crystallographers, using a,b,c for the dimensions of a unit cell with the length parallel to long aliphatic lipids
given by ½c and the long axis of the glyceride aligned with the a axis.
107Suwalsky, M. Tapia, J. Knight, E. (1986) X-ray studies on phospholipid bilayers. VI: Comparative hydration
Effects on oriented films Macromol Chem, Macromol Symp 2 pp 105-112
90 Neurons & the Nervous System
Phospholipid a length, b length, ½c length, S surface area, ( )2
DMPE 7.56 9.82 51.10 37.1
DLPE 8.00 9.85 46.32 39.4
DPPE 8.50 10.24 56.00 43.5
DMPC (DML) 9.40 10.03 54.84 46.7
* at humidity between 86 and 92%. ½c represents the repeat distance, small d, of one bilayer. The actual
length, large D, of one DMPE molecule has been given as 50.65 by the same team.
The acronyms beginning with a D for di– must be looked at carefully when attempting to understand the
electronic performance of the outer bilayer of a type 2 neural lemma. The implication is that both lipids
of the molecule are the same, which normally does not occur in biological phospholipids, except possibly
those of type 1 membranes acting as excellent insulators. The expanded nomenclature of McIntosh is
needed when discussing specific areas of the lemma of neurons (Section 2.1.4.5).
Suwalsky describes the space group of the phospholipids as P2 and notes “the unit cell is monoclinic with
orthogonal axes, pseudocentered in the C phase.” He also notes, “There is also a considerable number of
hydophobic interactions between neighboring hydrocarbon chains.” He does not expand on the character of
these interactions or whether they involve double bonds.
The INTRODUCTION of Suwalsky et al. is repeated in the Suwalsky text and asserts, “They are zwitterionic
molecules of amphipathic nature with a tendency to aggregate, i n the presence or absence of water, in bilayers
which exhibit complex lyotropic and thermotropic polymorphism.” The DISCUSSION provided in this paper is
quite concise, and important;
“An analysis o f the results permit to conclude that the four phospholipids show several common structural
features, including the following:
a) Their hydrocarbon chains are mostly parallel and fully extended, packed as close as possible.
b) The polar groups are coplanar and lie perpendicularly with respect to the hydrocarbon chains.
c ) The molecules stack laterally to form monolayers. Bilayers are formed through molecular interactions at the
ends of the hydrocarbon chains i n such a way that the monolayers are related by two-fold rotation axes
perpendicular t o the planes.
d) Hydrophobic interactions between the hydrocarbon chains and electrostatic attractions between opposite
charges of neighboring polar groups stabilize the bilayer structure.
At the same time the four phospholipids present some interesting differences such as:
a) The bilayer repeat distance o f the acylphosphatidylethanolamines DLPE, DMPE and DPPE d i f f e r i n that
order by about 5 . This is not surprising as this distance approximately corresponds to the length o f the four
methylene groups they differ in their hydrocarbon chains.
b) The packing i s closer in the acylphosphatidylethanolamines than in DML (DMPC), an effect which might be
due t o the smaller volume of t heir terminal amino groups.
c) DML presents higher degrees o f hydration than the other phospholipids at about the same relative humidities.
On the other hand, excess of hydration does not seem to affect significatively the packing arrangement of the
acylphosphatidylethanolamines as compared to DML.
All these similarities and differences might be related to the functional role played by the phospholipid bilayers
in the cellular membranes.” In the context of this work, the functional role includes a significant electronic role
in neural signaling.
It is important to note that the multi-letter acronyms above do not define the specific lipids of a given molecule
in all cases, especially their state of saturation. The more complete terminology appearing in the 1990's, such as
POPC for 1-palmitoyl 2-oleoyl, sn-glycero 3-phosphocholine, is critically important (Section 2.1.4.5) to the
understanding of the electrical performance of the outer bilayers of the lemma. The dipole bonds associated
with the lipid components define the dopant level of the lipid when viewed as a semiconductor. This dopant
level greatly impacts the resistivity of the local region of the outer segments of the lemma (Section 2.1.4.4). It
accounts for the range of 1000:1 in the resistivity of natural bilayers in the table from Quinn (1976). He shows
an even wider range, 106:1 for synthetic phospholipid bilayers, based apparently on a literature search.
Ziblat et al. (2010) used the capital D to refer to specific lipids, as in dipalmitoylPC, rather than the less specific
diacylPC of the 1980's. In their paper, they used both the labels DPPC and POPC as appropriate to describe the
symmetrical and asymmetrical lipid PC cases.
2.2.1.4 The Chemical theory of the plasmalemma at the end of 20th Century)
The Neuron 2- 91
The text of Deamer et al108. demonstrates the demarcation between the 20th and 21st Century in understanding the
plasmalemma of a neuron. While a tribute to Overton, it shows that the turn of the end of the 20th Century
proves Overton wrong in the light of semiconductor physics (see also Section 2.1.4.1). The recitation of the
permeability of a plasmalemma of a neuron, assumed to be a homogeneous material and following Nernst’ Law,
is replaced by a bilayer plasmalemma where each layer is known to be “amphipathetic or a polar lipids”
containing both a polar and lipid groups. Films of such amphipathetic molecules are known to be highly
impenetrable to either polar or lipid molecules, contrary to Nernst’ Law (page 69-72 in Deamer et al. written by
Pohorille et al109.). This fact caused the concept of pores or channels through the plasmalemma to arise.
After over 20 years, no data has yet to be presented demonstrating the EXISTENCE, even transient
existence, of pores through the bilayer of a plasmalemma of a neuron.
Chapter 4 by Paula & Deamer in the Deamer et al. text expands on the discussion in Pohorille et al. They note
on page 78
“We now know that despite being approximately the same size, solutes as sodium ions, hydrogen ions,
water, and oxygen permeate the lipid bilayer at rates that vary by 12 orders of magnitude. How could
such a vast difference in permeation rates be imposed by a seemingly simple bimolecular layer of
amphiphilic molecules?”
Part of the answer is simplicity itself; the ions mentioned are much larger in diameter when in the hydrated
state (figure in Section 2.1.4.3.2). As it will be shown in this work, the hydrogen ion is replaced by the much
smaller electron based on semiconductor physics; this makes the size differential even larger. This is also
recognized on page 78,
“Surprisingly, hydrogen ions (protons) penetrate the same bilayer at rates 5 orders, of magnitude faster
than other monovalent cations.”
This fact is also simply explained under the principles of semiconductor physics; a proton does not flow through
a liquid-crystalline semiconductor, it is replaced by a “hole,” an electron moving to replace a physical absence
of an electron from another nearby ion in the liquid-crystalline material. While the motion of the apparent hole
is slower than the normal electron flow in the opposite direction, the “hole velocity” is characteristic of a p-type
semiconductor. On page 94, they come closer to the semiconducting “hole” when speaking of 14 carbon
phosphatidylcholines, PtdCho, (a chemical known to be a dominant constituent of plasmalemma) they assert,
“Here the best explanation is that very short-lived strands of hydrogen-bonded water in the defects allow
protons to cross by hopping along hydrogen-bonded chains of water molecules, a mechanism that is not
available to other cations.”
This is an absurd explanation, except for the assumption that the PtdCho strands perpendicular to the
plasmalemma surface are highly hydrogen bonded to each other.
In Section IV, they discuss the their concept of permeation through transient pores followed by Section V on
their concept of proton permeation. They cling to conventional chemical theory rather than semiconductor
physics, and using ridiculous thin membrane thicknesses in their graphics (Section 2.2.2.3.1 ).
The remainder of their chapter assumes a homogeneous plasmalemma that obeys Nernst’ Law in contradiction
to the plasmalemma defined by Pohorille et al. The many graphs included can by discarded as inapplicable to
the actual plasmalemma situation.
On page 87, in summarizing their chapter, they reverse their position on page 69 by noting,
“When calculating permeability coefficients according to the solubility-diffusion mechanism, it is crucial
to use hydrated ionic radii, as bare radii give values that are orders of magnitude below experimental
results. This is most apparent for protons, which give absurd values if the bare radius is used. It has
been shown that ionic permeation can be described properly by using hydrate radii in conjunction with
the solubility-diffusion mechanism [of page70for the inhomogeneous material] (Paula et al, 1990,
108Deamer, D. Kleinzeller, A. Fambrough, D. eds. (1999) Membrane Permeability: 100 Years since Ernest
Overton. NY: Academic Press
109Pohorille, A. New, M. Schweighofer, K. & Wilson, M. (1999) Insights from computer simulations into the
interaction of small molecules with lipid bilayers In Deamer, D. Kleinzeller, A. Fambrough, D. eds. Membrane
Permeability: 100 Years since Ernest Overton. NY: Academic Press Chapter 3
92 Neurons & the Nervous System
Figure 2.2.2-1 The differentiation of a stem-cell into a
variety of neurons. Other cell types are shown for
orientation and discussion purposes. See text.
1998).”
2.2.1.5 The dipole potential of the biological bilayer membrane (BLM)
When addressing the chemoreceptor modalities of the neural system, it will be appropriate to address another
quantum mechanical concept, the dipole potential of a highly polar phospholipid molecule forming specialized
regions of neural lemma (type 4 lemma). The dipole potential of each layer of a bilayer exhibits a dipole
potential in the 250 to 600 mV range, although since the two layers are arranged back to back, the potential
across the membrane is nearly zero. However, the potential of the interstitial space between the bilayers can be
substantial and is subject to the transduction mechanisms of sensory operation (Sections 8.5 & 8.6). Gennis has
provided considerable data and several citations relative to the dipole potential and surface potential of type 4
lemma110.
2.2.2 Development of the functional structure of the neuron
A brief discussion of cell evolution and differentiation will appear first in this section to aid in orienting the
reader. The section will then develop the structural features of a neuron that are directly related to signaling.
This will provide the groundwork for the next section that will discuss the paradigm shift necessary on this more
detailed understanding of the neural system.
2.2.2.1 Evolutionary path from stem-cell to neuron
Figure 2.2.2-1 provides a roadmap for the differentiation of a proto-cell (stem-cell) into one of a variety of
neurons. A stem cell can differentiate into one of at least four different cell families. The family of most
interest here is the neuro-secretory family, B. This family is primarily involved in signaling within the organism
but does support exocrine signaling. It can readily be divided into three major subfamilies depending on how
signaling is accomplished. The first is any form of signaling not involving the neural system (and assumed to be
chemically-based). The second is the conventional neuron-to-neuron signaling. It will be shown this method
involves only electrons and their
counterpart, “holes.” The third
is the large class of neuron to
non-neuron signaling that
encompasses both the paracrine
situation, the conventional
hormonal system consisting of
endocrine and pericrine
situations and the exocrine
situation. It will be shown the
pericrine and endocrine
situations involve neuro-
hormonal agents that can be
classed as neuromodulators.
These neuromodulators affect a
wide variety of cell types, not
just neurons. The pericrine
situation will be introduced in
Section 2.7.2.
The biological community has
defined communications within
the organism very broadly. It is
critically important that this term
be clearly defined in this work.
Signaling in the broad biological
sense will be addressed first.
Signaling can be considered any
mechanism by which two cells
communicate their mutual
location, or their intent, in order
110Gennis, R. (1989) Biomembranes. NY: Springer-Verlag Chap 7
The Neuron 2- 93
to support morphogenesis beyond that related to the genetic code. This signaling occurs within a single
organism. At this level, the mechanisms of signaling are not well understood but are assume to involve chemical
agents. The implementation of neural paths along a nerve or as the nerve extends would appear to involve this
type of signaling.
Signaling of a more time sensitive character, supporting a wide range of bodily activity and involving signal
transmission speeds at rates on the order of one meter per second or less can be accomplished by conductive
flow via the vascular or lymphatic (ducted) systems of the body. This is the domain dominated by the endocrine
system.
Signaling of a time critical character and involving signal transmission speeds at rates on the order of four
meters/second or faster can only be accomplished within the neural system itself. This mode of transmission is
dependent on the speeds achievable by electronic propagation (not chemical means). The capability of the
neural system implemented to satisfy this high signaling rate requirement is so useful, it has been expanded into
a much more capable neural system. This capability was implemented using groups (knots) of neurons to
perform more complex signal manipulation. This expanded capability eventually evolved into major neural
centers containing many knots of neurons. These became known as brains.
Simultaneous with the development of neural signal manipulation was the development of dedicated modalities
of sensing both the internal and external environments of the organism.
With this rise in neural signaling capability, an additional neuro-chemical signaling mechanism was introduced
that has come to be known as the exocrine system. The exocrine system, in conjunction with the olfactory
system has resulted in the pheromone system of inter-organism communications within a species.
Spaargaren, et. al. explored the subject of biological communications recently from the conventional
perspective111. They did not recognize the existence of electrolytic signaling throughout the neural system nor
the mechanisms used within neurons to achieve very high signal transmission speeds.
Their introduction defines the scope of their discussion. “Optimal functioning of an organism is only possible if
the individual cells that make up the different tissues and organs are able to communicate with one another in
order to coordinate their growth, division, development, differentiation, and organization.” Thus, their work
focuses on the non-neural signaling (#1) in the above figure. Their discussions of all three areas of
communications within an organism remained primarily conceptual at that time and can be considered largely
archaic at this time. It will be shown that the classical neurotransmitters of 20th Century biology (prior to 1995)
are not related to signaling within the neural system. They play a significantly different role.
This work will develop the primary role of the neural system as the source of the initial hormones of the
hormonal system (Chapter 16).
2.2.2.2 Local view of neuron formation from a stem-cell
Figure 2.2.2-2 provides a caricature of the development of a functional neuron from a simple cell, a neurogen.
In the current vernacular, the neurogen is called, or is derived from, a stem-cell. The process is straight forward
but sophisticated. The metabolic and growth aspects of the cell will not be addressed here.
In order to provide a foundation for the following paragraphs, it is useful to define a reference situation which
will be called a fundamental cell: i. e. a living organism consisting of a continuous, single outer membrane
enclosing a variety of cytological elements. The outer membrane is more commonly called the plasma
membrane, and is recognized to be a bilayer consisting of two leaflets as described earlier. This situation is
represented in frame (A). The majority of the plasma membrane is of type 1 lemma. The outer membrane
necessarily contains a site of type 3 lemma for exchanging materials between the interior of the cell and the
surrounding electrolytic matrix and potentially contains a type 3 lemma acting as a secretory site. Sensory
neurons, those originating afferent neural signals generally contain secretory sites. Similarly, a variety of
neurons terminating efferent paths are characterized by their secretory capability. A nucleus is shown at an
arbitrary location in each frame of the figure for completeness; it plays no role in neural signaling.
From an electrochemical perspective, the fundamental cell is a region enclosed by a plasma membrane. The
inside of the cell is filled with a heterogeneous electrolyte of finite conductivity. The cell is surrounded by an
electrolyte of finite conductivity containing bioenergetic materials capable of supporting a glutamate cycle as
111Spaargaren, M. Delaat, S. & Boonstra, J. (1993) General mechanistic patterns of signal transduction across
membranes, Chapter 1 in Shinitzky, M. ed. Biomembranes: Signal Transduction Across Membranes. NY:
Balaban Publishers
94 Neurons & the Nervous System
part of an electrostenolytic process (Chapter 3). Both of these electrolytes may be more completely described as
to their viscosity and ionic content. The electrolyte within the cell is generally gelatinous and may be in a true
liquid crystalline form. The external matrix may also be gelatinous or a liquid crystalline material.
Somewhere on the surface of the membrane is an area of type 2 membrane supporting an electrostenolytic
process, E S. (indicated by the rectangular bar at the bottom of the cell in frame (A). Because of this
electrostenolytic activity, the cytoplasm of the cell exhibits a negative electrical potential with respect to the
external electrolyte under quiescent conditions. Little or no energy is required to maintain this quiescent
condition because a majority of the plasma membrane is an electrical insulator and impervious to the flow of
both ionized atoms and fundamental electrical charges
It is tantalizing to consider the possibility that the initial purpose of the electrostenolytic process
(Section 3.2) was to inflate the individual cell to a spherical shape by the well known electrostatic
principle that like charges within a closed space will seek to distance themselves from each other.
As the neurogen evolves into more specialized forms, a variety of internal membranes may be formed within the
cell and multiple electrostenolytic sites may be formed on the surface of the cell.
The Neuron 2- 95
Figure 2.2.2-2 Cytological evolution of a cell to 1st and 2nd order neuron. The black bars
represent areas of type 2 lemma. (A), a simple cell or neurogen, a stem-cell in the current
vernacular. The nucleus, a potential secretory site and a potential material transfer mechanism
are shown. A nucleus is shown at an arbitrary location, it plays no role in neural signaling. (B),
two variants of the 1st order neuron. (C), a second order neuron. (D), a fully functional neuron
within a neural signaling path. See text.
96 Neurons & the Nervous System
2.2.2.3 The first order neuron, non-functional
Frame (B) illustrates the 1st order neuron at two separate stages of development. There is no data to define
which occurs first. On the left, the cell is seen to have formed three separate plasma enclosures through the
development of interior membranes connected to the plasma membrane by lap joints. At the center of the cell,
the two interior membranes have become juxtaposed so as to form a potential Activa (shown by the vertical
black bar). However, all of the plasmas remain at essentially the same electrical potential. On the right, an
alternate first step is shown where the cell has formed the same three separate plasma enclosures through the
development of the same lap joints. It has then proceeded to create two more areas of specialized plasma
membrane supporting additional electrostenolytic activity. The three plasmas are now capable of sustaining
different electrical potentials depending on the precise nature of the electrostenolytic activity at each site on the
surface of the plasma membrane. However, no electrically active junction has formed within the cell.
The Neuron 2- 97
Figure 2.2.2-3 Subcellular fraction of gap
junctions isolated from rat liver.
(204,000X) See text. From Gilula (1975).
2.2.2.3.1 Examples of lap joints & electrostenolytic mechanisms
It is important to establish two features of a neuron before proceeding. Eckert112, in 1988, said “Membranes are
never seen to terminate with free ends; they always form enclosed compartments.” While a useful pedagogical
concept, there is some question about this statement based on Figure 2.2.2-3 at a magnification of 204,000x
taken from the work of Gilula113 and the work of many others. Although drawing conclusions about three-
dimensional structures from two-dimensional images is always dangerous, it would appear that Eckert’s
statement should be broadened to at least allow for lap joints between membranes. Because of the bi-leaf
structure of individual membranes, it appears that individual membranes cannot end by tapering away to zero
thickness. They can and in fact do end abruptly. Thus, lap joints may be used to form tight junctions. After
forming a tight junction, the membrane may end abruptly. This would insure that there is no communication by
diffusion among the three electrolytic chambers involved in a typical structural junction.
In the left of Figure 2.2.2-3, there is a piece of membrane which appears to be of finite length, to end abruptly
on each end and to be sandwiched in between two separate membranes. Many other examples of abrupt
membrane terminations are seen in the figure.
On the right of this figure, there is another
interesting example. A membrane is shown
forming a complete loop. Although the original
caption by Gilula, speaks of this non-junctional
membrane as contaminating the fraction; this
author would take a different view. Specifically,
the loop forms a separate conduit that extends out
of the plane of the figure. The out-of-plane
portion of this conduit can include a wide variety
of functional elements. These elements can
change the potential of the plasma inside the
conduit relative to other plasmas, connect with
other neurons through a gap junction etc. It is
interesting to note the preponderance of three
membrane sandwiches in this figure. It is also
interesting to note the significant defocusing of the
image of the membrane in the center of the figure
and at lower left. This defocusing may be due the
membranes departing from the focal plane of the
microscope. However, this is unlikely due to the
depth of focus of electron microscopes and the
apparent perpendicularity of the membrane to the
focal plane. An alternate suggestion is that these
“fuzzy” areas are sites of charge accumulation and
are involved in some form of electrostenolytic
process (Chapter 3). The focus of Electron
microscopes is easily disrupted by electrical
charge present in the focal plane. Thus, a revised
caption for the orginal figure might read: “Arrow
points to an area of membrane separating two
plasmas and actively involved in the electrical
circuitry of the cell.”
Electron microscopy invariably shows that the bilayer of a membrane is about 75 ±15 Angstrom thick. When
combined into a bilayer, the membrane is typically 160 Angstrom thick and appears as two distinct dark lines
separated by a space appearing lighter. This sandwich is usually defined as consisting of two phosphoglyceride
layers, the hydrophobic tail of the two layers facing each other (the light area) and the two hydrophilic heads
facing outward (the two dark areas).The practical width of the membrane may be wider than the above value due
to the specific structures associated with the hydrophilic heads. By reversing the contrast of the microscope
imagery, as in the above figure, the outer edges of the membrane, sometimes described as the Helmholtz
regions, are better illustrated. Frequently, the sandwich is not symmetrical. The head group facing “outward” in
112Eckert, R.(1988) Animal Physiology. 3rd ed. NY: W. H. Freeman pg. 65
113Gilula, N. (1975) Junctional membrane structure In Tower, D. ed. The Nervous System NY: Raven Press
figure 6
98 Neurons & the Nervous System
a cell wall is normally mostly choline related (typically phosphatidyl choline or PC) and the head group facing
“inward” is composed mostly of ethanolamine related ligands (typically phosphatidyl ethanolamine or PE). In
the case of stage 2 lemma, the head of the outward facing phospholipid is more complicated chemically and acts
as a chemical receptor in a variety of stereochemical situations.
2.2.2.4 The configuration of the fully functional second order neuron
(C) in the above figure shows the cell continuing to evolve. It now exhibits three separate internal plasmas, each
of which exhibits a different electrical potential compared to the surrounding electrolyte due to the
electrostenolytic sources present. There is a fully formed Activa at the juxtaposition of the left and right-hand
internal membranes. The cell remains in overall electrochemical equilibrium. However, the Activa is fully
functional and it influences the potential between the various plasmas. The relationships between the potentials
of these plasmas will be discussed further in Section 2.3 following the development of additional background
material. Synapses are also shown between the left and right plasmas and the presynaptic and post synaptic
neurons.
2.2.2.5 Preview of the fully functional neuron in a neural signal path
(D) shows the fully functional neuron interfaced with two adjacent cells to form a continuous neural signal path.
These intefaces, or synapses, also include Activas and are represented by the two vertical black bars. If the
electrostenolytic processes have provided the correct biases to the internal Activa and a charge is injected into
the dendroplasm of the neuron from the axoplasm of the neuron shown in partial view on the left, the Activa will
cause a charge to appear in its axoplasm. This charge will change the potential of the axoplasm. A change in
this potential will cause charge to be transferred to the dendroplasm of the neuron shown in partial view on the
right via the synapse shown. Thus, signaling will have been achieved. This signaling is inherently analog in
character.
Cole was the first investigator to recognize the unique electrical properties of the synapse formed between
neurons. His discussion of these properties occurred in 1968. It truly described the properties of an Active
configured as an “active diode” (Section 2.4.2). His discovery of these electrical properties were baffling to
those without any training in semiconductor physics.
The Neuron 2- 99
2.2.2.6 Fully elaborated schematics of fundamental neurons
Recent texts on neuroscience and neurology have not discussed the detailed schematics of neurons. Previous
texts have relied upon schematics of common cells to describe neurons. This reliance has constrained
understanding of the fully elaborated neuron. This section provides an overview of the fully elaborated neuron
prior to providing all of the data substantiating the model. This additional material will be provided within the
following sections of this volume.
Figure 2.2.2-4 reproduces a common representation of a neuron and its interconnections from a histological
perspective114.
The nucleus (open circle) plays no role in the electrolytic operation of the neuron. Antidromic axons may
contact a neuron in multiple ways. The most common is the axodendritic synapse that can occur anywhere on
the dendritic structure. Less common is the axopoditic synapse where the axon contacts the base region of the
Activa within the soma of the neuron. The label axosomatic synapse is archaic. It does not describe the actual
functional arrangement. The poditic terminal may arborize. In that case the arborization coming to a focus on
the pointed top of the neuron is the dendritic arborization. The arborization connecting to the neuron around its
basal periphery constitutes the poditic arborization. A neuron so arborized is frequently labeled a bi-stratified
neuron. The axospinous synapse appears to be particularly important in forming memory engines within the
stage 4 neurons. The contact between the axons and the dendritic spines have been shown to be quite dynamic
in their existence. The axon hillock is a region of low electrolytic impedance where the electrical signal at the
output of the Activa is particularly easy to measure (especially if the neuron is generating monopulses (action
potentials. Axons do not normally bifurcate except at Nodes of Ranvier.
Figure 2.2.2-4 A composite neuron–Synapses may form on different elements of
a neuron. Presynaptic terminals or boutons may contact dendrites directly
(axodendritic synapse), contact dendritic spines (axospinous synapse), or
contact the poditic (base) region of the Activa within a neuron (axopoditic
synapse). See text. Modified from Cohen, 2016.
114Cohen, R. (2016) Cell biology of the synapse In Pfaff, D. & Volkow, N. eds. (2016) Neuroscience in the 21st
Century, 2nd Ed. NY: Springer
100 Neurons & the Nervous System
The axons on the right may contact other neurons through electrolytic synapses, contact muscle tissue through
chemical synapses or release endocrine chemicals when the neuron is acting as glandular tissue.
2.2.2.6.1 Examples of lap joints & electrostenolytic mechanisms
Cantarow & Shephartz provided a detailed schematic of a prototype cell in 1967115. Figure 2.2.2-5 extends
their schematic to include the additional functions associated with a neuron (a neuro-secretory cell). The central
portion of the figure is similar to the Cantarow & Shephartz cell, with some of their detail omitted. The left-
most portion adds the unique neural functions found in all neurons. The right-most portion adds the unique
secretory functions. Both the neural and secretory portions are found in nearly all sensory neurons and are
critical to the operation of the digestive system. However, the sensory neurons are more complex and are
discussed initially in Chapter 8.
The bilayer form of BLM’s was discussed in the previous section. This figure highlights the lap junctions
necessitated by this form. This form requires all junctions between membranes consist of lap joints (as shown
along the top edge of the figure only to save space). The outer perimeter of the neuron is defined as the
plasmalemma, even though parts of it may be formed of axolemma, dendrolemma, etc.
The neural portion consists of three distinguishable chambers (conduits) that will be described in detail in the
following sections. Note the narrow region of the podite conduit containing podaplasm and separating the
dendrite and axon conduits. The secretory portion may or may not be a separate chamber, independent of the
soma.
115Cantarow, A. & Schepartz, B. (1967) Biochemistry, 4th Ed. London: W. B. Saunders. pg 2
The Neuron 2- 101
Figure 2.2.2-5 A more fully elaborated schematic of a fundamental neuron. All
membrane junctions are lap joints (as shown only along the top edge). The
housekeeping functions shared with the prototype cell are shown in the center.
The label “Vitamins & Hormones” includes other complex molecular entities.
FA; fatty acids. AA; amino acids. The additional secretory functions are shown
on the right. The additional neural functions are shown on the left. Dotted shapes
on the left are portions of adjacent neurons. Note the three separate conduits
associated with the neural portion, including the podaplasm filled podite. See
Text.
The general signal flow within a neuron consists of “holes” traveling orthodromically along the signal path when
within membranes and between membranes within junctions. As a result, electrons are found to flow
antidromically (toward the initial sensory location) along the signal path, as shown by the vertical arrows on the
left. Electrons associated with the electrostenolytic (biasing) function move into the various conduits and soma
of the neuron from the INM. This is accomplished by hole transport within the membrane.
Cantarow & Shephartz describe the inter neural matrix as a protein-mucopolysaccharide complex. This
terminology combines (confuses) the basic matrix and the materials diffusing through it.
The type 1 membrane shown in the figure is impervious to all biological molecules, electrons and holes. The
type 2 membrane is impervious to biological molecules but directionally semipermeable to electron and holes.
The type 3 membrane is impervious to electrical charges but semipermeable to large biological molecules (and
other molecular complexes). All electrical activity associated with the neuron is associated with type 2
membrane. Some type 2 membrane is associated with the electrostenolytic process providing electrical bias to
102 Neurons & the Nervous System
the individual conduits and chambers of the neuron. Other type 2 membrane forms the active semiconductor
devices between the conduits within a neuron and between the conduits of separate neurons. The requirement
that type 3 membrane be impervious to electrical charges is seen in the membrane separating the neural conduits
from the Soma. Operation of the neuron requires electrical isolation while requiring the transfer of materials for
maintaining homeostasis and growth.
The individual segments of type 3 membrane shown at the bottom of the housekeeping portion may be specific
to individual materials. As noted elsewhere, the biological membrane is largely impervious to simple metallic
ions, such as sodium and potassium. While sodium and potassium may exist at very different concentrations on
opposite sides of the plasma membrane, this difference is not associated with the transport of the simple ions
through the membrane. These material may be transported within larger, electrically neutral, molecular
complexes.
Cantarow & Shephartz provide additional detail concerning the materials manufactured within each of the cell
elements shown. The key functions not addressed by them are the production of secrete-able proteins (such as
opsin in the case of the photoreceptors), and the release of glutamate into the surrounding inter neural matrix
(INM) to support electrostenolytics (Chapter 3)..
The conversion of glucose into glutamate within the neuron surfaces an interesting situation. The formation of
glutamate via glycolysis and the TCA cycle is an anaerobic process. It requires other amino acids and releases
either carbon dioxide or water during the processing. Thus the powering of the neural portion of the neuron is
anaerobic! However, the carbohydrate metabolism within the neuron is aerobic! This difference makes it
necessary to be precise when discussing the metabolism of the neuron.
The absolute number of chemicals needed to support the homeostasis of a neuron illustrates the difficulty in
describing specific disease conditions and the potential for a condition to be related to multiple shortfalls in
supplies. It also illustrates how multiple pharmaceuticals could interfere with a specific absorption site and
result in the same disease.
The chemical operation of the neuron in support of neural signaling will be developed in detail in Chapter 3.
The process is shown schematically by the curved arrow and electron flow symbol associated with each neural
chamber. Later material will suggest that at least sections of the plasma membrane are bilaterally symmetrical
in permeability to glutamate. It is not clear whether there is a membrane separating the housekeeping and
secretory functions.
Cantarow & Shephartz (along with the rest of the neuroscience community up to this day) were unaware of the
operation of the Activa within and between neurons. The synaptic gaps involve the transfer of electrons (or
holes) between neural conduits. Fully elaborated neurons do not secrete any material within the synaptic gaps
shown. The earlier figures found in the neuroscience literature do not address these functions in sufficient
detail116. They will be addressed below in detail. The caricature provided by Shepherd is unable to account for
a number of features of real neurons, specifically the ability of charge to move the length of a two millimeter
axon segment within a fraction of a millisecond. The actual rate of electronic signal transmission along an axon
segment significantly exceeds one thousand meters per second. However, the Nodes of Ranvier introduce
significant delay. The average signal velocity is near 4 meters/sec. Even this number remains far above the
proposed chemical transmission (by diffusion) at a fraction of a meter per day.
116Shepherd, G. (1988) Neurobiology, 2nd Ed. NY: Oxford University Press. figure 3.14
The Neuron 2- 103
Figure 2.2.2-6 Schematic of a complete visual sensory neuron. The figure is similar
to the previous except for the generalized label, protein, being replaced by opsin at
upper right and the redrawing of the signal input structure at the upper left. See
text.
2.2.2.6.2 The fundamental sensory neuron
The fully elaborated neuron of the previous figure can be detailed to represent a visual sensory neuron as shown
in Figure 2.2.2-6. The secretory mechanism has been tailored to secrete opsin, the protein forming the disks of
the outer segment of the photoreceptor neurons.
The figure is very similar except in the upper right and upper left. In this case, the secretory function is active.
A protein is secreted into the surrounding medium. This protein can be either structural (forming a physical
structure with significant mechanical properties) or chemical (generally used to coat the outside of the neuron in
the vicinity of type 2 lemma). The variations in this area will be discussed in the following specific sections. In
either case, the initial signal is generated by the transfer of energy to the base region of the 1st internal Activa
shown symbolically at the upper left. The energy is transferred to the base region of the Activa formed by the
constriction of the dendroplasm to form a microtubule. This transfer of energy generates a free electron in the
base region of the Activa that constitutes the initial electrical signal. This electron passes through the collector
region of the Activa and into the exterior fluid matrix bathing the sensory neuron at that location.
For the remainder of this Chapter, the elements of the cell related to housekeeping, growth, glandular and
functions other than signaling will not be considered. As an example, the nucleus is not of significance
to this discussion. These elements will be assumed to be walled off from the electrical signal carrying
portions of the cell by the internal membranes, dendrolemma, podalemma and axolemma of the neuron.
104 Neurons & the Nervous System
2.2.2.7 Structural features of the second order fundamental cell
As noted above, a neuron includes a variety of internal membranes in addition to the enclosing membrane.
Furthermore, the enclosing membrane may consist of more than one layer of membrane (each a bilayer by
themselves) at some locations. The majority of each membrane, based on area, is composed of type 1 BLM.
The type 1 BLM is impervious to both electrical charges and molecular materials (whether ionized or not).
Besides forming a physical barrier, it acts as a dielectric contributing considerable capacitance between the
electrolytes on each side of the membrane. It is the regions of type 2 and type 3 BLM that define the overall
performance of the neuron. These membranes may provide a variety of functions beyond those of interest here.
From the electrical perspective, these membrane configurations provide at least the following functions:
+ partitioning the cell electrically from the exterior environment
+ partitioning the cell electrically into internal regions containing different heterogeneous materials.
+ supporting an electrical potential between the above regions and/or the external environment.
+ controlling the electrical impedance between the above regions.
+ provide an active device “based on transistor action” between some of the above regions and/or
the exterior of the cell.
The presence of a single type 2 region of membrane between two plasmas, supported by electrostenlytics, can
provide both an impedance between these two regions and a change in potential between these regions–two very
useful mechanisms in electrical circuits. As mentioned previously, the impedance of a BLM does not represent
a resistive element. Using Thevinen’s Theorem, the impedance of the membrane can be represented by a diode
in parallel with a capacitance.
Here again, it is important to point out that Thevinen’s Theorem does not apply to
more complicated circuits which include a variable impedance unless the voltage or
current level is specified. Specifying these levels complicates the application of
Thevinen’s Theorem greatly.
The electrostenolytic process acts as a current source, injecting electrons into the space on the opposite side of
the membrane from the point of chemical reaction. The current source is accompanied by an electrical
impedance that is a function of the active area of the electrostenolytic process on the membrane and both the
reaction kinetics of the process and the hydraulic system providing the reaction constituents and removing the
reaction products.
The presence of two very closely spaced membranes can provide even greater electrical complexity and
opportunity. The scope of these complexities and opportunities is directly related to the distance between the
two membranes. Here again, the literature is not well focused. For this work, three classes of juxtaposed
membrane pairs will be defined based on the distance between the edges of the two membranes:
+ Tight junctions, spacing typically zero Angstrom (definition probably inadequate)
+ Gap junctions, spacing typically 20-50 Angstrom
+ Chemical junctions, spacing typically greater than 200 Angstrom
The tight junction by definition does not allow for the presence of any independent electrolyte to exist between
the two membranes. The gap junction limits the material between its two surfaces to liquid crystalline material.
The chemical junction can maintain a conventional fluid environment between its two surfaces. The last two
junctions are those generally related to neural signaling processes. The gap junction is used in internal Activa,
in Nodes of Ranvier and in synapses.
Figure 2.2.2-7 is significantly modified from Pappas to illustrate the typical gap junction based on the above
terminology and this work117. A comparison between the variants in thickness of the various phospholipids (and
117Pappas, G. (1975) Junction between cells. In Weissmann, G. & Claiborne, R. ed. Cell Membranes:
Biochemistry, Cell Biology & Pathology. NY: HP Publishing Co. Chap 9, pp 87-94
The Neuron 2- 105
Figure 2.2.2-7 Caricature of a gap junction
as it appears in cross section in the
neurological system. Two type 1
membranes are shown at the top of the
figure (symmetrical lipid layers). Two type
2 membranes are shown at the bottom
(asymmetrical lipid layers). Modified from
Pappas, 1975.
their extension justifying physical channels between the two plasmas) is instructive. The labels have been
changed to allow the figure to represent a broader range of situations. In the case of the Activa within a given
neuron, the two plasmas are both internal to a given neuron (cell). The space marked interplasma space may
also be internal or external to a given neuron (and may in fact be a third plasma space within the same neuron).
In the previous figure, this internal space was defined as the podite conduit and was filled with podaplasm, an
electrolyte similar to that filling the other spaces.
The typical gap junction involves a space between two membranes that is so narrow that large molecules can not
persist there. They are essentially squeezed out of this space during the formative process due to Brownian
Motion. The material remaining within the gap junction is generally a liquid crystalline matrix of semi-metallic
water molecules. While membranes are frequently made up of back-to-back arrangements of the same lipids
(type 1 lemma and resulting in a highly effective electrical insulator), this need not be the case. In the gap
region, each membrane is made up of two asymmetrical lipid layers (type 2 membranes). This is indicated in the
figure by filling the heads of some of the lipid
molecules. The resulting configuration consists of
two electrical diodes connected back-to-back via a
single liquid crystalline, and semiconductive layer
of metallic water. This configuration is critically
important to the operation of the neural system as
shown in the following paragraphs.
The thickness of 80 Angstrom in the case of type 1
lemma may be significantly larger in type 2 lemma
because of the length of the phospholipid
involved. This added thickness may be a way of
locating areas of type 2 lemma.
The conventional explanation of how electrical
charge is transferred from plasma #1 to plasma #2
is to conceptualize large channels traversing the
gap capable of transporting large ions or
molecules (so-called neurotransmitters in the
chemical theory) across the barrier. Such
hypotheses require complex structures (frequently
labeled vesicles) within the membranes capable of
disgorging and accepting these materials within
the gap region. A distinction needs to be made
between such vesicles found within the gap region
and those found near the gap region. The actual
gap region is generally less than 500 nm, or one
wavelength of visible light, in diameter.
If the alternate case (the transfer of charge by the
flow of electrons) is examined, the materials
present can support the flow of this current
without the need for any physical channels. The
channels for electron flow within the semi-metallic
water material are quantum-mechanical and not
“physical.” The channels for electron flow within
the membranes are the long lipid structures within
the individual molecules. In this case, the vesicles
are found to be structural elements forcing the
mechanical formation of the individual electrically
active regions to be discussed in Section 2.3 The
vesicles are not active in signaling.
2.2.2.7.1 The molecular structure of the
junction between two membranes
Figure 2.2.2-8 provides a cross sectional view of
two membranes brought into close proximity.
Each membrane is the same as that shown in
Section 0.2.1.3 The two solutes are labeled the
dendroplasm and the axoplasm. The numbers 1
through 7 are those assigned by a cytologist to a
106 Neurons & the Nervous System
Figure 2.2.2-8 Structure of the Activa at the atomic level. In operation, the
configuration consists of two bilayer membranes (BLM) in close proximity and
appropriate voltages applied between the dendroplasm, the axoplasm and the
material in the junction area between the two bilayers (the podaplasm). The
lattices in the junction area are confined and form semi-metallic water while
those on the extreme left and right surfaces are more conventional water.
Detailed atomic structure of an individual membrane from Pearson & Pasher,
1979.
seven-layer junction between two bilayer membrane walls. Note they usually see layers 1, 3, 5 & 7 as dark lines
and assign 2, 4 & 6 to the light spaces between these lines. It is seen from this figure that the characters of these
spaces are different. Whereas 2 & 6 appear empty, 4 has a distinct character. In fact, the material represented
by 4 is critical to the operation of the neurons. A similar material that is performing a different function is found
between layers 1 & 7 and their respective plasmas. It would be advisable to number these regions 0 & 8 when
speaking of the functional performance of such a sandwich.
Note the complex molecular structure at the interface between each plasma and the corresponding membrane.
These areas are described in terms of relatively weakly bound water. The structure in the junction area, between
the two membranes is highly confined and consists of semi-metallic water. There is no physical movement of
ions within this overall structure at biological temperatures. No ions move through either the hydrophobic liquid
crystalline lipids or through the liquid crystalline semi-metallic water. This is true even under the influence of
external voltages.
Water ice exists in a large variety of forms. Chaplin has addressed its many forms at temperatures below
zero Celsius118. Forms of ice have also been encountered at higher temperatures in situations where the
molecules have been constrained in their movement to below the Brownian motion expected at that
temperature. After discussing lower temperature ices, Chaplin notes, “but other ices have been found at
confined surfaces. 'Metallic' water, where electrons are freed to move extensively throughout the
material and the atoms of water exist as ions, probably exists as an antifluorite type structurem.” and in
footnote m, “The antifluorite structure consists of a face centered cubic (FCC) unit cell with oxygen
anions occupying the FCC lattice points (corners and faces) and hydrogen cations occupy the eight
tetrahedral sites within the FCC lattice.” Metallic water is not an official name for any other form of ice
at this time.
The term semi-metallic water will be used here because only the electrical properties of the material are
of interest.
When configured as shown, the areas marked 3, 4 & 5 exhibit unique quantum-mechanical properties. These
properties result in a unique electrical feature as well. This feature is defined as an Activa. The unique
118Chaplin, M. (2011) Water Structures and Science http://www.lsbu.ac.uk/water/ice.html
The Neuron 2- 107
electrical feature of the Activa and the overall structure will be explored further in Section 2.3.
2.2.2.7.2 Spines along the dendrites of neurons
Particularly in stage 4 & 5 analog neurons, the dendrites are frequently found to exhibit thousands of spines
along their length, each spine in functional contact (synapse) with an antidromic axon. It is reported these spines
are frequently dynamic. Their synapse with an axon are presumed to mediate memory. The individual spine is
minuscule; Araya119 noted,
“Spines consist of a small head ( ~1 μm head diameter and <1 fL volume), separated from the parent
dendrite by a slender neck (<0.2 μm diameter) (Fig. 5). Spines were first described by Santiago Ramón y
Cajal in 1888. He was the first that stated that spines are real structures and not just an artifact of the
fixation technique or silver precipitates, as believed by many other scientists at the time. Ramón y Cajal
hypothesized that spines serve to connect axons with dendrites and that these structures are the places
where synaptic contacts are made rather than directly on the dendritic shaft. This revolutionary idea sets
the basis of his neuron theory. This theory indicated that neurons are independent units that connect to
each other via their axons and spines, instead of a continuous network, as the reticular theory stated.”
Figure 5 of Araya provides an electron micrograph of a layer V dendrite with multiple spaced spines. The
electrical circuit of a spine proposed by Araya is primitive. He speaks of it as simplified. It does not comport
with the active nature of a synapse. The Araya paper is extensive and worthy of further study. He discusses
both chemically and electrically supported synapses at spines. He asks several questions that are difficult to
answer in the absence of a better model than he employed;
“Several questions arise from these observations: Firstly, what are the molecular and biophysical
mechanisms (passive and/or active) by which spines behave as electrical compartments? Secondly, how
are synaptic inputs spatially and temporally distributed along the dendrites of a pyramidal cell? And
finally, under what physiological circumstances can spines undergo activity-dependent structural changes
that can modify the synaptic weight and thus the input/output properties of pyramidal cells?”
These questions are particularly difficult with regard to his figure 16 showing sub threshold and suprathreshold
axon waveforms. Based on a totally electrolytic model, these waveforms are easily interpreted (Section 9.1
addressing stage 3 signal propagation neurons). Araya also has difficulty when ascribing excitatory and
inhibitory properties to particular synapses rather than to non inverting inputs at dendrites and inverting inputs at
podites (the actual situation).
Araya closes with a long set of calculations considering the dendrite as a Rall-type cable. These lead essentially
nowhere without considering the synapse an active electrolytic diode, whether associated with a spine or not.
Such synapses do not support “backpropagating” signals. He also speaks of “Excitatory postsynaptic potentials
(EPSPs)” and “Spontaneous EPSPs (sEPSPs)” being simultaneously recorded at the soma and two apical
dendrites sites from layer V neocortical pyramidal neurons when apparently isolated, in-vitro. He cites Williams
& Stuart, 2002. Their discussion and data is in conflict with the common chemically based theory of the neuron.
See further discussion of their work below.
2.2.2.8 Electrical features of the second order fundamental cell
2.2.2.8.1 The electrical description of the conduit wall
As developed in Section 1.2.4, the basic structural form of the individual conduit of a neuron is that of a
sausage, a cylindrical structure terminated by two spherical caps and filled with an electrolyte. This basic
structure is frequently replicated, sometimes extensively, at an ever decreasing scale in the ramification of a
neurite tree or near the pedicles of an axon. However, the basic structure remains the same virtually everywhere
in a neuron.
The vast majority of the conduit wall consists of type 1 BLM. Thus, the majority of the surface of a conduit is
inert. It is impervious to both electrical charges and molecular transport. The conduit behaves primarily as a
dielectric separating two conducting materials. Thus its principle characteristic is its electrical capacitance.
119Araya, R. (2016) Dendritic morphology and function In Pfaff, D. & Volkow, N. eds. (2016) Neuroscience
in the 21st Century, 2nd Ed. NY: Springer pages 297-332
108 Neurons & the Nervous System
Small areas of the surface of the conduit are formed of type 2 and type 3 BLM. These areas continue to act as
dielectric mediums for electrical purposes. However, they also exhibit additional properties that will be
discussed below.
Lehn has spent considerable effort attempting to show how the molecules in a bilayer membrane can conduct
electricity120. He notes they can conceivably transport charge by “electron hopping” (hole conduction in the
terminology of this work) or by electron conduction along a continuous conjugation path formed by -bonds.
He also addressed the problem of suitable polar groups at the hydrophilic surfaces of such molecules to support
electrical connection to the surrounding aqueous fluid. While his work has shown that films of molecules
exhibiting -bonds exhibit a wide array of optical polarization effects, he has not established that biological
bilayers exhibit significant electrical conductivity. The long chain lipids forming the majority of the individual
molecules of the conduit wall are not conjugated. Hence, they are capable of supporting hole conduction by
electron hopping but not -bond conduction. By employing large adjacent groups of such molecules, significant
conductivity can be achieved at the impedance levels used in neurological circuits.
2.2.2.9 Electrical features of the second order fundamental cell
It came to be realized in transistor technology that a semiconducting material exhibited unusual conductivity
characteristics which could not be explained simply by electrons moving through the conduction band of the
material; it was necessary to also consider the movement of “holes” located in the valence band. These holes
were locations in the crystal lattice where electrons were missing. The total current through the bulk material
was the summation of the current due to movement of both the electrons and the holes. It was found that, if two
pieces of this material containing different levels of dopant were brought into very intimate contact, the
electrons and holes were subject to the conflicting pressures of the laws of diffusion and electrical potential.
These realizations provided the explanation of the rectifying characteristic of these materials (and other
materials that had been used for years without a clear knowledge of how they worked). The active process was
described as occurring at a junction between two such materials and the resulting device was described as a
junction diode. It exhibited a conductance which was asymmetrical and described by the diode equation, I =
Io(exp((V/Vo) - 1).
Further work led to the understanding of how two such junction diodes worked when they were brought into
intimate contact. If two of these junctions were manufactured such that the cathode area was very thin and
shared by the two diodes, the resultant device consisted of two junctions in intimate contact in a back-to-back
configuration. Depending on what voltages were applied to these devices, very strange things happened. If one
diode was forward biased, it was easy to inject a current into the device from the emitter into the common base.
If simultaneously, the third terminal was reverse biased with respect to the base, a current would appear at the
collector essentially equal to the current injected at the emitter. This current is directly proportional to the
current injected into the input diode and exhibits no relationship to the impedance of the output diode.
This “transistor action” was accounted for based on the action of the electrons and holes in the material
responding to the laws of quantum-mechanics in addition to the requirements of the laws of diffusion and
electrical fields. “Transistor action” resulted in spite of the presence of opposing electrical potentials.
Significant power amplification was possible through this process since the input current was at a low
impedance level and the output current was at a high impedance level.
Amplification is frequently a difficult concept for the uninitiated. It is fundamentally a concept based on
the ratio between the power associated with a signal at the output of a circuit divided by its value at the
input to the circuit. If the input and output circuits are at the same impedance level, the amplification is
given by the output voltage divided by the input voltage. It is possible to have significant amplification
with the same voltage amplitude signals at input and output if the impedance levels are different. The
second Activa in each sensory neuron is used to reduce the output impedance of the axoplasm potential.
The terms voltage gain and current gain are terms used in the vernacular to express amplification without
regard to the associated impedance levels.
2.2.2.9.1 Electrical description of the electrostenolytic process
While the area of a typical conduit devoted to type 2 BLM is quite small, it is very important. This area still
exhibits a capacitance as calculated above. However, it also exhibits a nonlinear resistive impedance
characteristic of an electrical diode. The permeability of this area of the BLM is highly asymmetrical to the
120Lehn, J-M. (1995) Supramoleculear Chemistry. NY: VCH page 100-110
The Neuron 2- 109
transport of elementary electrical charges. In the absence of the reactants associated with the electrostenolytic
process, this area of type 2 BLM when combined with the rest of the conduit can be represented by a diode in
parallel with the capacitance of the overall conduit. The diode is oriented so that it cannot sustain a positive
potential within the conduit relative to the surrounding medium. Any such potential will cause electrons to flow
through the diode from the exterior environment into the interior and neutralize the original potential. The diode
is of very high quality and it can sustain (in conjunction with the capacitance) a negative potential for a long
period of time (typically many hours).
Where the type 2 BLM is designed to support the electrostenolytic process, a stereochemical aggregate of
molecules on the outer surface of the membrane is able to cause the local membrane outer surface to become
negative relative to the interior plasma. This quantum-mechanical potential is sufficiently strong to cause an
electron to be injected into the interior of the conduit, employing its diode characteristic, for every molecule of
reactant. As a result, the interior of the conduit becomes negative relative to the surrounding INM. The
maximum value of this potential based on the conversion of glutamic acid to GABA is between 150 and 154
millivolts (Chapter 3).
The ability of the electrostenolytic process to sustain this potential in the presence of other circuit elements
depends on the reaction kinetics of the process and the relative availability of the reactants. From an electrical
perspective, the electrostenolytic process can be modeled as a current source in parallel with a resistive element
or a voltage source in series with a resistive element. The latter will be the most useful in the work to follow.
The operation of the electrostenolytic process explains a process recently reported in the chemical
literature, but without supporting the frivolous designation of a “reversed electron transport121” or “uphill
electron transfer122” phenomenon.
Subsequent discussion will evaluate whether the typical electrostenolytic process employs type 2 lemma, or
whether the combination described above is more properly described as type 4 lemma, like that employed by the
chemical sensory neurons (Chapter 8)
2.2.2.9.2 Electrical description of gap junction between two membranes
The importance of the liquid crystalline state of matter in biology has not gained wide appreciation in the
biological community. Liquid crystalline materials exhibit unexpected electrical properties. Basically, they
exhibit unusual electrical conductivity--frequently in asymmetric ways and in only certain planes. These
properties are due to the semi-crystalline structure of the membranes and the presence of specific electrical
species within these structures. Such structures can be described as biological semiconductors and bring to
biology much of the flexibility found in Solid State Theory--specifically, “transistor action.” “Transistor action”
was first described in the 1950’s to explain some unexpected effects measured in unusual configurations of a
semi-conducting material, specifically “doped” germanium. Adding minute amounts (parts per billion) of a
dopant to a part of a crystalline structure of germanium created these quantum-mechanical properties in an
otherwise molecularly symmetrical material.
It is proposed here that certain BLMs when brought into intimate juxtaposition exhibit “transistor action” and
provide the nonlinear current-voltage relationships observed in neurons. This capability has not been defined
previously in the literature. It is entirely independent of any ions moving through any membranes associated
with the neuron.
When two areas of type 2 BLM of the correct polarity are brought into close juxtaposition to form a gap
junction, and electrically biased appropriately, a unique electrical situation is observed. As shown in [Figure
2.2.2-7], the entire structure is liquid crystalline. Figure 2.2.2-9 illustrates the electrical circuits describing the
above physical configuration. The circuit in frame A represents the two asymmetrical BLM’s as individual
diodes connected to a common ground terminal representing the junction area. The letter designations will be
defined more explicitly later. For now, the terminal marked E represents the electrolyte forming the
dendroplasm to the left of the junction. The terminal marked C represents the axoplasm to the right and the
terminals labeled B represent the “base” terminal of each diode. This is the conventional circuit based on
conventional physics. The battery symbols shown represent small quantum-mechanical potentials associated
121Friedrich, M. & Schink, B. (1993) Hydrogen formation from glycolate driven by reversed electron transport
in membrane vesicles of a syntrophic glycolate-oxidizing bacterium Eur J Biochem vol 217, pp 233-240
122Elbehti, A. Brassuer, G. & Lemesle-Meunier, D. (2000) First evidence for existence of an Uphill Electron
Transfer through the bc1 and NADH-Q oxidoreductase compleses of the acidophili obligate . . . . J Bacteriol
vol 182(12), pp 3602-3606
110 Neurons & the Nervous System
Figure 2.2.2-9 Electrical representations of a gap junction. A; the circuit based
on conventional physics. B; the circuit based on quantum-physics. C; an
alternate physical representation of B. D; a positive voltage, Eee, applied to the
emitter of C but not to the collector. No current flows in the collector circuit. E;
A reverse bias, Ecc, is applied to the collector terminal. A current flows in the
collector circuit F; standard symbology for the biological Activa. See text.
with the diodes. These batteries cannot support external current flow. They are frequently described as cutin
potentials, V-sub-. Currents can be passed through either diode in the directions shown upon application of a
positive potential to E or C (relative to the ground potential at B) that exceeds the intrinsic potential of the
diodes (shown by the battery symbols). The two diodes will operate entirely independently.
Frame B shows an equivalent circuit representing a fundamentally different situation. If the base regions of the
two diodes (marked B) are sufficiently close together (and formed from the same liquid crystalline
medium–semi-metallic water), they must be considered to operate in the quantum-mechanical domain (where the
rules of conventional physics do not apply). It will be shown in Section 2.3 that this is the actual situation found
in every neuron of the animal system. While both diodes will still conduct currents when forward biased as
above, the performance of the overall circuit cannot be predicted by the laws of conventional physics under
other bias conditions.
The configuration of frame B was that originally described by the inventors of the man-made transistor.
The Neuron 2- 111
However, an alternative configuration soon developed that made it easier to understand the phenomenon
involved. Frame C shows a redrawing of frame B to represent the molecular structure in the previous figure.
This format is continued in frames D, & E. In frames C, D & E, the currents must change direction as they
travel through the common liquid crystalline region if they are to exit through the “base” terminal, B.
Look at the potentials applied to the terminals marked E (emitter) and C (collector) relative to the base terminal
B, individually. If the voltages are both positive, it would be expected that the currents Ie and Ic of frame C
would flow in the directions indicated. They do. In frame D, the collector terminal is at zero and no current
would be expected to flow through that terminal regardless of the current through the emitter terminal (which in
this case is positive). This is observed to be true. In frame E, the collector terminal is made negative. This
reverse biases the diode associated with the collector lead and no current would be expected to flow in this lead.
In the absence of any current in the emitter lead, this is the observed condition. However, if current is injected
into the liquid crystalline material via the emitter terminal, E, while the collector is reverse biased, a current is in
fact measured in the collector lead. This current flows in the opposite direction to the expected current and is
nominally equal to the injected current (98–99.5% depending on quality of manufacture). This current is the
result of transistor action in a liquid crystalline semiconductor device. This transistor action is the key to the
operation of the entire neural system.
An arrow has been added to frames E & F to define the base current, Ib. The relationship, Ie = Ib + Ic is an
important and deterministic one. The ratios between these currents are specific for a given device, that will
henceforth be labeled an Activa in this work. In man-made transistors, the ratio of collector to emitter current
and base to emitter current are indicative of the quality of the detailed manufacturing process used. The
significance of this relationship in biological Activa will be developed in Section 2.4.3.3.
The direction of the arrow representing Ic makes it clear that the source of this current is a generator in parallel
with the diode representing the BLM forming the collector portion of the Activa
The high transfer efficiency of electrons from the emitter terminal to the collector terminal of an Activa, over
95% in real neurons, is impressive. It is discussed further in Section 2.4.3. This transfer is achieved without
any chemical process whatever. Neither a chemical reaction nor the secretion of a so-called neurotransmitter is
required.
Frame F shows the adoption of a standard symbol to represent this phenomenon, “transistor action.” The letter
A is shown above the base symbol to indicate it is an Activa, a natural active semiconductor device found in all
neural systems. When biased as shown, a conventional current injected at E will cause a conventional current to
flow at C in the directions shown in spite of the reverse bias applied to the collector terminal (the flow of
electrons is actually in the opposite directions). This symbol will be used in the remainder of this work to
indicate the site of transistor action within a gap junction.
The location of the arrowheads within the symbology of frames E & F are significant. In frame E, and the
earlier frames, the device is drawn entirely symmetrical. However, frame F shows only one arrowhead,
associated with the emitter terminal. In the standard symbol of a transistor, the arrowhead is associated with the
emitter terminal. This terminal is forward biased and current flows into it. The collector terminal is reverse
biased and, in the absence of current in the emitter circuit, no current flows in the collector circuit. Hence, no
arrowhead. In fact, any junction type transistor (or Activa) is internally symmetrical. The directions of current
flow are determined by the bias potentials applied to the device and the quantum mechanical character of the
materials forming the device. In the case of an Activa, the device is described quantum-mechanically as a pnp-
type liquid crystal semiconductor- based transistor. This designation indicates that the semi-metallic water
forming the central liquid crystalline material of the Activa is of n–type. The two type 2 BLMs contribute p-
type semiconducting material. The majority of charge carriers in n-type semiconducting material are electrons.
The majority of charge carriers in P-type semiconducting material are holes, with number of electrons being in
the minority. Textbooks on semiconductor physics should be consulted for details in this area. Sections 1.3.2.2
& 2.2.1.3 discusses the concept of holes very briefly. No Activa of the opposite variety, npn-type, have been
found in neural systems.
The individual features, and limitations, associated with Activa will be developed incrementally in the
following sections.
2.2.3 The three terminal biological transistor
If it were possible to bring into intimate contact, two asymmetrical membranes such that their cathodic terminals
merged quantum-mechanically and it were possible to vary the voltages on the two outer surfaces with respect to
the voltage associated with the central region between them, transistor action would result. The resultant device,
called an Activa, would exhibit near electrical autonomy between the two external surfaces, except for the
112 Neurons & the Nervous System
Figure 2.2.3-1 Three terminal active biological
device, the Activa. (A) A cross section of the
junction between two membranes. Equivalent
chemical and electrical schematics are shown. (B)
Equivalent circuit of (A) if the two bases are
intimately related quantum-mechanically. Note
the “A” above the base region in (B). The
conventional currents are positive for a positive
voltage Veb. (D) Output current Ic versus the
collector potential Vcb where Vcb is negative.
common current appearing to flow between the two surfaces*. Figure 2.2.3-1(A) and (B) illustrate this
extremely useful configuration. Frame (B) introduces the conventional transistor symbol modified to include an
“A,” to designate an active biological semiconductor device, the Activa.
The configuration shown in (A) was introduced
incrementally in earlier parts of this chapter. In
this frame, the arrows indicate the direction of
conventional current flow. The direction of actual
electron flow is in the opposite direction. The
space between the two membranes is labeled B
and is shown as an extremely thin region of
different composition than the two membranes. It
is defined as the base. The base is conductive to
electrons and holes but not ions. The left-most
surface is labeled E, for emitter and the right-most
surface is labeled, C, for collector. These labels
correspond to the language of the solid state
physicist. Conventional current is introduced into
the base region from the emitter. A nearly
identical conventional current originates in the
base and emerges at the collector. Frame (B)
shows the shorthand notation corresponding to the
physical conditions of frame (A). The arrowhead
highlights the emitting (or injection) of
conventional current into the base region. This
arrowhead also suggests the low electrical
impedance of this input structure when properly
biased. The lack of an arrowhead on the collector
lead is suggestive of the high electrical impedance
of this circuit when properly biased.
The Activa in this three-terminal form is the basis
for the operation of the signal handling
characteristics of all neurons. Note the back-to-
back connection of the two pn diodes in frame (A).
This orientation leads to the designation pnp for a
structure of this type. In the absence of transistor
action, no current will flow between the emitter
and the collector sides of this structure.
To achieve “transistor action,” three conditions must be met:
+ each membrane “system” must be operational; that is the membrane must be of the right constituency
and be bathed on each side by an appropriate electrolyte.
+ the input membrane must be forward biased so as to conduct current relatively easily and the output
membrane must be reverse biased so that it does not easily conduct current.
+ the distance between the adjacent membrane walls must be less than the distance required for
transistor action, i.e., a charge passing through the input membrane will continue on and pass through the output
membrane in spite of the opposing polarity of the output membrane. The required distance is less than 10 nm
(100 Angstrom).
The electrical characteristics of the Activa under these conditions are relatively simple. The input impedance of
the device is relatively low and the output impedance of the device is quite high. The input characteristic is that
of a forward biased diode in series with a battery as developed earlier. The output characteristic is represented
by a very high impedance as expected from a reverse biased diode in series with a small battery. No current
flows in the output circuit in spite of the external bias supplied to the device. However, a current will flow in the
output circuit equal to the current in the input circuit due to “transistor action.” Since the output current is
essentially the same as the input current, the transfer characteristic, i. e. the output current as a function of the
*In man-made transistors, the output current as a function of the input current is given by
I(out) = I(in)*(1 - α) where α is usually 0.01-0.02 depending on the quality of the manufacturing process.
The Neuron 2- 113
input voltage, is also given by the diode equation plotted against different coordinates. These characteristics
are illustrated in Figure 2.2.3-2(C) & (D).
Frame (C) displays the input, or emitter, current as a function of emitter-to-base potential within the operating
range of the device. Since the collector current is essentially the same as the emitter current, the vertical axis
shows both labels. For the pnp-type semiconducting device found in all neurons, the current increases with a
positive increase in emitter-to-base potential. Therefore, the flow of electrons also increases but in a negative
direction. The diode characteristic is offset by the presence of the intrinsic membrane potential, Vm, of the
emitter-to-base membrane. This parameter is usually symbolized by V-sub- in electrical engineering texts.
Frame (D) displays the output current of the Activa as a function of the collector-to-base potential. As long as
the collector potential is more negative than required to reverse bias the collector, the output current is directly
proportional to the input current and is independent of the collector potential as shown. The size of the intrinsic
membrane potential of the collector-to-base membrane is usually too small to be plotted on this graph.
The symbol for the biological transistor does not show the internal voltages implied by the symbol “A.”
However, they are shown explicitly in the conventional equivalent circuit for a biological transistor. This
notation will be developed further in Section 1.3.
To aid in the modeling of neural circuits, it is important to define the fundamental properties of the Activa. As
in the case of man-made transistors, the Activas can vary in gross properties based on their construction.
However, once made, their fundamental properties vary only with temperature.
The following sections will define the principle fundamental parameters and performance parameters of the
Activa. The physical dimensions will only be discussed obliquely. Chapters 9 & 10 will explore these
parameters in detail.
When examining the face of one membrane of a gap junction, an orderly pattern is frequently discerned. This
pattern is generally described as a close packed hexagonal arrangement of domains, each about 150 Angstrom
across32. This dimension describes the “unit Activa.” Figure 2.2.1-2 shows a similar organization but for a
“gap junction” found in the liver of a rat. It is useful to differentiate between the dimensions describing the
smallest functional Activa, the unit Activa, and the larger arrays of Activa that appear as a single unit under
lower resolution microscopy. The total diameter of the individual disks of Activas found within the neural
system are indicative of their current carrying capacity in support of a particular application.
2.2.3.1 Comparing the Activa to a man-made transistor
There are two distinct classifications of man-made transistors, those described as junction transistors and those
described as field effect transistors. Junction transistors show a continuity between the current into the emitter
terminal and the current out of the collector terminal. Field effect transistors (FET) exhibit a current that is
proportional to the potential on a gate but no current flows through that gate (at low frequencies). Only junction
devices have been found among biological semiconductor devices, Activas. Neither FETs, or the more widely
known MOSFETs and CMOSFET’s are used in biology!
One of the common methods of creating man-made junction transistors capable of handling high power levels is
to use replication techniques and then wire the various devices in parallel. As will be shown in Chapter 10,
biological devices also use this technique frequently. As indicated in Section 2.2.3.3, individual devices,
defined here as a unit Activa, are formed into an array on the surface of the plasma lemma and connected to a
common dendroplasm.
There are two fundamental forms of man-made junction transistors, those with a base material that is a single
element, such as silicon or germanium, and those with a base material that is a compound, such as gallium
arsenide, mercury cadmium telluride, etc. The compounds offer lower band gaps in their electronic structures
than do the elements. The n-type material forming the base in the Activa consists of liquid crystalline semi-
metallic water. When in the liquid crystalline or crystalline phase, water is a compound with a very low band
gap.
There are also two fundamental types of man-made junction transistors, those with an n-type base material and
those with a p-type base material. To date, all known biological transistors have semi-metallic water as a base
material. This material is of the n-type. As noted earlier, all known biological transistors are of the pnp type.
32Cole, K. (1968) Membranes, Ions and Impulses. Berkeley, CA: University of California Press pg 515
114 Neurons & the Nervous System
2.2.3.2 The Ebers-Moll model and the Early Effect
Ebers and Moll provided an early detailed model of the operation of an active semiconductor device like the
Activa33. Versions of the Ebers-Moll model of such devices have appeared in many textbooks. However, they
do not always appear in the same form. Some of the versions are simplified to meet the author’s goals. This is
particularly true in texts for non-electronics majors34. Millman & Halkias develop the concept in two different
chapters of their book and lean upon a simplified equation (3-9) in a third chapter35. They provide a pair of
equations related to the model whereas many authors only present one. In their presentation in Section 5-12,
they rely upon the diode equation with the offset potential (or cutin potential), V, equal to zero. This is
acceptable when dealing with collector saturation potentials that are many times higher than V. However, this
is not the case in most biological circuits. An even more complete presentation than that in Millman & Halkais
is required under these conditions. This more complete presentation replaces the emitter minus base potential,
VEB, by by the more precise potential, VEB -V.
When evaluating a biological transistor, an Activa, it is also important to be aware of the Early Effect. This
Effect, discussed in Section 5-5 of Millman & Halkias, documents the reduction in output signal as a function of
input signal due to the reduction in the space charge within the base region. Although evidence of this Effect
was not found in the biological literature, the literature does not exhibit the precision required to recognize this
Effect explicitly.
2.2.3.3 The fundamental electrical parameters of the unit Activa
Attempting to specify the fundamental electrical parameters of a unit Activa or of a given Activa array is
difficult based on the available literature. The diameter of the membrane area under test has generally been set
by the size of the electrical probe. This value has been used under the assumption that the membrane is uniform
throughout the area being examined. This assumption is not valid. The test protocol should determine the size
of the active region of membrane under test. The most critical parameters are those found in the diode equation
discussed previously. The best available sources of current-voltage data applicable to an Activa appear to be
Luttgau (Yau) and Eliasof (Section 1.5.1.2).
2.2.3.3.1 The offset parameter, aka the Band Gap
Only limited data is available in the literature concerning the diode characteristic of the Activa. The data of
Eliasof and also Yau, discussed in Section 1.5.1.2, can be used. However, that data was not collected under the
desired conditions. It was collected using a Leyden jar rather than a Ussing apparatus. Therefore, the current-
voltage characteristics include a resistive impedance due to the electrolytes on each side of the membrane.
These impedances obscure the underlying diode characteristic associated with the membrane. By looking at the
data as an ensemble, a trained eye can estimate the diode characteristic to a first approximation. The data
appears to converge to a value very similar to the current-voltage characteristic provided by Luttgau36 and
reproduced by Yau37. Luttgau presented a characteristic obtained with a pseudointracellular solution on one side
of an asymmetrical membrane and a “Normal” Ringer’s solution on the other. He then introduced variable
amounts of Ca2+ and Mg2+ into the pseudointracellular solution. By using the characteristic for zero amounts of
added cation, a very good approximation to the desired diode characteristic is obtained.
These two sources indicate a band gap for the water-based material forming the PN junction in the PNP
Activa of 10mV at 300 K This low value suggests the involvement of EZ Water as developed in detail in
Section 8.1.3.3 of Processes in Biological Vision. “Exclusion Zone” water, EZ water, is found when water is
confined to spaces of 200 microns, or possibly greater, that are stable for extended periods. The zones are
particularly known to form when between hydrophilic gels, such as the lemma of neurons, .form the confining
space. The exclusionary zone eliminates all other materials from the zone and probably forms a pure liquid-
33Ebers, J. & Moll, J. (1954) Large-signal behaviour of junction transistors Proc IRE Vol. 42, pp 1761-1772
34Horowitz, P. & Hill, W. (1989) The Art of Electronics, 2nd ed. NY: Cambridge University Press, pg 80
35Millman, J. & Halkias, C. (1972) Integrated electronics, NY: Mc Graw-Hill, chapters 3, 5, & 19
36Luttgau, H. ed. (1986) Membrane Control of Cellular Activity. Stuttgart: Gustav Fischer, pp 343-366
37Yau, K. (1994) Phototransduction mechanism in retinal rods and cones. Invest. Ophthal. Vis. Sci. vol. 35, pp
9-32
The Neuron 2- 115
Figure 2.2.3-2 Band gaps of EZ Water & bulk water compared with Germanium
and Silicon. The EZ water band gap (possibly heavily doped) is determined from
the data of Eliasof et al and Yau et al. Note scale change at discontinuity. See
text.
crystalline with in the zone.
Assuming his Normal Ringer’s solution does not disturb the Helmholtz layer of bound water immediately
adjacent to the plasma membrane, the data of Luttgau provides the best available estimate of the offset
parameter of the in-vivo membrane generally associated with an Activa of a synapse. This configuration
consists of a cytoplasm on the internal side of a membrane and a water molecules on the external side. The
offset parameter, band gap, has a value of 10 mV at 300 Kelvin. Data has not been found that unambiguously
defines the offset parameter for the Activa formed within a cell. The offset parameter of these Activas may have
a value of near zero because of the similar composition of the fluids on each side of the membrane.
Figure 2.2.3-3 compares the radically lower band gap for the Biological Activa when employing EZ Water, and
conventional bulk water with a band gap of 9.2 volts (range of 8.7 to 10.9 volts). Also shown for reference are
the band gaps of undoped Germanium and Silicon. Bischkoff et al38. have performed an exhaustive analysis of
the literature concerning the band gap of bulk water. The problem is a difficult one to model. They did not
consider EZ Water.
There is another option that is explored in Section 8.1.3.3.8 of Processes in Biological Vision. and reproduced
in Section 2.2.3.3.5 of this chapter.
The narrow band gap of EZ Water when employed in the Activa of a neuron is remarkable; but it accounts for
the remarkably low power consumption of the 100 billion neurons in the CNS, less than 25 Watts, total, in
humans (Section 1.1.8.2.1).
The band gaps noted in the textbooks for Germanium and Silicon vary considerably in numerical value. The
38Bischoff, T. Reshetnyak, I. & Pasquarello, A. (2021) Band gaps of liquid water and hexagonal ice through
advanced electronic-structure calculations Phys Rev Res vol 3, Article 023182
DOI: 10.1103/PhysRevResearch.3.023182
116 Neurons & the Nervous System
precise value is a function of temperature (see next subsection), the dopant level of the sample, and how the
value of the point on the curve is chosen. These parameters are seldom specified.
The key to the low power operation of the neurons appears to be the EZ Water within the PN
junction within each Activa. More research in this area will pay significant dividends.
2.2.3.3.2 The thermal parameter
The thermal parameter, VT, is given in several papers in the literature as equal to 25 mV or 26 mV. 26 mV is
the theoretical value for a device operating at 300 Kelvin. 26.7 is the equivalent value at 310 Kelvin (98.6 F)
and a value of 25 mV could be expected in cold blooded animals at laboratory temperatures. Thus, the
theoretical value of this parameter only varies by about 1.7 mV over the biological range. Obviously, greater
care will be required in the laboratory to measure this parameter accurately.
2.2.3.3.3 The reverse saturation parameter
The reverse saturation current parameter, I0, can be determined from a variety of diode characteristics in the
literature. However, determining the reverse saturation current density, I0/unit area, is more difficult. Most
authors have not given the precise area of the membrane under test and most authors have not made
measurements up to a voltage of -150 mV which would give the most precise value. Most of the available data
suggests a reverse saturation current, I0, between 18 and 25 picoamperes for the typical biological diode.
The estimated reverse saturation current density of the giant axon of squid is less than 0.01 ma/cm2 based on
Cole39. It is difficult to determine from Cole what area was assumed in his measurements. It may have been
larger than the actual type 2 region of membrane.
2.2.3.3.4 The forward transconductance
A characteristic that is frequently very important in understanding the operation of a neuron and its conexus is
the forward transconductance of the Activa. The transconductance is the ratio of the change in current at the
collector to the change in voltage between the emitter and base terminals. The symbol used is gm. There is no
direct data available for this parameter and it varies with the equivalent area of the Activa (sum of the unit
Activa areas) within the neuron.
Values for this parameter will be developed in later chapters of this work.
2.2.3.3.5 The heavy doping of the forward biased PN of an Activa–Quantum Tunneling
The extreme range between the band gap attributed to EZ Water in Section 2.2.3.3.1 and bulk water suggests
there may be an additional mechanism involved. The frequently mentioned close relation ship between EZ
Water and gels, may suggest a heavy doping of the EZ Water by elements of the gel, or other dopants resulting
in the mechanism known in semiconductor physics as “tunneling.” This is a widely used technique in industry.
It may have a presence in Neuroscience as well.
This subsection is reproduced from Section 8.1.3.3.8 in Processes in Biological Vision
The possibility of tunneling in a forward-biased PN junction in an Activa to explain the remarkably low
(apparent) band gap of about 50 mV must be considered. Millman & Halkias40 presented a useful summary of
the tunneling mechanism, although they refer to a conventional metallic diode,
“THE TUNNEL DIODE
When the concentration of impurity atoms in a p-n diode is very high (say, 1 part in 103), the depletion
layer is reduced to about 100 Angstrom. Classically, a carrier must have an energy at least equal to the
potential-barrier height in order to cross the junction. However, quantum mechanics indicates that there
is a nonzero probability that a particle may penetrate through a barrier as thin as that indicated above.
39Cole, K. (1968) Op. Cit. fig 4:52
40Millman, J. & Halkias, C. (1972) Integrated Electronic: Analog and Digital Circuis; and Systems. NY:
McGraw-Hill
The Neuron 2- 117
This phenomenon is called tunneling, and hence these high-impurity-density p-n devices are called tunnel
diodes, or Esaki diodes. This same tunneling effect is responsible for radioactive emissions and
high-field emission of electrons from a cold metal.
Energy-band Structure of a Highly Doped p-n Diode
The condition that the barrier be less than 100 Angstrom thick is a necessary but not a sufficient
condition for tunneling. It is also required that occupied energy states exist on the side from which the
electron tunnels and that allowed empty states exist on the other side (into which the electron penetrates)
at the same energy level. Hence we must now consider the energy-band picture when the impurity
concentration is very high. In Fig. 19-10 (not reproduced here, similar to the figure in Section 8.1.3.4.4),
drawn for the lightly doped p-n diode, the Fermi level EF lies inside the forbidden energy gap. We shall
now demonstrate that, for a diode which is doped heavily enough to make tunneling possible, EF lies
outside the forbidden band.”
Figure 19-11 is also not reproduced here; it applies to a reversed-bias condition. The next two figures are
discussed by them together. Figure 19-12 is reproduced as Figure2.2.3-3
Figure 2.2.3-3 discusses the the energy Diagram for a forward-biased, heavily doped, PN junction and the
following figure 2.2.3-4 discusses the resultant volt-Ampere diagram, frequently described as the I-V diagram.
“The Volt-Ampere Characteristic
With the aid of the energy-band picture, a of Fig. 2.2.3-3 and the concept of quantum-mechanical
tunneling, the tunnel diode characteristic of Fig. 2.2.3-4 may be explained. Let us consider that the
p material is grounded and that a voltage applied across the diode shifts the n side potential with respect
to the p side. For example, if a reverse-bias voltage is applied, we know from Sec. 3-2 that the height of
the barrier is increased above the open-circuit value EO. Hence the n-side levels must shift downward
with respect to the p-side levels, as indicated inthe previous figure for the reversed-bias condition . We
now observe that there are some energy states (the heavily shaded region) in the valence band of the p
side which lie at the same level as allowed empty states in the conduction band of the n side. Hence these
electrons will tunnel from the p to the n side, giving rise to a reverse diode current. As the magnitude of
the reverse bias increases, the heavily shaded area grows in size, causing the reverse current to increase,
as shown by section 1 of Fig. 2.2.3-4.
Consider now that a forward bias is applied to the diode so that the potential barrier is decreased below
EO. Hence the n-side levels must shift upward with respect to those on the p side, and the energy-band
picture for this situation is indicated in Fig. 2.2.3-3(a). It is now evident that there are occupied states in
the conduction band of the n material (the heavily shaded levels) which are at the same energy as allowed
empty states (holes) in the valence band of the p side. Hence electrons will tunnel from the n to the p
material, giving rise to the forward current of section 2 of Fig.2.2.3-4.
As the forward base is increased further, the condition shown in Fig. 2.2.3-3(b) is reached. Now the
maximum number of electrons can leave occupied states on the right side of the junction, and tunnel
through the barrier to empty states on the left side, giving rise to the peak current Ip in Fig. 2.2.3-4. If
still more forward bias is applied, the situation in Fig2.2.3-3c is obtained, and the tunneling current
decreases, giving rise to section 3 of Fig.2.2.3-4. Finally, at an even larger forward bias, the band
structure of Fig. 2.2.3-3d is valid. Since now there are no empty allowed states on one side of the
junction at the same energy as occupied states on the other side, the tunneling current must drop to zero.”
Several investigators have noted that the electrons tunneling from the conduction band to the
valence band do so at the speed of light.
“In addition to the quantum-mechanical current described above, the regular p-n junction injection
current is also being collected. This current is given by Eq. (3-7) and is indicated by the dashed section 4
of Fig. 2.2.3-4. The curve in Fig.2.2.3-4b is the sum of the solid and dashed curves of Fig 2.2.3-4a, and
this resultant is the tunnel-diode characteristic of Fig. 2.2.3-4b.”
118 Neurons & the Nervous System
Figure 2.2.3-3 “Energy-band diagrams in a heavily doped p-n diode for a forward
bias. As the bias is increased, the band structure changes progressively from (a)
to (d). The horizontal arrows identify the tunneling current. From Millman &
Halkias, 1972.
Frame (b) shows the optimum tunneling situation, assuming both bands involved in tunneling are uniform in
their density profiles. This corresponds to a maximum tunneling current, IP, in the next figure. This condition is
labeled “resonant tunneling” in “University Physics, vol. 3, Section 7.6"41 There is not actually any resonance
condition present from an engineering perspecitive.
4 1 L i ng , S . ( on l i n e ) U ni v e rs it y P h y si c s , V o l 3 , S e c ti o n 7 .6 O p e n S t a x
https://openstax.org/books/university-physics-volume-3/pages/7-6-the-quantum-tunneling-of-particles-throu
gh-potential-barriers
The Neuron 2- 119
Figure 2.2.3-4 The I-V Diagram resulting from tunneling in a forward-biased diode.
(a) The tunneling current is shown solid. The injection current is the dashed
curve. The sum of these two gives the tunnel-diode volt-ampere characteristic,
which is shown in (b). From Millman & Halkias, 1972.
Figure 2.2.3-5 A tunnel diode I-V
characteristic. From Agosta, 2018.
Figure 2.2.3-4 shows the resultant I-V Diagram.
The Forward voltage ratio between VP and VF may be significant in terms of
the Effective Band Gap of EZ Water shown in Section 2.2.3.3.1 of “The Neuron
& Neural System.”
Agosta42 has provided the I-V characteristic for a
commercial BD–4 tunnel diode exhibiting a VP of
45 mV designed for oscillator service due to its
negative resistance region, reproduced in Figure
2.2.3-5. The VV is at 220 mV at room
temperature. The conventional substrate is
Germanium. The figure shows the typical band
gap of Germanium on the right (Blue). What
would a tunnel diode I-V characteristic made from
a PN junction of EZ Water substrate, and doped
with a component of type 2 lemma, look like?
42Agosta, C. (2018) Tunnel Diode Oscillator Essentials. NY: Clark University cagosta@clarku.edu
120 Neurons & the Nervous System
Figure 2.2.3-6 I-V characteristic for
Bi2Se3 for various band gaps. The band
gaps of the undoped material is shown at
upper left. From Fluckey et al., 2022.
A similar figure appears in Fluckey et al43. for a different combination of semiconductors, reproduced as Figure
2.2.3-6.
2.2.3.3.6 An alternate theory of charge
transport along a lipid, Molecular
Charge Tunneling
This material is present as a matter of record.
It involves basic research that is note
particularly appropriate to a phospholipid-
based bilayer lemma of a neuron.
Recently, an alternate theory of tunneling, as a
concept, has arisen among chemists at Harvard
University. The tunneling may be labeled
Molecular Charge Tunneling through a membrane
consisting of sulfur-based lipids. The work has
been at the basic research level and has not been
applied to the bilayer lemma of a neuron. The
work parallels the earlier work of others to
develop a room temperature plastic cable to
replace metallic cables. (Section 5.2.4.1). To date,
the current work has limited to lipids consisting of
-bonds, whereas the earlier work usually
involved one or more -bonds. No theory
underlying the current work has been expounded as of 2023.
The paper of Miller44 summarizes many numerical values prior to a search for a fundamental equation
describing trapped electron at cryogenic temperatures, citing Marcus et al., 1954.
The biologist community complicated matters by initially focusing on proteins and cytochromes rather than
outer lemma of cells. Schmallegger et al45.performed charge transfer experiments on a single layer of
Phospholipid 1,2-Dimyristoyl-sn-glycero-3- phosphocholine (DMPC) and asserted, citing Wegner 2005, that the
low value of ΔG‡ ~ 40 kJ/mol supported a tunneling mechanism [while also supporting other mechanisms, such
as any Hydrogen Bond, editor].
Belding et al46. investigated tunneling in a sulfur-based lipid of the self-assembled monolayer, SAM, type.
AuTS/S(CH2)2CONR1R2//Ga2O3/EGaIn, where R1 and R2 are alkyl chains of different length The AuTS is a
template-stripped gold substrate. While crediting Hegner et al., 1993, the stripping technique, that group
actually developed the technique using silver. They did not describe the CON in their expression but the figures
indicates it is -N--C=O group with the C connected to the (Ch2)2 chain. The Ga2O3/EGaIn indicates a popular
method of probing a sample deposited on a substrate at the time.
43Fluckey, S. Tiwari , S. Hinkle, C. & Vandenberghe, W. (2022) Three-Dimensional-Topological-Insulator
Tunnel Diodes Phys Rev Appl vol 18, Article 064037 DOI: 10.1103/PhysRevApplied.18.064037
44Miller, J. (1975) Reactions of trapped electrons by quantum mechanical tunneling observed by pulse radiolysis
of an aqueous glass J Phys Chem vol 79(11), pp 1070-1078
45Schmallegger, M.Barbon, A. Bortolus, M. et al. (2000) Systematic Quantification of Electron Transfer in a
Bare Phospholipid Membrane Using Nitroxide-Labeled Stearic Acids: Distance Dependence, Kinetics, and
Activation Parameters Langmuir vol 36, pp 10429-10437
46Belding, L. Root, S. Li, Y. (2021) Conformation, and Charge Tunneling through Molecules in SAMs
J Am Chem Soc vol 143, pp 3481 3493
The Neuron 2- 121
Figure 2.2.3-7 (No caption in original) Comparing diode & resistive circuits.
Although labeled Ordered and Disordered, the reason for the diode in the left
circuit and the resister in the right may be the formation of an electrical junction
between the gold substrate and the terminal sulfur in the SAM. This would
account for both the diode and the (static) voltage source on the left frame. See
text. From Belding et al., 2021.
The stated objective of the Belding et al. paper was,
"The objective of this work was to determine if disordered conformations and ordered conformations of
homologous molecules differed significantly in the rates of tunneling through them at a common voltage
(+0.5 V).
They provide data on the thickness of the molecular array as a function of the number of C + N atoms. They
did not provide any data on the time delay as a function of the number of atoms. The current density decreased
rapidly as the logarithm of the total number of atoms.
A problem is presented by a "teaser" figure presented next to the Abstract but not discussed in the Abstract or
text in detail.. Figure 2.2.3-7 reproduces their unnumbered "teaser" figure. The teaser labels the left frame as
Ordered and the right frame as Disordered. While the actual circuit overlay shows a diode in the left frame and
a resistor in the right frame. The Ordered array is not likely to acquire a diode junction due to the order of its
array. It is more likely to acquire a diode structure due to the interface between the terminal sulfur and the gold
substrate. Sulfur is an atom existing in many electronic and crystalline forms. It is known to form both aurous
sulfide, Au2S, and auric sulfide, Au2S3. Thus, it is possible the diode junction is formed by a chemical bonding
between the terminal sulfur and the gold substrate OR excess sulfur and the gold substrate. This bonding would
also introduce a potential barrier, that could be represented by the static voltage, V, which is not discussed in
any detail in the original paper. Thus, a problem with the technique may be responsible for the formation of an
electrical junction at the substrate interface in the left frame and not in the right.
Figure 1 of their paper explains their ordered and disordered configurations.
Members of their team, Yoon et al47 presented parallel studies using a silver substrate that recognized the
problem of the potential of silver combining with the terminal sulfur to form an electrical junction at the
substrate interface (figure 1a). They also recognized the complexity of their Ga2O3-bulk eutectic gallium/indium
alloy, EGaIn, interface. They note,
"One goal of the field of molecular electronics is to relate the electrical behavior of molecular junctions
to the chemical structure of the molecules they incorporate. Molecular rectification the asymmetric
response of currents to applied potentials of equal magnitude but opposite sign in
electrodemolecule(s)-electrode junctions was an early justification for the study of molecular electronics.
The potential to control rectification by designing molecule(s), and/or their contacts with the electrodes
in these junctions, has been the subject of a number of theoretical and experimental studies."
"We determined experimentally that rectification (Figure 1b,c) in this system stems from the BIPY
47Yoon, H. Liao, K-C. Lockett, M. ( 2014) Rectification in Tunneling Junctions: 2,2 -Bipyridyl-Terminated
n Alkanethiolates J Am Chem Soc vol 136, pp 17155 17162 dx.doi.org/10.1021/ja509110a |
122 Neurons & the Nervous System
terminal groups in the SAM, and not from other features of the EGaIn-based junction." (where BIPY is a
4-methyl-2,2'-bipyrid-4'-yl group, a 2-cycle heterocyclic group)
Yoon et al. have explored a variety of SAMs and have noted in their Introduction,
"The higher current is at negative polarity (e.g., the electrode close to the Fc group is oxidizing). The
mechanism of this rectification is well defined (detailed energy diagrams for rectification are discussed
elsewhere(Nijhuis et al.)): it involves a change in mechanism, from tunneling across the entire molecule at one
bias, to hopping (from the Fc to the electrode due to energetic proximity of HOMO of Fc ( 5.0 eV) to the Fermi
level of the Ga2O3/EGaIn electrode ( 4.3 eV) at zero bias) followed by tunneling at the opposite polarity. The
generality of rectification in SAM-based junctions remains unclear, as does the range of mechanisms that can
produce rectification."
The paper cited by Yoon et al. discusses the quantum energy diagram underlying the theory of their complex
molecule, Nijuis et al48, is also basic research and is accompanied by an extensive attachment..
The Abstract of Nijhuis paper notes,
"The HOMO level has to be positioned spatially asymmetrically inside the junctions (in these experiments, in
contact with the Ga2O3/EGaIn top electrode, and separated from the Ag electrode by the SC11 moiety) and
energetically below the Fermi levels of both electrodes to achieve rectification. The HOMO follows the
potential of the Fermi level of the Ga2O3/EGaIn electrode; it overlaps energetically with both Fermi levels of the
electrodes only in one direction of bias."
This is a highly restrictive condition on the overall bias of the molecular configuration.
Wimbush et al49. reviewed the properties of a varieties of SAMS using the same liquid-metal top electrodes of
an eutectic Ga–In (EGaIn) alloy with a superficial layer of Ga2O3.
There is no evidence found in the literature that either chemists or biologists have documented a time delay
associated with tunneling among lipids OR the potential of a diode formed by a Ordered lipid of a biological
bilayer lemma, each bilayer consisting of molecules containing two strands of a phospholipid, of a neuron.
48Nijhuis, C. Reus, W. Whitesides, G. (2010) Mechanism of Rectification in Tunneling Junctions based on
Molecules with Asymmetricaj Potential Drops J Am Chem Soc vol 132, pp 18386-18401
49Wimbush, K. Reus, W. van der Wiel, W. et al. (2010) Control over Rectification in Supramolecular
Tunneling Junctions Angew Chem vol 122, pp 10374 –10378 DOI: 10.1002/ange.201003286
The Neuron 2- 123
2.2.3.4 Proposed use of a heavily doped forward biased PN in an Activa
As Wegner et al50 begins their paper. they note,
"Electron tunneling processes have been found to play pivotal roles in solid-state physics (Esaki, 1974),
chemistry (Miller, 1975), and biology (de Vault et al., 1967)."
There are many similar processes in chemistry and biology that are similar to tunneling, but none have been
explored in the depth to that of the Esaki (tunnel) diode semiconductor (which has been a commercial success
for many years and its operation is described at the quantum level in Section 2.2.3.3.5.
There is very good indirect evidence for the band gap of the forward-biased PN junction of the Activa, within
any neuron, based on Esaki (Section 2.2.3.3.5). See Eliasof et al. in Section 1.5.1.2 using a natural biological
PN junction within a lemma, and Mueller & Rudin in Section 2.6.1.2.2 using a synthetic PN junction of
sphingomyelin (a similar phospholipid to natural membranes). In man-made PN junctions, the dopant
level is usually determined by the manufacturing recipe. We do not have the recipe for natural PN
junctions within natural lemma.
The determination of the actual dopant level achieved is a very difficult measurement. Wallis & Kabos51
have published a chapter in a NIST-sponsored book on measurement techniques limited to metallic substrates.
They focused on the scanning microwave microscopy and scanning capacitance microscopy.
There is little information concerning the use of Esaki tunnel diodes, except in microwave oscillators, where
they excel, and no information concerning the presence of the n substrate formed of EZ Water.
Wikipedia offers some nomenclature of interest here,
"In semiconductor production, doping is the intentional introduction of impurities into an intrinsic
semiconductor for the purpose of modulating its electrical, optical and structural properties. The doped
material is referred to as an extrinsic semiconductor.
Small numbers of dopant atoms can change the ability of a semiconductor to conduct electricity. When
on the order of one dopant atom is added per 100 million atoms, the doping is said to be low or light.
When many more dopant atoms are added, on the order of one per ten thousand, 1 in 104, atoms, the
doping is referred to as high or heavy. This is often shown as n+ for n-type doping or p+ for p-type
doping. A semiconductor doped to such high levels that it acts more like a conductor than a
semiconductor is referred to as a degenerate semiconductor."
Figure 2.2.3-8 shows a predicted I-V characteristic based on the above discussion, for a heavily doped EZ
Water in combination with a type 2 lemma in a confined space (nominally 2-3 nanometers, or 0.002-0.003
microns for a gap junction, Section 2.4.2). This could be a portion of an Activa, a Node of Ranvier or a
conventional synapse. With a slight circuitry modification it could be the first Activa of a stage 1 sensory
neuron.
2.2.3.4.1 Estimates of the I-V characteristic of heavily doped forward biased PN of an
Activa
The main interest in the electrical engineering field has been in the negative resistance (section (3) of the
theoretical I-V characteristic) region of the tunnel diode, or Esaki Diode in honor of the inventor. Esaki won a
Nobel Prize for this work.
In this application to the nervous system, the interest is in the sections 2 & 3. Section 2 forms a I-V response
which could form an input impedance which would be at a much lower absolute voltage than expected in the
simple presence of bulk water in the n region of a PN junction.
50Wenger, O. Leigh, B. Villahermosa, R. et al. (2005) Electron Tunneling Through Organic Molecules in
Frozen Glasses Science vol 307, pp 99-102 DOI: 10.1126/science.1103818
51Wallis, T. and Kabos, P. (2017), Chapter 11. Dopant profiling in semiconductor nanoelectronics In
Measurement techniques for radio frequency nanoelectronics. Cambridge University Press, Cambridge,
[online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=922346
124 Neurons & the Nervous System
The presence of a high level of doping in the n region of a PN junction seems to generate a region of the I-V
characteristic that shows a peak response near 0.050 electron Volts ( 50 milli-electron-Volts) regardless of the
substrate used. Hall52 has noted even binary substrates like Gallium Antimonide doped with Arsenic exhibit the
same tunneling I-V characteristic (his figure 2). This is in comparison to the estimated voltage field of 40 and
60 milli-Volts estimated from the graphs of Eliasof et al. in Section 1.5.1.2 for a biological, specifically sample
sEAAT2B.
As noted in Section 1.5.1.2, the energy acquired by an electron falling through a one electron-Volt
field is defined as acquiring one volt of potential energy.
The estimate of 40 to 60 mV is the band gap of the PN junction. This estimate straddles the measured value of
the of many investigators, using many different doped substrates.
Mueller & Rudin demonstrated this band gap (~ 50 mV) in at least one of their biological samples (Section
2.6.1.2.2).
A listing53 by the USA Government begins with two recent papers discussing Gadolinium doped water in
connection with Cerenkov radiation (Gamma ray detection). The second paper report on a USA Patent
#8,373,133.
Several investigators have noted that the electrons tunneling from the conduction band to the valence band do so
at the speed of light. Cerenkov radiation results from energy absorbed by a material with a speed of light below
the free-space speed of light.
52Hall, R. (1960) Tunnel Diodes IEEE Explore vol January, 1960, pp 1-9
53https://www.science.gov/topicpages/g/gadolinium+doped+water
The Neuron 2- 125
Figure 2.2.3-8 EZ Water vs bulk water band gap as used in an Activa, a Node of
Ranvier OR synapse. The band gap of EZ Water is 20:1 narrower than that of
bulk water due to the tunneling (Esaki) mechanism. The result is a band gap due
to tunneling that is equal to that measured by Katz in 1949. EZ Water exhibits
both band gaps due to separate underlying mechanisms as indicated in Section
2.2.3.3.5. Only the band gap due to tunneling is used within the neural system.
Figure 2.2.3-8 compares the band gap of EZ Water with the band gap of bulk water. EZ Water exhibits both
band gaps due to separate underlying mechanisms as indicated in Section 2.2.3.3.5. Only the band gap due to
tunneling is used within the neural system. The band gap of EZ Water at nominally 50 millivolts agrees with the
value measured by Katz in 1949 (Section 2.2.4.1).
Both band gaps are active at the same time as they originate due to two separate mechanisms; tunneling on the
left and a conventional thermal mechanism on the right. The mechanism of tunneling solves the open questions
concerning the input impedance characteristic of the first Activa in all of the sensory neurons (Section 2.2.4.1)
2.2.3.4.2 Proposed symbol for an Activa exhibiting Esaki tunneling at its Input
The standard symbol for a forward biased Esaki Tunneling diode and a standard PNP transistor are shown in
frame (TOP) of Figure 2.2.3-9. Frame (Bottom) shows potential symbols for a PNP Activa exhibiting a
forward biased tunnel diode at its input. The manner in which the high level of doping is achieved at the input
junction may effect the symbology but not necessarily the operation of the Activa.
126 Neurons & the Nervous System
Figure 2.2.3-9 Proposed symbols for doped PNP activa based on standard
symbols. Top row; standard Esaki (tunnel diode) and standard PNP transistor.
Bottom row, right; dopant in EZ Water (crystal) forming base region. Right;
dopant in lipid forming the phospholipid of the outer lemma of the type 2 BLM of
each Activa. Only the bottom half of the base shows the wings of the Esaki
Diode.
2.2.3.4.3 Options for a heavily doped PN (Esaki) diode achieving oa EG ~50 mV.
There are two option for achieving the heavily doped condition for a PN diode to achieve the necessary band
gap, EG. One is through doping of of the BLM constituting the P material; the other is through doping the EZ
Water, in liquid crystalline form, constituting the N material. Either approach is on the frontiers of science. The
optimum condition is shown in Figure 2.2.3-3b of Section 2.2.3.3.5 where EV of the P material = EF of the N
material and the EF of the P material = EC of the N material. The EF is the Fermi Level, EV is the valence band
and EC is the conduction band.
Note the arrow direction and the word Holes under the word Tunneling in Figure 2.2.3-3b. The word Holes
indicates the region of holes accepts electrons from the conduction band of the N material.
Note the probability that the type 2 lemma does not employ a conventionally described conjugated lipid in the
longer lipid in the phospholipids of the liquid crystal (Section 2.2.1.3.4). It is likely to employ DHA in this
position with its unusual CH2 group between pairs of double bonds,
2.2.3.4.4 Symbol of PtdIns showing multiple pi-bonds in multiple cis-bonds
The symbol for a heavily doped PtdIns phospholipid, using pi bonds as the dopant, as shown in Figure 2.2.3-
10.
The Neuron 2- 127
Figure 2.2.3-10 PtdIns shown with four
double cis-bonds. Each double cis-bond
contains one sigma-bond and one pi-
bond. The pi-bond in each cis-bond acts
as the dopant. The right hand lipid is
Arahidonic acid. Added text to graphic
from Charlesy, 2021.
128 Neurons & the Nervous System
Figure 2.2.3-11 “Unsaturated fatty acids, lipids.” Right column Indicates number
of carbons and double bonds. Wikipedia. Ahem et al., 2021.
A Table of other dopant configurations appears in Figure 2.2.3-12.The first numeric in the right column as the
length of the lipid counting from the ether oxygen. The second numeric gives the number of double bonds
counting from the same location.
Ahem et al. note,
“ Humans and other animals lack the desaturase enzymes necessary to make double bonds at positions
greater than Δ-9, so fatty acids with double bonds beyond this position must be obtained in the diet.”
The entire book by Ahem et al54.is available for free and incorporates stick figures for virtually all fatty
acids.
2.2.3.4.5 PtdIns using a heavily doped p-type semiconductor
The variations in PtdIns (nine isomers) leads to confusion in the literature. Frequently an investigator does
54Ahem, K. Rajagopal, I. & Tan, T. (Online) Biochemistry Free For All 1.3 Oregon State
http://biochem.science.oregonstate.edu/content/biochemistry-free-and-easy
The Neuron 2- 129
not clearly identify the isomer he is working with. Section 8.5.1.6 provides the relationship between salt
(NaCl) and PtdIns and Section 8.5.4.4 reviews the details of the difficulties of discussing PtdIns. No
discussion of PtdIns as a doped semiconductor was located.
Within the last five years, the medical community has shown an interest in PtdIns, frequently under the label,
PI. Wikipedia55 has noted,
“PI has a polar and non-polar region, making the lipid an amphiphile. Phosphatidylinositol is classified
as a glycerophospholipid that contains a glycerol backbone, two non-polar fatty acid tails, a phosphate
group substituted with an inositol polar head group.
The most common fatty acids of phosphoinositides are stearic acid in the SN1 position and arachidonic
acid, in the SN2 position.”
See Section 2.2.3.4.4 for the explicit formulas for these fatty acids. The phosphoinositides is a broader
class than the glycerophospholipid.
The problem remains, the semiconductor properties of PtdIns when in the liquid-crystalline state (as it occurs
in the lemma of a cell) remains undocumented. Therefore, whether the pi-bonds of liquid crystalline
PtdIns can be considered a dopant, in the sense of semiconductor physics, remains unknown.
Ridgway56, 57 co-edited two volumes of what was meant to be an authority on Biochemistry of Lipids,
Lipoproteins and Membranes (6th and 7th Editions). Neither edition addresses the liquid-crystalline nature of
cell membranes or PtdIns as a liquid-crystal within a cell membrane. It does not recognize the importance of
PtdIns in gustation where it is the principle sensory receptor in the sensing of salt (NaCl). See Section
8.5.4.4.
In chapter 7 of the 6th edition, he notes, isomers of PtdIns are not uniformly distributed in cellular
membranes.
“ PtdIns is present in most organelle membranes, but its concentration changes considerably. This
fluctuation occurs due to the role of PtdIns in signal transduction . . . .”
At least partly, this variation is due to the role of PtdIns in its role in type 2 cell membranes (Section
2.1.4.2.1).
“ Altering the fatty acid composition of phospholipids has far-reaching impacts on membrane and
cellular function [Hishikawa et al., 2014]. The introduction of polyunsaturated fatty acids (i.e.
arachidonic and eicosapentaenoic acid) during remodelling produces phospholipid species involved in
cell signalling and increases the fluidity and permeability of membranes. As well, increasing the
proportion of polyunsaturated phospholipids at the expense of saturated species promotes negative
curvature and headgroup packing defects in membranes.”
See Section 2.2.3.4.4 for the explicit formulas for these fatty acids.
The journal, Liquid Crystals, shold be searched for the latest data on PtdIns.
2.2.3.4.6 Brief data on the double bond of organic chemistry
Without providing additional background (see any text on physical chemistry), a description of the double
bond in the sigma-pi model shown in Figure 2.2.3-12. In this case only two of the p orbitals on each C
atom are involved in the formation of hybrids. Consequently sp2 hybrids are formed, separated by an angle
of 120°. Two of these hybrids from each C atom overlap with H 1s orbitals, while the third overlaps with an
sp2 hybrid on the other C atom. This overlap directly between the two C atoms is called a sigma bond, and is
abbreviated by the Greek letter σ. This orbital has no nodes : electron density exists continuously from
55https://en.wikipedia.org/wiki/Phosphatidylinositol
56Ridgway, N. (2016) Phospholipid synthesis in mammalian cells_In Ridgway, N. & McLeod, R. eds.
Biochemistry of Lipids, Lipoproteins and Membranes, 6t h Ed. NY: Elsevier Chap. 7
57Ridgway, N. (2022) Phospholipid synthesis in mammalian cells_In Ridgway, N. & McLeod, R. eds
Biochemistry of Lipids, Lipoproteins and Membranes, 7t h Ed. NY: Elsevier Chap. 7
130 Neurons & the Nervous System
Figure 2.2.3-12 The sigma-pi model of a double bond. Three sp2 hybrids around
each carbon atom are indicated in color. Two of these overlap directly between
the carbon atoms to form the σ bond. Two p orbitals, one on each C atom, are
shown in gray. These overlap sideways to form a π bond, also shown in gray.
around one atom to the other atom.
The sp2 hybrid orbitals on each carbon atom involve the 2s and two of the 2p orbitals, leaving a single 2p
orbital on each carbon atom. A second carbon-carbon bond is formed by the overlap of these two remaining
p orbitals. This is called a pi bond, Greek letter π. The pi bond (π bond) has two halves—one above the
plane of the molecule, and the other below it. Each of the two electrons in the pi bond (π bond) exists both
above and below the plane of the four H atoms and the two C atoms.
The pi bond is at a higher energy state than the sigma bonds, and the electrons are less tightly bound. Ii
seems to me that in a quantum mechanical sense, these electrons will have a small but real probability of
being some distance from the parent atoms, making them capable of forming one or more "electron
donors"per molecule in a semiconductor sense.
2.2.3.4.7 PtdIns using a heavily doped n-type semiconductor
A potentially simpler form of PtdIns would be the case where the PN junction would involve only doping of
the n-type semiconductor. In this case, the EZ Water.
Colliex et al58. have provided details concerning the different modes of scanning transmission electron
microscopy, STEM, which might be useful in evaluating a heavily doped n-type semiconductor. They are
using a VG-HB501 system to achieve an acuity “varying between 0.5 and 2.0 nm depending on the
illumination aperture. In these circumstances the total probe current is of the order of 10~10 to 10 --9 A.”
Until recently, the study of biological tissue, with its high water content, was not compatible with electron
microscopy, with its high vacuum environment. Schuh & de Jonge59 has provided a method for avoiding
this problem in STEM using very thin windows to isolate the biological sample from the high vacuum, and
have demonstrated this capability using commercially available instrumentation. de Jonge60 has provided a
theoretical analysis of the capability, suggesting 2-3 Angstrom is achievable..
58Colliex, C. Jeanguillaume, C, & Mor, C. (1984) Unconventional Modes for STEM Imaging of
Biological Structures J Ultrastructure Res vol 88, pp 177-206
59Schuh, T. & de Jonge, N. (2014) Liquid scanning transmission electron microscopy: Nanoscale imaging in
micrometers-thick liquids C. R. Physique vol 15, pp 214–223
60de Jonge, N. (2018) Theory of the spatial resolution of (scanning) transmission electron microscopy in liquid
water or ice layers Ultramicroscopy vol 187,pp 113–125
The Neuron 2- 131
Figure 2.2.3-13 Template for demonstration of proposed band gap of the Activa.
All measurements to be made in absolute (DC) values. If a bipolar neuron is
used, it only has one input; the podite can be assumed to be grounded. If a stage
2 neuron with a differential input is used; the total voltage applied must be used.
E(dendrite) minus E(podite) must be used as the input.
While this capability was developed for water and ice, it should be available for the study of EZ Water.
2.2.3.5 Confirmation of the Activa’s input characteristic
The confirmation of the voltage range of the input characteristic of the Activa would confirm the proposal
that some form of tunneling is involved in reducing the band gap of the PN junction forming the input stage
of the Activa. This reduction is significant. It is a reduction from an undoped band gap of 10.0 volts to a
“doped” band gap of 50 mV, a ratio of 200:1 (Section 2.2.3.4.1) due to the implementation of a different
mechanism (Section 2.2.3.3.5) .
Experiments to confirm a band gap of 50 mV could be implemented using the stage 2 signal processing
neurons in-vivo, and in the dark, using the annotated Figure in Section 2.1.4.9 as a guide. Alternatives
would be other convenient stage 2 or 4 Activa where its input can be controlled and output can be isolated
during voltage measurements..
Demonstrating the band gap via DC measurements of the type shown in Figure 2.2.3-13 would constitute
proof of the proposal in Section 2.2.3.4.2.
2.2.4 Defining the conexus within a static neuron
132 Neurons & the Nervous System
This section will describe the electrical circuits associated with a neuron based on the discussion of the
previous section. It will develop an additional critical feature of neurons not previously documented in text
form. Circuits similar to the synapses found between neurons are also found inside of neurons. They
are found to occur wherever a gap junction is formed by areas of individual conduits exhibiting the necessary
juxtaposition of type 2 BLM. These circuits will be given the generic name conexus. A conexus is a circuit
containing at least one Activa along with the associated electrical elements required to bias the Activa, to
excite the Activa and to extract signals from the Activa.
The following subsections will describe the electrical, morphological and cytological features of two of the
three basic functional (active) circuits found within the neural system of an organism, the conexus within a
neuron and the conexus found between neurons. There is also a hybrid form, commonly called a Node of
Ranvier, that will not be discussed in detail until Chapter 3.
Brief note will be made of the fact that a single morphologically defined neuron may contain multiple
functional units that are given the name conexus. The fact that multiple conexuses can be found within a
single neuron forces a redefinition of the fundamental physiological unit in neuroscience. It is the conexus
that is the fundamental physiological unit of the neural system, not the neuron itself. The neuron
remains the fundamental morphological and metabolic unit of the neural system.
2.2.4.1 Defining the electrical circuits of a neuron
The fact that the neurons operate in a nonlinear impedance environment, at least in the second order, has
been recognized since the work of Katz 61. in 1949. Katz used the terms,
“The inwardly rectifying K+ (Kir) channel current was first identified electrophysiologically in high K+
depolarized skeletal muscle and was designated an anomalous rectifier K+ current.”
In those early days, the term “anomalous rectification” and “inward rectification” were found in the
literature. Recently, the expression has frequently been shortened to just rectifying channels. It is important
to understand the theoretical and practical voltage-current characteristic of a diode or Activa. This
characteristic is fundamental to the operation of all neurons. It plays a primary role in all experimental
investigations and the proper interpretation of all test results.. Katz used the term, “Kir” before the
announcement of the discovery of the transistor, the discovery of tunneling by Esaki in semiconductor
materials in 1957 and the elucidation of the exclusionary properties of EZ Water when confined to narrow
spaces (less than 500 microns) during the 1960's See the review by Dowben in 1969 (Section 2.2.1.3).
This section will compare the band gap of EZ Water of Section 2.2.3.4.1 with the input characteristic of
biological material by Katz.
The fundamental voltage-current characteristic of all diodes and active semiconductor devices is a simple
exponential function. As usually presented in conventional transistor circuits, the input impedance of a
typical Activa is shown in frame A of Figure 2.2.4-1.
61Katz, B. (1949) Les constantes electriques de la membrane du muscle. Archived des Sciences Physiologiques,
vol. 3, pp. 285-299
The Neuron 2- 133
Figure 2.2.4-1 Input impedance and output characteristic of common base
configured Activa. See text.
Under the proper bias conditions, and neglecting the small loss of current related to the base current, Ib, the
transfer impedance of an Activa is shown in frame B. It is identical in form to the input impedance within
the operating range of the device.
Replotting frame B as a function of the collector to base potential results in a very useful frame C, the basic
output characteristic of a neuron. It is identical in form to that of a man-made transistor.
If a resistive impedance is in series with the power source supplying the reverse bias to the collector terminal
is of finite impedance, the operating conditions applicable to the neuron can be described in frame D. For
zero current through the device, the potential VCB is equal to the supply potential shown as ECC. For finite
currents, the potential VCB is reduced by the voltage drop across the load resistance, RL, as suggested by the
dotted cross. If excessive current is called for by the input potential, a condition called saturation can occur.
134 Neurons & the Nervous System
Saturation occurs when the collector-to-base potential, VCB, falls below the emitter-to-base potential, VEB.
At this collector potential, the required bias conditions are no longer met and “transistor action” is lost.
For a typical neuron, an electrostenolytic potential, ECC, near –150 millivolts is used to power the collector of
the neuron. The quiescent collector (axon) potential, VCBQ, is typically near –70 millivolts for signal
processing neurons. For signal transmission neurons generating action potentials, the quiescent potential,
VCBQ, remains near cutoff, –150 millivolts. The operation of the neuron under non-quiescent conditions will
be discussed in Section 2.3.
The current capability of the neuron can be increased by enlarging the cross sectional area of the Activa. To
achieve large increases in current capacity, multiple Activa can be connected in parallel. Arrays formed of
individual Activa are commonly seen in electron micrographs. It appears that each Activa is formed by a
vesicle pressing one conduit membrane against the other. An electron micrograph showing an equally
spaced array of vesicles is frequently indicative of a similar adjacent array of Activa (Section 2.4.3.3 and the
freeze-fracture samples in Chapter 5).
The complexity of the electrical circuits within a neuron requires a much more detailed knowledge of the
concept of impedance than typically found within the field of chemistry (although the concept does appear in
chemical engineering). A large field of electrical engineering has developed to aid in interpreting these
relationships, which are frequently non-linear. The many tools of electrical of circuit theory cannot be
addressed here. However, it must be pointed out that Ohm’s Law (frequently quoted in the neural
literature) is not usually applicable to most neural circuits. Ohm’s Law does not apply to nonlinear
circuits or circuits containing an active power source. The broader concepts associated with Kirchoff’s Laws
must be used. Using Kirchoff’s Laws frequently involves applications of Thevinen’s Theorem, a theorem
allowing the replacement of a set of circuit elements connected in series with an equivalent set of circuit
elements connected in parallel. The choice of a set of series or a set of parallel elements may appear
arbitrary in the following material. However, Thevinen showed that the two forms are interchangeable if the
appropriate rules are followed.
In frame (D) of the previous figure, a useful technique was applied to describing the operation of an
electrical amplifier composed of an Activa and a finite impedance in series with the device and its power
supply. The concept is simple, the current through the collector element and the load element must be equal
if they are in series, and the voltage between the collector terminal and ground and the voltage across the
load impedance must sum to the power supply voltage. The only point on the graph of the collector current
versus collector potential where these two conditions are met is at the intersection of the load line and the
operating point of the Activa (the point marked by the dashed cross). It is important to note that there is no
requirement that the circuit elements be linear in the above formulation. This is particularly important in
neuroscience because very few linear dissipative impedances are found within the neural system. Diodes far
outweigh resistors in importance within the neural system.
Kirchoff’s Laws will be used sparingly in this section. However, they become much more important in
Section 2.3 where it is frequently necessary to consider combining several nonlinear circuit elements into a
single equivalent circuit element. A reader seeking to follow these manipulations in detail must be familiar
with Kirchoff’s Laws and the other rules of electrical circuit theory.
2.2.4.1.1 Rectification, frequently misconstrued in literature
Two facts, that have been largely overlooked in the literature, are important in experiment design. A diode
in the absence of any other electrical component is useless, especially for signaling purposes. Whether a
diode is considered a linear element in practice, a logarithmic signal compressor, or a rectifier depends on
the voltage level applied to it and the other circuit elements present. Under small signal conditions, a diode
can be considered a fixed impedance. If the signal is larger but its instantaneous value is always either
significantly larger or smaller than VT, the circuit is valuable as a signal compressor or expander. This is
the primary role of the diodes in the neural system. If very large signals are applied to the circuit containing
a diode and the instantaneous amplitude of the signal straddles the voltage VT, the signal appearing across
the diode will be significantly changed in shape (distorted). The diode will be acting as a rectifier. In the
neural system under in-vivo conditions, the absolute potential of all of the signals (which may include a bias
component) applied to the diodes are larger than VT. The resulting circuits operate as signal compressors
or expanders. It is only under artificial conditions created by man (or unfortunate lightning strikes), either
in-vivo or in-vitro, that the diodes may be driven into the “rectifying” region. In the laboratory, it is
important to recognize two facts:
+ that nonlinear amplification, either signal compression or expansion as a function of the applied parameter
is the normal condition. This nonlinear amplification can be further described as exponential in most cases.
The Neuron 2- 135
+ that rectification in the neural system (except in stellate neurons, Section 2.3.4.5.5) is due to poor
experiment design. Application of test stimuli of more than 100 mV do not emulate actual neural signals and
are frequently destructive of the tissue under test.
When investigators observe and speak of rectification in the neural system, it is normally; a property
introduced by their test configuration, and a pathological condition. This observation applies to both the
static neuron and the neuron under more dynamic conditions discussed in Section 2.3.
2.2.4.2 Defining the fundamental conexus within a neuron
2.2.3.4.2 The proposed I-V characteristic of a functional Activa MOVE INTO 2.2.4
To provide the necessary potentials to the emitter and base terminals of the Activa within a neuron, circuits
similar to the collector circuits of the previous figure are used, as shown in Figure 2.2.4-2(A). It appears
that all of the potentials supplied to the neuron are negative with respect to the surrounding medium. This
does not introduce a problem in meeting the bias requirements for transistor action, since it is the absolute
differences between these potentials that must satisfy the bias requirements. The specialized chemical
process providing these potentials will be discussed in Chapter 4. The vertical line above the frame is
designed to focus attention on the physical division of the Activa between two conduit membranes.
.
2.2.4.2.1 Overlay of electronic circuitry and cytology of a neuron
Figure 2.2.4-2(B) begins the process of merging the electrolytic circuitry of the neuron with the
conventional morphology and cytology of the neuron. The figure is at a scale that allows the cytology and
the electrical topology of the neuron to be compared easily. The shaded areas indicate type 2 areas of the
biological bilayer membrane forming the conduits of the neuron. The portion of type 2 BLM normally
associated with the poditic impedance, ZP, is not illustrated as a matter of convenience. The remainder of the
conduits are formed of type 1 BLM, except for a small area of type 3 membrane dedicated to supporting
carbohydrate metabolism. Both the type 1 and type 3 BLM are intrinsically impermeable to electrical
charges and the type 1 BLM is also impermeable to small molecules and all ions. The large areas of type 3
and inert type 1 membrane contribute considerable capacitance to the electrical characteristics of the
individual conduit. It is the areas of type 2 BLM that support, and participate in the signaling function. The
support is provided by the areas labeled as power sources. The symbology shown is simplified and uses only
fundamental electrical symbols. It only shows a diode in series with a small quantum-mechanical battery,
with the pair of elements shunted by a capacitance. In the case of the power sources, a more complex
arrangement will be developed below (Section 2.2.6).. The actual signaling function is shown by the
portions of type 2 BLM shown at the two ends of the figure. Here again the symbology is simplified. The
base of the diode is shown extending into the exterior space adjacent to the type 2 BLM.
A dashed box has been drawn around the elements of the neuron comprising the complete electrical circuit
centered on the Activa within the neuron. This group of electrical elements will be defined as a conexus.
Also shown by the horizontal black bar is the actual size of the region forming the Activa. It is
approximately 280 Angstrom wide, a dimension that can only be imaged with an electron microscope.
Figure 2.2.4-2(C) provides a similar image at a lower magnification that allows the morphology of the cell
to be compared with its electrical topology. In this frame, the symbology of the Activa using primitives has
been replaced by the more compact symbol for an electrolytic semiconductor device, the Activa. Notice the
minimal functional role played by the nucleus of the neuron. The role of the nucleus plays an important role
in the neuron, but the role is fundamentally metabolic. The area of the conexus remains enclosed in a dashed
box. The symbol for the impedance ZP has been replaced by the symbol for a power source for consistency
and an additional terminal is shown within the dashed box. Its role will be developed in Section 2.3. Two
important features will be developed more fully below. The reticulum found inside most neural conduits
describes a demarcation between the relatively liquid, but viscous nature of the core of the signaling conduits
and the surrounding material. This material tends to be more complex in chemical and physical character.
For the moment, the electrical signal is shown flowing along the “wire” representing the electrical
characteristics of the content of the reticulum. The type 2 BLM at the ends of the figure are shown as
forming parts of an Activa that could be completed through cooperation with another adjacent neuron.
These regions will be developed more completely in Section 2.2.4.3.
136 Neurons & the Nervous System
Figure 2.2.4-2 Overlay of electronic
circuitry of a fundamental neuron on its
topography. See text.
2.2.4.3 Defining the third operational
terminal of & within a neuron
The three-terminal character of the Activa
suggests that the neuron is also fundamentally a
three terminal device. By exploring the cytology
of a neuron in detail, it can be shown that many
neurons do in fact exhibit three electrically
isolated conduits associated with the internal
conexus. This conduit can assume a variety of
morphological shapes as will be illustrated below.
This additional conduit will be labeled a podite.
This conduit shares many common features with
the dendrite and the two will frequently be
referred to using the generic term neurite.
Recognizing this third fundamental circuit related
to a neuron introduces a broad range of additional
capabilities not previously explained in the
literature. The principle capabilities are two; the
ability to generate signal amplification and the
ability to invert the electrical polarity of a signal.
2.2.4.3.1 Additional capability provided
by the poditic conduit/terminal
–Differential input
It took only a short time for electrical engineers to
discover the transistor, when configured like frame
A above, offered an additional useful
characteristic. Recall that the equation describing
the current through an Activa, like a transistor, is a
fixed one based on the quality of the manufactured
device. Up until now, the static transfer characteristic has been described in terms of an injected emitter
current resulting from a change in the emitter voltage relative to the base voltage (the so-called common base
configuration). If the emitter to base voltage is changed by injecting a current into the base terminal, the
resulting emitter and collector currents must be much larger than the base current to satisfy the basic current
equation. Whereas the collector current is necessarily slightly smaller than the emitter current in the
common base configuration, the situation for the common emitter configuration is quite different. The
collector current is typically 100 to 300 times higher than the base current, depending on the intrinsic quality
of the device. This represents a considerable current gain (output current at the collector divided by the
input current at the base) that can be used to achieve significant signal amplification. The base terminal is
described as a high impedance input terminal because of this capability. Only a small current is required to
achieve a given (significant) base to emitter voltage change.
Figure 2.2.4-3 presents the transfer characteristic of a common emitter configured Activa. Besides the high
current gain exhibited by this configuration, note the inversion of any change in current. A negative going
increase in base current results in a positive increase in collector current. The common emitter circuit
operates as a signal inverter. The current gain associated with the common emitter configuration is not as
uniform as that of the common base configuration. It varies with collector to base voltage. Whereas the
dynamic output impedance of this circuit, change in collector voltage divided by the change in collector
current (and discussed further in the next section), is about 4,000 megohms, the transfer impedance is much
higher. The load line suggests the impedance of the electrostenolytic collector supply is also about 4,000
megohms. The signal gain is about 50:1. These are the numbers for a very small neuron such as might be
found within the brain. They suggest how difficult it is to make measurements on the vast majority of
individual neurons.
The Neuron 2- 137
Figure 2.2.4-3 Transfer characteristic of a
common emitter configured Activa. Note
the inversion of the collector current
relative to the base current. Also note the
small change in current gain, iC/iB with
changes in collector voltage.
Figure 2.2.4-4 illustrates the fundamental neuron
with its differential input structure. The top frame
shows the morphological representation. The
dendrite typically extends from the apical portion
of the neuron. The podite typically extends from
the periphery of the base of the neuron. The axon
typically extends from the center of the base of the
neuron. The lower frame shows the electrical
equivalent showing the Activa of the typical lateral
neuron, AL, with both of its input structures both
arborized. This configuration is frequently labeled
as a “bi-stratified neuron.”
2.2.3.4.3 The pros\posed cross section of a functional Activa EMPTY
138 Neurons & the Nervous System
Figure 2.2.4-4 Differential input structure
of a typical lateral neuron. Top; typical
morphology of a lateral neuron. Bottom;
typical electrical equivalent circuit of the
lateral neuron showing the differential
input structure. The dendrite or emitter
input is non-inverting unity gain input,
Vin(1). The podite or base input is an
inverting input where the gain depends on
the impedance of the driving circuits and
the load shown between the base and
local ground.
The circuit shown is that of a common analog
signal processing neuron in stages 2, 4 and 5 of the
CNS.
By appropriate biasing and choice of the load
impedance in the base lead, it can be converted
into a monopulse oscillator of stage 3A producing
action potentials in response to the input potentials
on its differential inputs (Section 9.4.3).
The Neuron 2- 139
2.2.4.4 Illustrating the neuron using electrical engineering symbology
The nominal neuron found throughout the neural system, with the exception of the stage 1 sensory neurons
that are more complex 2-amplifier devices, can be described quite easily using current electrical engineering
terminology. Each neuron is a three-terminal device (not a two-terminal device as commonly considered in
biology), where the count reflects the number of signaling terminals. In addition, each neuron is supported
by two (non-signaling) power supply terminals. The power supply aspects of the circuit are developed in
greater detail in Section 3.2.2. Figure 2.2.4-5 shows the roles of glutamate and GABA separated from their
historical roles. This historical role was based primarily on their ubiquity relative to neurons and not their
functional characteristics. The names glutamatergic and GABAergic are obsolete. The terminals of the
neuron are more appropriately labeled non-inverting (the dendritic input) and the inverting (the poditic
input). The single axon output is shown. All synapses associated with the dendritic tree introduce signals
that are applied directly to the emitter terminal (the non-inverting input) of the Activa within the neuron. All
synapses associated with the poditic tree introduce signals that are applied directly to the inverting input and
connected to the base terminal of the Activa within the neuron. The roles of glutamate and GABA are
separated into their neuro-facilitator and neuro-inhibitor roles (replacing their archaic labels of
neurotransmitters).
Glutamic acid (glutamate) is shown as participating in the electrostenolytic process, where Glutamate is
captured at the mGluR receptor on the surface of the type 2 lemma and performs the reaction;
Glutamate –> GABA + CO2 + electron
where the electron is injected into the axoplasm of the neuron and the GABA + CO2 are released into the
matrix surrounding the neuron.
Every neuron exhibits a positive going, non-inverting, amplifier input and a negative going, inverting,
amplifier input. These inputs are unrelated to activity at the source and drain terminals of the neuron. When
operating in stage 3 pulse mode (generating action potentials), the neuron’s consumption of glutamate and
creation of GABA are proportional; and both the consumption and creation are proportional to the pulse rate
driving the neuron. This interpretation explains the ubiquitous presence of glutamic acid and GABA
throughout the neural system.
A separate input is shown for possible neuromodulators (such as L-dopamine).
This figure uses the symbology used in Electronics for an Operational Amplifier to
provide the necessary number of external connections to an individual neuron and
to provide the differential input structure. The output/input = gain of the neuron
is nominally = 1.00, not the very high gain associated with the commercial
operational amplifier.
140 Neurons & the Nervous System
Figure 2.2.4-5 The role of glutamate and GABA in powering the neuron using the
symbology of electrical engineering. The signal inputs are labeled +, non-
inverting (or excitatory) and –, inverting (or inhibitory) in line with their function.
Glutamate is shown as the source of energy to the circuit (neuro-facilitator) with
GABA shown as a residue being drained away (neuro-inhibitor). See text.
The Neuron 2- 141
Figure 2.2.5-1 Fundamental morphological
forms of neurons.
2.2.5 Preview of forms and amplifier capabilities found within neural systems
The cytological form of neurons is frequently discussed without clear differentiation between potential
forms. Similarly, the observed functional performance of a neuron is frequently discussed without taking
note of the form of the conexus within the neuron. This section will briefly develop these two subjects.
2.2.5.1 Preview of neuron morphologies using electrolytic theory–ETN
Figure 2.2.5-1 illustrates a common labeling of neuron based on their external appearance. The descriptions
shown in A & B have been used forever to indicate the number of arms radiating from the soma containing
the nucleus. In fact, the location of the nucleus is irrelevant to the operation of the neuron. Both of these
illustrations relate to a fundamental neuron, exhibiting one dendritic tree whose trunk interfaces with the
trunk of one axon at an Activa (or array of unit Activas). Based on the number of arms extending from the
Activa, these can both be considered bipolar fundamental neurons. The dendritic tree connects to the emitter
terminal of the Activa. The axon connects to the collector terminal of the Activa. The signal out of a bipolar
neuron is in fact the same polarity as the signal input to the neuron via the dendrite. Confusion can be
avoided by labeling the monopolar neuron, the unipolar neuron.
Frames C & D show the next level of complexity in neurons. A separate functional structure, described as a
podite is shown. This structure is associated with the base region of the Activa within the neuron. It
introduces the signal inversion capability to the neuron. The signal out of the neuron is of opposite electrical
polarity as the signal input via the podite.
Frame C illustrates what is frequently described as
a bi-stratified dendritic tree. It is usually described
as having one dendritic tree emanating from the
point of the neuron opposite to the axon and a
second tree emanating from the rim of the neuron
perpendicular to the axis between the first tree and
the axon. The position of this second tree is
believed to be diagnostic for the poditic input
structure. In very complex neurons, it is possible
to exhibit multiple trees as in frame D, and the
generic label multipolar is frequently seen.
Alternately, the label stellate (star-like) neuron is
frequently encountered to suggest the neuron has
multiple poditic trees radiating from a nominally
circular base of the soma. The morphological
designation, stellate, is unfortunately not indicative
of the operational mode of the neuron discussed in
the next section.
Greenfield has illustrated these forms in a more
artistic form62.
Frame E illustrates a commonly observed
configuration, a stage 3 projection neuron. This
neuron is fundamentally a bipolar neuron (one
dendritic tree and a poditic contact to the extra-
neural matrix) where the axon has been segmented by Nodes of Ranvier. This type of neuron is designed to
project neural signals over significant distances (several meters in the case of large mammals). It will be
shown that each Node of Ranvier acts as a signal regenerator that eliminates the subject of signal attenuation
as a function of distance within the stage 3 neuron. As in the case of the simpler neurons, this neuron can be
ramified to include multiple dendritic trees, multiple poditic trees and multiple axons.
By combining the Activa found within neuron with those found between neurons, a complete fundamental
signaling path is defined. A signal introduced into the first dendroplasm (or podaplasm) can be reproduced
62Greenfield, S. ed. 1999) Brain power : working out the human mind. Boston, MA: Element
142 Neurons & the Nervous System
(in modified form if desired using analog signal processing) at the last axoplasm of the circuit at any desired
distance from the source.
2.2.5.2 The fundamental neural signaling path of biological systems
Noback has provided the conventional definition of a neuron shared by many authors. “The neuron is the
keystone; it is the morphologic unit, the functional unit, and the ontogenetic unit of the nervous system63.”
While this is a satisfactory introductory definition for pedagogy, it is not scientifically adequate. Shepherd
& Koch have recently taken a big step forward by describing the synapse as the basic functional unit of
neural circuits64. However, their discussion is based entirely on the conventional chemical view of the
synapse that is not supported here. They also remain unaware of the Activa within each neuron and the
commonality of the conexuses within the soma of the neuron, within the synapses and within the Node of
Ranvier. These relationships will be discussed thoroughly in Chapter 10. It will be shown that there is a
functional unit that is frequently replicated within a single neuron, and between neurons. This replicated
conexus is properly defined as the functional unit of the neural system, and within the neuron itself. It is the
Activa, and its supporting plasma conduits and electrolytic elements, that form the fundamental functional
unit, the conexus, of the neural system.
The signal transport role supporting the collection of sensory information and distribution of commands can
be described functionally by Figure 2.2.5-2(a). A signal (Iin) is delivered to a series of electrolytic conduits
as shown. A message related to that signal is propagated along the neural system until it emerges at the
output as a signal, Iout. This figure highlights the fundamental functional unit enclosed by the small dashed
box. This unit includes a junction plus a pre-junction electrolytic conduit and a post junction electrolytic
conduit. The following material will show that this fundamental unit can be described as in (b). In this
figure, the junction between the two electrolytic conduits may be connected to an additional source of
electrical bias. Under the appropriate conditions, the circuit of (b) can be portrayed as in (c). In (c), the
junction is portrayed as an electrolytic transistor, known as an Activa, that operates exactly like a man-made
transistor.
The configuration of the fundamental functional unit of the neural system in (c) exhibits great flexibility. By
varying the associated components and biases, the circuit can be made to operate in a variety of electrically
functional modes as suggested by (d), (e) and (f). Chapters 8, 9 & 16 will develop these capabilities in
detail. The generic functional unit of the neural system is best described by frame (f). It consists of an
Activa and its associated electrolytic circuit elements. These elements are typically parts of the preceding
and subsequent conduits.
63Noback, C. (1967 The Human Nervous System. NY: McGraw-Hill pg 28
64Shepherd, G. (1998) The Synaptic Organization of the Brain, 4th ed. NY: Oxford University Press pg 3
The Neuron 2- 143
Figure 2.2.5-2 Fundamental functional form of the neuron and its electrical
variations. A; the nominal signaling path of the neural system. The inner box
encloses a minimal physiological unit (the conexus) of the neural system. The
outer box encloses multiple conexuses as typically found within an individual
signal projection neuron, a fundamental metabolic unit. B; the Activa within a
conexus shown in electro-cytological form. C; the Activa within a conexus
shown in standard symbolic form. D, E & F are discussed in the text.
2.2.6 Details of the static electrical properties of neural conduits
Each neural conduit of a neuron is similar in physical construction and composition. It is the auxiliary
electrolytic elements that distinguish one conduit from another. These elements consist of various diode
derived resistive impedances, a capacitance related most directly to the surface area of the conduit, an
electrical power source, and the Activa at each end of the conduit. In the case of the axon, there is also the
option of an exterior myelin wrapping designed to minimize the total capacitance of the conduit with respect
to the extra-neural matrix.
The total capacitance and the capacitance per unit length of the axon plays a major role in stage 3 neuron
operation (Section 2.6.2.4).
As noted earlier, the typical lemma frequently exhibits specialized regions associated with the above
functional electrolytic elements. These specialized regions generally exhibit the same capacitance values as
any other bilayer lemma, but their resistive characteristics can be substantially different.
Because of the significantly different properties of symmetrical and asymmetrical BLMs, it is important to
go beyond the description of the cell membrane using averages. The topology of the individual
phospholipids may need to be mapped. As a minimum, the degree of electrical asymmetry of each region of
the membrane needs to be specified.
The type 1 lemma is symmetrical and always a virtually perfect insulator. The type 2 lemma is asymmetrical
by definition.
144 Neurons & the Nervous System
Normally, the equivalent circuit of the type 2 lemma is characterized by the cathode of a diode being in
contact with the “exterior” of a conduit and the anode being connected to the interior of the conduit. There
may be exceptions to this orientation in stage 8 cardiocyte cells.
2.2.6.1 Equivalent circuit of the axon element
The electrical characteristics of the axon have been studied the most because of their presumed dominance in
the historical common wisdom. It has been due primarily to the ease of access to axons. The dendrites are
generally very small structures and the poditic structures have not generally been identifiable through
morphology. These structures will be addressed independently in this section.
Over the years, a series of ever more complex two-terminal networks have been presented in the literature
that purport to represent the active characteristics of “the axon” or of “the axon membrane.” From an
analyst’s perspective, the proposed networks have gotten out of hand. The original two-terminal network of
Huxley et. al. consisted of three current paths and one capacitive path in parallel, each connecting to the
“inside” and the “outside” of the plasma membrane. Shepherd shows a total of seven paths65. Demir et al.
have recently shown eleven independent paths and introduced an unexplained symbol to represent some sort
of resistance66. Each current path consisted of a battery and a “variable resistor” in series. Subsequent to
Huxley et al., the polarity of the batteries frequently varied in subsequent transcriptions, analyses, and
expansions of these simple circuits (example, Nickerson & Hunter67). These networks have no significance
in the world of electrical engineering. They all reduce to a much simpler circuit. Their purpose appears to
be strictly pedagogical or at best conceptual and requiring many words to elucidate the actual concept. The
original network of Hodgkin & Huxley is shown in Figure 2.2.6-1(A). The circuit was highly conceptual at
the time and no reason could be found in their papers for the battery in series with the load resistance, RL. In
the original paper, the authors were careful to specify that they were reporting on a membrane. They did not
claim to be reporting on a functional neuron, a functional axon, or even an operating axon, in that paper.
The variable resistors were seldom discussed in detail. There has been no discussion of what is controlling
their variation although Raymond & Lettvin68 offer the important observation: “It is obvious that gNa and gK
are not two-terminal elements but three-terminal elements; they are governable conductances in much the
same way as is any junction transistor . . .” The idea is right, these proposed impedances are typically three-
terminal impedances controlled dynamically by an unknown hand.
Figure 2.2.6-1(B) shows a more precise representation of a portion of neural membrane using the style of
Huxley, et. al. The membrane is represented on the right as consisting of a single conductive path and a
single capacitive path. The conductive path consists of a diode and a battery in series. The symbol, idiff
represents a conventional current entering the plasma through the membrane; the symbol, ediff, represents the
equivalent electron current flowing out of the membrane from the plasma. In this representation, the circuit
on the left represents both the electrostenolytic source biasing the plasma to a negative potential and the load
impedance. The load impedance is shown as external to the equivalent circuit of the membrane alone.
There are problems with both of these representations. In (A), no means is provided to determining the
value of the individual resistances although it is stated that they vary with time and the membrane potential.
This statement implies that there must be other elements to the circuit.
(B) is more explicit in defining the membrane as an impedance, Zm – a diode, in series with a voltage, Em.,
both shunted by the intrinsic capacitance of the lemma. These are intrinsic parameters of the bilayer
membrane. There are no undefined variable impedances. However, it does not separately identify the
different types of lemma present. The circuit on the left represents the electrostenolytic process biasing the
axoplasm of the complete neuron. It includes both the load impedance and a battery. The battery potential,
Vsten, is normally much higher than the intrinsic potential, Em, of the membrane. The electrostenolytic
source is the subject of Chapter 3.
65Shepherd, G. (1988) Neurobiology, 2nd ed. NY: Oxford Press Pg. 114
66Demir, S. Clark, J. & Giles, W. (1999) Parasympathetic modulation of sinoatrial node pacemaker
activity in rabbit heart: a unifying model Am J Physiol Heart Circ Physiol vol 276, pp H2221-H2224
67Nickerson, D. & Hunter, P. (2010) Cardiac Cellular Electrophysiological Modeling Cardiac Electrophys Meth
Models, Part 2, pp135-158
68Raymond, S. & Lettvin, J. (1978) Aftereffects of activity in peripheral axons as a clue to nervous coding. In
Physiology and Pathobiology of Axons, Waxman, S. Ed. NY: Raven Press pp. 203-225
The Neuron 2- 145
The above representations are incomplete. The actual operation of the axon compartment can be understood
using a more complete end view of an axon shown in (C). This frame segregates the membrane of an axon
into four identifiable regions shown here as quadrants separated by the lines at 45 degrees.. Two of the
regions are normally in contact with the extra-neural matrix. The other two are not. In the latter case, each
of the regions is in intimate contact with another conduit of the neural path. When biased properly, these
two conduits constitute an Activa and exhibit “transistor action.” The emitter terminals on the left appear as
diodes in series with an impedance, ZP. Any change in current, Iin ,resulting from a potential, Vin, will result
in an equal change in current to be injected into the axoplasm causing a depolarization. This depolarization
of the axoplasm will cause a change in the current flowing out of the axoplasm through the right Activa.
Simultaneously, the electrostenolytic supply will begin to cause current to flow out of that channel to restore
the quiescent condition.
It is important to note the pure capacitance in the upper quadrant. A majority of the membrane of any
conduit is type 1 lemma and not designed to pass any current. The lower region represents a key element of
the overall axon. Like the lemma in the left and right quadrants, the lemma is type 2. Although the
membrane itself appears much the same visually as the type 1 lemma, it is intrinsically and functionally
different. The membrane exhibits a finite impedance and an intrinsic membrane potential as shown. This
portion of the membrane, when coated with an electrostenolytic material, can introduce an electron flow into
the axoplasm by electrostenolytic action. This current will generate a voltage across the combination of all
of the current paths represented by the various lemma. There is a source impedance associated with this
electrostenolytic source. This impedance is the load impedance of frames (A) and (B).
The relationship between the electrostenolytic source, the source impedance and the net impedance of the
diodes in parallel determines the quiescent potential, or resting potential, of the axoplasm. To a large extent,
it is this axoplasm potential that is measured in experiments.
If the overall circuit in (C) is disturbed by connection to a test set, the quiescent potential and any changes in
current flow must be evaluated by adding the test set equivalent circuit to the electrolytic configuration in
frame (C). Hodgkin and Huxley reported that the impedances, which they showed as resistances in frame
(A), varied with the potential of the plasma. It will be shown this is exactly what is expected of the network
of frame (C). In their early papers, they did not address the question of whether their calculated impedances
were due to the static or dynamic characteristics of the equivalent diode.
It becomes obvious from frame (C) that the method of sample preparation plays a large role in the measured
characteristics of a single section of neural conduit, whether it is called an axon, a dendrite or a podite.
146 Neurons & the Nervous System
The Neuron 2- 147
Figure 2.2.6-1 Illustration of the various electrical equivalent circuits representing
individual specialized regions of the axolemma. A; the 2-terminal equivalent
circuit of the isolated axolemma based on the constrained analysis of Hodgkin
& Huxley and others. B; the more general network associated with the
axolemma that can be used in several specific applications. C; a composite
representing a longitudinal cross section of an axon before it has become
extended horizontally. The boundary layer between the axolemma and the
axoplasm is needed to properly understand the operation of the conduit. The
Activa on the left represents the internal connection with a dendrite. This region
of the axolemma is of type 2. Conventional current is injected into (electrons
actually leave) the boundary layer by transistor action. [all arrows in frame C
represent conventional currents]. The Activa on the right represents the synaptic
connection with an orthodromic axon segment or dendrite. This region of the
axolemma is of type 2. Conventional current leaves (electrons actually enter) the
boundary layer by transistor action when the axoplasm depolarizes. The
capacitance at the top represents the type 1 membrane used for a majority of the
axolemma surface. The network at the bottom represents the type 2 membrane
region used to polarize the axoplasm combined with the electrostenolytic source
(battery). A conventional current leaves the boundary layer when the axoplasm
becomes depolarized. The axoplasm remains iso-electric through out the
process due to the mutual repulsion among the electrons within the axolemma.
148 Neurons & the Nervous System
2.2.6.2 Equivalent circuit of the dendritic element
2.2.6.2.1 Background literature
Describing the electrical circuit of the dendrite is complicated by the extreme variation in its topography.
Stuart, et. al. have recently edited a broad discussion of the dendrite69. It continues the policy of discussing
the morphology and chemical functions of the dendrite while only discussing its signaling function from the
most global perspective. This work takes exception to their basic premise on page 232 that “The action
potential is the final output signal of most neurons.” As will be discussed in Chapter 9, less than 5% and
probably less than 1% of all neurons have action potentials as outputs. Only projection neurons in stage 3
generate action potentials.
The complex topography of the dendrites, and frequently the podites as well, leads to difficulty in
determining the electrical topology that best describes the element. For the longer uniform stretches of
dendrite, it can be modeled as a distributed transmission line similar to equivalent structures of an axon.
Where branching is prevalent, it is more useful to represent each branch as a lumped equivalent of the
distributed parameters. In both cases, the conduits are unmyelinated and the capacitance per unit length
dominates, but do not eliminate, the inductance per unit length (Chapter 9). Segev & London have
reviewed various dendrite models in Chapter 9 of Stuart, et. al. Segev & London have followed the
approach of Rall70, who ignored any inductance present. Rall typified the approach used from 1900-60.
The dendrite is modeled as a cylinder but it is studied by a patch approach where only the time constants
related to the resistive and capacitive parameters of the cylinder wall were studied. Rather than use a second
order Euler (alternately Cauchy) equation, they employed a simpler first order differential equation with
constant coefficients. The result is an infinite series solution to a wave equation instead of a closed form
solution based on sinusoids. It is suggested that a more conventional electrical circuit theory approach to
this problem would provide better results in a closed form. This would be particularly true with regard to the
excessively long time delays predicted by their approach. At the impedance levels involved, the impedance
of the various inductances is much smaller than the resistances they shunt. See Section 9.1.1.3..
In the absence of a complete circuit model for the neuron, Segev & London struggle with the mechanism of
signal amplification in the neuron. Although they do not define the soma specifically, they appear to be
treating it morphologically as the portion of the cell other than the dendrites and axons. They do speak of
the source of the action potential as occurring at generally unspecified locations internal to the soma.
Segev & London have made considerable progress in recording the steady state electrical properties of the
dendrites, and sometimes relative to the associated axon. However, the asymmetrical waveforms shown for
the response to a simple pulse in their dynamic signal experiments all suggest significant impedance
problems in their test configuration due to the high impedance levels.
The above assumptions have a major impact on the seven insights, based on the passive (RC) cable model,
presented in their paper. By recognizing the presence of inductance in the dendritic circuits, time constants
at least one or two orders of magnitude lower would be calculated. Similarly, the voltage attenuation for
dynamic signals would be considerably lower. Finally, the time delays based on an RLC circuit, where the R
is usually negligible would lead to much lower time delays within the dendrites. By recognizing the
presence of an Activa within their soma, operating in the current summation mode, their comments about
window duration for signal summation take on a different meaning.
2.2.6.2.2 Equivalent circuit in this work
Because of the much higher transit velocity for dendritic signals deduced from other works, typically 40
times higher than in Segev & London, and the short physical distances involved, it is best to consider the
fundamental dendrite as a set of individual coaxial cylinders. The intrinsic inductance and capacitance of
such a structures is easy to calculate.
69Stuart, G. Nelson, S. & Hausser, M. (1999) Dendrites. NY: Oxford Press
70Rall, W. et. al. (1959-92) Extensive bibliography in Stuart, et. al. Op. Cit. pg 228-229
The Neuron 2- 149
Figure 2.2.6-2 Electrical equivalent circuit of
the poditic conduit. The base region of the Activa
is typically surrounded by the podaplasm. Other
contacts to the base region are out of plane. Any
boundary layer surrounding the base region is
Ohmic.
Once a an equivalent dendrite circuit is obtained by combining the set of coaxial cylinders, an equivalent
circuit much like [Figure 2.2.6-1] can be drawn, by changing axoplasm to dendroplasm and interchanging
the titles of the Activa on the left and right. The “base of exit Activa” becomes the base of input Activa and
moves to the left. The “base of internal Activa” and the line marked podalemma move to the right. In most
cases, the battery associated with the load, RL, is very small or negligible in the dendrite case..
2.2.6.3 Equivalent circuit of the poditic element
As seen in the above figure, the cytological structure of the poditic conduit is somewhat different from that
of the dendrite and axon. The podaplasm occupies the remainder of the plasma within the exterior
membrane that is not isolated within the dendritic or axonal conduits and not isolated as part of the nuclear
system. As shown, there is a specialized region of the podalemma for purposes of the electrostenolytic
process. It is shown as the horizontal black bar similar to the horizontal black bars associated with the
electrostenolytic terminals of the dendrite and the axon. The diagonal black bar on the surface of the
podalemma indicates a potential specialized zone for purposes of receiving a neural signal. This site will be
discussed in Chapter 9. Prior to complete genesis of the cell, the podaplasm occupies the space between
the dendritic and axonal conduits. As these two conduits become juxtaposed, the space between these two
structures becomes very small, typically 50-100 Angstrom. The majority of the chemical species of the
podaplasm are forced out of this area by the rules of Brownian Motion. The remaining species is believed to
be water in the form of a liquid crystal, known as semi-metallic water.
Figure 2.2.6-2 describes the cytology and individual electrical equivalent circuit of the poditic portion of the
neuron. The input and electrostenolytic interfaces are the same as for the dendrite and the axon. However,
the output configuration is different. The podaplasm is in direct contact with the base region of the internal
Activa of the neuron. If there is a boundary layer between the podaplasm and the base region, it appears to
provide an Ohmic electrical contact (a finite and symmetrical resistance) between the two. This allows
electrons to flow from inside the podalemma into the base region of the Activa. This flow is shown by the
arrow with the asterisk for a point.
The electrostenolytic potential shown in series
with the load, RL, may be very small or negligible
in the poda circuit (except in the case of the
cardiocytes (Section 2.7.4).
2.2.7 Recent organic field effect
transistor (OFET) and potentially
bipolar junction transistor devices
Because of the recent literature, it has become
important to differentiate between putative organic
chemistry-based semiconductor devices and
biological chemistry-based semiconductor devices.
The organic materials generally involve
conjugated hydrocarbons of commercial
manufacture. The following papers refer to
organic semiconductor devices generally
exhibiting very low charge mobilities based on
diffusion of molecules or larger chemical
structures diffusing through or along organic
molecular substrates. The devices do not exhibit
the fundamental features of active semiconductor
devices, signal amplification and/or charge
injection against an electrical gradient. The
devices resulting from these investigations are most appropriately labeled dopant dependent resistors,
DDR’s. These may be the analog of FET operating as voltage dependent resistors, VDR’s71.
Many of the papers fail to describe the type of solid-state semiconductor junction FET they are attempting to
emulate.
71Millman, J. & Halkias, C. (1972) Integrated Electronics: Analog and digital circuits and systems. NY:
McGraw–Hill Chapter10, pg 339
150 Neurons & the Nervous System
- - - -Optional
It is difficult to determine how the putative CWA sensory equipment described in the literature actually
works. Most of the descriptions rely more upon only partially defined concepts than on recognized
principles. The problem centers around the definition of an Organic Field–Effect Transistor, OFET. Figure
2.2.7-1 attempts to categorize the proposed OFET’s, and related Organic Bipolar Junction Transistor, OBJT.
It attempts to relate these designs to a variety of solid state semiconductor FET’s It also categorizes one
biology–based active electrolytic semiconductor device, previously named by this investigator, the Activa.
The key to sensing these materials rapidly and consistently is with a man-made sensor device patterned after
the mechanisms employed in the biological olfactory modality of animals (Section 8.6). The biological
systems typically respond to similar chemical stimulants within seconds of the stimulant reaching the mucosa
associated with the olfactory epithelium layer within the nasal cavity. The interaction always involves a dual
antiparallel coordinate bond, DACB, between stimulant and receptor; it is never the result of a chemical
reaction involving valence band electrons. Section 3.2.2.3.4 addresses the DACB.
Figure 2.2.7-1 Hierarchy of potential CWA sensory equipment ADD. The arrows
indicate the type of active device explored by the various investigators in spite
of the name they might have given their devices. See text.
The Neuron 2- 151
To understand the potential forms of OFET’s is to relate them to well known types of man–made FET’s as
shown on the left most column. These devices offer current–voltage characteristics that vary significantly.
Figure 2.2.7-2 provides an overview of these differences. In the enhancement mode, the drain current rises
as the gate-to-source voltage, VGS increases and is always positive. In the depletion mode, the drain current
rises as the gate-to-source voltage increases but is always a negative value. Frame (b) shows the transfer
curve associated with these two types of MOSFET’s. Note, the curve is a generally linear curve relative to
the current vs gate-to-source voltage. It is not exponential in character.
As is apparent from figure 2c of the Okamato et al. paper, their device does not correspond to the
current–voltage relationship for a common-source p–channel FET. The range of gate voltages in Okamato et
al. are inverted and highly exponential instead of varying linearly. Except for the highly exponential
distribution in the gate voltage parameter, and the very low drain current, their device corresponds more
closely to a p–channel enhancement-type MOSFET. It is possible the VGS curves shown in their figure are
not based on a fixed VDS value. In the case of a variable VDS value, the VGS curves shown are not related to
each other.
For reference, state-of-the-art production MOSFET: gate length = Lg 0.1 μm The staff of the EE
Department at the Univ. of South Carolina has provided a concise review of electrical parameters associated
with semiconductors72. They note the mobility of charges varies by 1000 among materials. However, the
availability of free charges varies by 1023 among materials. Undoped silicon has an intrinsic value of n = 1.3
x 1010 cm3. In silicon, doping can easily increase the availability of electron (or holes) by 105 to 108 to 1. It
is the number of available electrons or holes, and not the charge mobility, that is the dominant semiconductor
parameter.
In organic, and biological, chemistry, the double bond of carbon, specifically the
-bond, can act as a donor
type of dopant and act as a source of electrons within a liquid-crystalline structure.
All successful man-made organic transistors demonstrated to date appear to have been of the field-effect
transistor type, FET’s, sometimes described as organic thin-film transistors, OTFT’s and organic
electrochemical transistors, OECT’s.
Figure 2.2.7-2 Typical drain characteristic & transfer curve for a common source
n-channel MOSFET. (a); the drain characteristic. Note this device can operate
in the enhancement mode as well as the depletion mode. (b); the transfer curve
(for VDS = 10 volts). For p-channel devices, the sign associated with all voltages
are reversed. From Millman, 1972.
72University of South Carolina Electrical Engineering Staff (2017)
http://www.ee.sc.edu/personal/faculty/simin/ELCT102/18%20Semiconductors.pdf
152 Neurons & the Nervous System
Sirringhaus et al73. have published a paper related directly to the question of organic semiconductors. The
information may or may not be applicable to the Activa of biology. Their focus is on multiple ring
homocyclic compounds with some multiple ring hetrocyclic compounds. They do not specifically address
liquid crystalline lipids but they do address high-mobility conjugated polymers. The paper is focused on
basic physics, and the term “hopping” is generally used as the term equivalent to hole transport.
It appears that the mobility of the “plastics” investigated by the above authors is much lower than
encountered in asymmetrical lemma of biological cells. See Section 2.2.7.4.
Tybrandt et al74. have described what they label as an all-organic junction transistor device. They describe
their device as an ion junction transistor device and note it is of the PNP type. They also presented a
conference paper describing their work from a different perspective75.
Although their investigations constituted exploratory research into the potentials of their proposed organic
bipolar junction transistors, BJT, their configuration was actually that of an organic field effect transistor,
OFET. it was not intended to simulate a biological BJT. Their words, in the context of electrical
engineering would suggest that further investigation is needed. Their text does not describe any “transistor
action” related to the injection of any charge into the collector region against the charge gradient. Further
analysis of their device will surely confirm that the device is a dopant-dependent resistor, DDR and does not
utilize ions in its charge transport mechanism (between the labeled emitter and collector). They suggest that
their device be known as a PNP BJT. It is not (for details, see Section 2.2.7.3).
2.2.7.1 Background from the recent literature
Caizhi and colleagues have provided an extensive review of the state of the art in this area as of 201476. they
cite several papers77,78,79. Nikoluo & Malliaras presented a very informative paper on OTFT’s80. The field
has been burgeoning since 2012.
Torsi et al. have provided a tutorial (ca. 2013). “The functioning principles of electronic sensors based on
organic semiconductor field-effect transistors (OFETs) are presented. The focus is on biological sensors but
also chemical ones are reviewed to address general features.” In their case, function is used in the
engineering sense, related to circuit level details. Their focus is on point of care, POC, applications. They
note, “In general organic field-effect transistor, OFET, sensors use -conjugated organic semiconductors
73Sirringhaus, H. Sakanoue, T. & Chang, J–F. (2012) Charge-transport physics of high-mobility molecular
semiconductors Phys Status Solidi B vol 249(9), pp 1655-1676
74Tybrandt, K. Larsson, K. Richter–Dahlfors, A. & Berggren, M. (2010) Ion bipolar junction transistors PNAS
vol 107(22), pp 9929–9932
75Tybrandt, K. Larsson, K. Richter–Dahlfors, A. et al. (2010) Addressable delivery systems based on ion
bipolar junction transistors http://ma.ecsdl.org/content/MA2010-01/13/788.full.pdf+html
76Caizhi, L. Zhang,M. Yao, M. & Yan, F. (2014) Flexible Organic Electronics in Biology: Materials and
Devices Adv Mater vol 27(46), pp 1–35 DOI: 10.1002/adma.201402625
https://www.researchgate.net/publication/268229545_Flexible_Organic_Electronics_in_Biology_Materials
_and_Devices
77Torsi, L. Magliulo, M. Manoli, K. & Palazzo, G. (2013) Organic field-effect transistor sensors: a tutorial
review Chem Soc Rev vol 42, pp 8612– 8629 Volume 42 was a themed review of chem & bio detection
78Dumitru, L. Torsi, L. Magliulo, M. Manoli, K. & Palazzo, G. (2014) Low-voltage solid electrolyte-gated
OFETs for gas sensing applications Microelectron J vol 45(12), pp 1679-1683.
79Lin, P. Yan, F. (2012) Organic thin-film transistors for chemical and biological sensing Adv Mater vol 24,
pp 34–51
80Nikolou, M. & Malliaras, G. (2008) Applications of Poly (3,4-Ethylenedioxythiophene) Doped With
Poly(Styrene Sulfonic Acid) Transistors in Chemical and Biological Sensors Chem Rec vol 8(1), pp 13–22
The Neuron 2- 153
(OSC’s) as electronic materials and are endowed with biological recognition capabilities by proper
functionalization or integration of bio-systems. The paper reviews many definitions of terms, based on the
IUPAC and other sources. They do introduce hopping and localized traps in the electronic configuration of
the materials. Both thin-film and thick-film fabrication techniques are reviewed. Their section entitled,
“Bio-recognition events at functionalized OFET interfaces” hints at how to fabricate the sensory receptors
defined in this work for OR 1 through OR 9 (Section 8.6). Their scheme using OFET’s would offer poorer
performance than available using the proposed biological BJT’s (Section 2.1.4.9).
Dumitru et al. discuss an electrolyte gated OFET, an EGOFET that can operate at less than –0.4 volts. Their
initial operating devices showed excellent performance based on conventional input and output
characteristics (Section 2.2.7.7). More data needs to be collected to provide a complete data sheet for an
EGOFET device. While their threshold voltage and on/off current ratio were quite good, their mobility, ,
remained quite low.
Nikolou & Malliaras did briefly discuss the use of bilayer lipid membrane (BLM) in their ion selective
membranes, but apparently not in the configuration of typical BLM’s employed in biological semiconductor
devices (their figure 6) and cited Bernards et al81. of 2006. Nikolou & Malliaras also cited a paper by
Bernards & Malliaras82. It discussed both ion transport and hole transport. A book edited by Bernards et
al83. also appeared in 2006. Chapters 7 and 9 provide additional useful information to this discussion.
2.2.7.2 Difference in organic vs biological semiconductor devices
Current research (2017) in active organic semiconductor devices is focused on utilizing ionic filter materials
closely tied to plastic materials frequently used in gas chromatography columns. These are generally cross-
linked poly molecular plastics of undocumented molecular structure and arrangement, poly
(3,4-Ethylenedioxythiophene), PEDOT, in the Tybrandt case. These materials are frequently known to
separate (disassociate) ions under specific and frequently demanding diffusion conditions. In this
application, the conditions are much less demanding. They are generally doped with an experimentally
known but poorly documented agent, Polyanion poly(styrenesulfonate), PSS, in the Tybrandt case. The
method of doping is not generally described in significant detail from the perspective of a semiconductor
analyst.
In contrast to the research in organic semiconductors, the biological semiconductor materials are usually well
characterized in both their chemistry and their structural arrangement. The structural arrangement typically
involves a two layer sandwich of liquid crystalline phospholipids arranged as a bilayer lemma (wall of the
biological cell). The phospholipids differ, at least locally, between the two bilayers in the case of type 2
lemma. The active semiconductor device is typically formed when two such lemma are brought into
juxtaposition at the atomic level. The dimensions involved are measured in Angstrom, not fractions of a
millimeter, and there is no surface coatings associated with, or between, the lemma in their final
configuration (except some potential water molecules). The conductivity is due to either desaturation of the
phospholipid chains or the arrangement of the molecules in a semi-crystalline lattice arrangement. Charge
transport is usually by “hole transport” within the lattice rather than by “ion transport” between individual
molecules as in the organic semiconductor configuration. There is a possibility of hydrogen bond
“hopping.” Whether this mechanism is hole-based or ion-based may be a matter of definition.
The measured electrical performance of the organic devices constructed as above are in the realm of volts
and milliamperes, whereas the those of the biological devices are in the realm of millivolts and picoamperes.
The impedance levels and time constants are about two orders of magnitude different. Bergerren et al.,
(page 272) writing in Bernards et al, (2006) note current OFET’s operate about 108! slower than silicon
transistors.
Thus, at this time, the fields of organic semiconductor research and biological semiconductor research are in
totally different realms.
81Bernards, D. Malliaras, G. Toombes, G. & Gruner, S. (2006) Gating of an organic transistor through a bilayer
lipid membrane with ion channels Appl Phys Lett vol 89, paper 053505 DOI: 10.1063/1.2266250
82Bernards, D. A.; Malliaras, G. (2007) Steady-State and Transient Behavior of Organic Electrochemical
Transistors Adv Funct Mater vol 17(17), pp 3538–3544 DOI: 10.1002/adfm.200601239
83Bernards, D. Owens, R. & Malliaras, G. eds. (2006) Organic Semiconductors in Sensor Applications NY:
Springer
154 Neurons & the Nervous System
2.2.7.3 “Active” semiconductor device of Tybrandt et al.
The Tybrandt et al. device is shown in Figure 2.2.7-3. Their frame A suggests a pn junction involves three
physical layers. This is not the case in a conventional pn junction of semiconductor physics where only two
materials of different electronic state are brought into close proximity, resulting in a “space-charge density
variation” of about 0.5 microns, extending into both materials, but no requirement for a third interposed
physical layer. Figures 1 & 2 of Mafe & Ramirez. have provided the correct interpretation of this
configuration showing the result is an excellent quality pn junction diode84. Figure 2 is extended to show the
reverse polarization breakdown region without providing calibrated scales. They note that this breakdown
region is the location of water disassociation. Although not useful in creating a BJT, Trivedi, et al. discussed
this disassociation mechanism in detail85.
Frame B is largely self-descriptive when supported by frames C & D. The material labeled PEG constitutes
their “crosslinked PEG gel (referred to as the junction)”. They did not discuss the orderliness or orientation
of the PEG molecules with reference to the other layers in their device. “The emitter and collector are then
connected by a junction consisting of a neutral cross linked poly(ethylene glycol) (PEG) gel layer (Fig. 1 C
and D).” The orderliness and orientation of the molecules in the liquid-crystalline lemma of an asymmetrical
biological membrane are critical to the operation of a biological BJT.
Their symbol in frame E is modified in several ways from the universal standard symbol for a non-ionic pnp
BJT, the base material is shown as a box instead of a vertical line and the emitter and collector leads are
connected to the base at the edges of the box rather than along the length of the vertical line.
They assert, “Inspired by the similarities of pn-junctions and bipolar membranes, BMs, we have developed a
solid-state ion-based bipolar junction transistor (IBJT). Its use as a circuit element for neurotransmitter
delivery was demonstrated by its dynamic control of the physiological micro-environment of neuronal cells
via acetylcholine (ACh) delivery. Based on the theory of ion transport through selective membranes, a
Figure 2.2.7-3 An organic bipolar junction transistor, BJT. A; a caricature of an
organic junction diode. B; their BJT circuit diagram. C; the labeling of their
m a t e r i a l s . P D M S ; p o l y d i m e t h y l s i l o x a n e . P E D O T ;
poly(3,4-ethylenedioxythiophene). PEG; cross-linked poly(ethylene glycol). PET;
Polyethylene terephthalate. PSS; Polyanion poly(styrenesulfonate). SU-8; a
commonly used photoresist. –IB(A+); base current, shown injected into the
emitter, PSS. D; The morphology of their BJT. IC(M+); current through PEG. E;
their proposed symbol for a pnp, ion-based,IBJT device. See text. From
Tybrandt et al., 2010.
84Mafe, S. & Ramirez, P. (1997) Electrochemical characterization of polymer ion-exchange bipolar
membranes Acta Polymer vol 48, pp 234-250
85Trivedi, G. Shah, B. Adkikary, S. et al. (1996) Studies on bipolar membranes React Funct Polymers vol 28,
pp 243-251
The Neuron 2- 155
model of operation is proposed and compared with the characterization.” They did not describe the BM they
were attempting to emulate.
SU-8 is a commonly used (organic) epoxy-based negative photoresist used in nano–scale transistor
manufacturing. Negative refers to a photoresist whereby the parts exposed to UV become cross-linked, while
the remainder of the film remains soluble and can be washed away during development. “Fumatech FAB;
An anion-selective membrane, is applied over
the PEG gel, defining the base.”
Frame B in the figure illustrates the device wired into the common-emitter configuration. Their figure 3
attempts to demonstrate the operation of their device as an organic pnp BJT, but they do not demonstrate
that it is due to ionic currents within the device, nor is it operating at voltage and current levels similar to
those of a biological pnp BJT semiconductor device, an Activa.
They claim a static current gain of Ic/Ie = 10:1 at VEB = 4 volts, under common base conditions,
Unfortunately, the gain of an active semiconductor device is not defined under static conditions. It is only
defined under incremental conditions, and technically only as a ratio of output power to input power86. A
current gain, , for a semiconductor device is usually defined under common-base conditions and is typically
on the order ofIc/Ie of 50 to 200 for solid state semiconductor devices. A voltage gain is usually defined
under common-emitter conditions. There is no indication in their paper that they actually achieved
“transistor-action.”
Their figure 4, reproduced as Figure 2.2.7-4, shows how their device could act as an on-demand dispenser
of acetylcholine. The device is quite slow as shown by the time scale, but it is causing the controlled release
of acetylcholine as measured by Ca2+ release into the simulated paracrine space.
86See any engineering textbook on active vacuum tubes or semiconductor devices.
156 Neurons & the Nervous System
Figure 2.2.7-4 The IBJT as an addressable delivery point for modulation of
neuronal cell signaling. (A) Schematic illustration of the IBJT in a circuitry.
SH-SY5Y cells were cultured on top of the collector electrode and ACh was
placed on the emitter electrode. When switching on the device, ACh migrates
through the E-C circuit and is released to the cells. (B) Intracellular Ca2+ recording
of ACh stimulated SH-SY5Y cell. Switching VEB on/off regulates ACh delivery,
which then modulates the cellular Ca2+ response.” See text. From Tybrandt et
al., 2010.
The Neuron 2- 157
More details of the circuit and its operation are needed than the six-page limit on PNAS articles allows.
Several other papers have been published by members of the same team87,88,89. The Simon Kurup et al. paper
presents a large amount of background data leading to the first Tybrandt paper.
A major point to note is;
Their circuit(s) operates at collector voltages in the 10–40 volt range rather than the 154 mV range of actual
biological devices. Their devices can only be considered simulations of actual biological circuits using non-
biological organic materials (as the names of their chemicals listed in the first figure attest).
They did not justify the use of many euphemisms for the parameters of a neuron based on the chemical
theory of the neuron. As an example, they did not explain how their concept of a bipolar membrane, BM,
could be considered analogous to the bilayer membrane, BM, forming the outer lemma of a biological
neuron. Their introduction of “a neutral intermediate membrane layer, separating the two charged
membranes “ of their pn junctions is not in conformance with generally accepted conditions within a pn
junction of solid state physics. Neither did they explain how they created dynamic “nanochannels and
nanoporous membranes”, ionic channels, through their “cross-linked PEG gel (referred to as the junction)”.
PEG is nominally an excellent insulator that if properly doped, or desaturated, may support “hole transfer”
along its long molecular chains. It is not known to support ionic conduction.
They also did not measure their Ca2+ levels in their simulated neurons. Quoting the Simon Kurup et al.
paper, “we used SH-SY5Y cells as bio-sensors, since cholinergic Ach receptor stimulation, using 10 μM
ACh, is known to induce Ca2+ influx. Cells cultivated on the target electrode were loaded with the
ratiometric Ca2+ fluorophore Fura 2-AM.” They also asserted, “This series of experiments demonstrates
that i) ACh can be transported through the PEDOT:PSS polymer; ii) transport through the polymer does not
affect ACh’s biological activity. . .”
2.2.7.4 “Active” semiconductor devices of Okamato et al. & Mitsui et al.
Several papers have appeared with the same core investigators listed in the author’s listing, not necessarily in
the same order. These papers assert they involve active organic semiconductor devices. However, they fail
to demonstrate their electrolytic device configurations exhibit the critical frequencies associated with any
active semiconductor device (transistor).
Okamato et al have published on high mobility organic semiconductors90. They report mobilities up to 9.5
cm2/V S and thermal durability of 150C using conventional plastic substrates.
“A gold electrode (30 nm) was vacuum deposited after F4–TCNQ (1 nm) was vacuum deposited on the
crystal so that the device geometry of top-contact configuration is completed. Because the acceptor layers
are only under the electrodes, it does not influence the channel mobility itself; however, the transfer
characteristics are greatly changed with the insertion of F4–TCNQ for some devices. The typical length ( L )
of the channels was 0.1 mm.”
Okamato et al. also developed the goals of their program clearly. One of their goals was to establish stable
operation of their devices at temperatures above the biological range.
87Simon, D. Kurup, S. Larsson, K. et al. (2009) Organic electronics for precise delivery of neurotransmitters
to modulate mammalian sensory function Nature Materials vol 8, pp 742 - 746
88Tybrandt, K. Larsson, K. Kurup, S. et al. (2009) Translating Electronic Currents to Precise
Acetylcholine–Induced Neuronal Signaling Using an Organic Electrophoretic Delivery Device Adv Materials
vol 21(44), pp 4442-4446
89Simon, D. Jager, E. Tybrandt, K. et al. (2009) An organic electronic ion pump to regulate intracellular
signaling at high spatiotemporal resolution IEEE Xplore DOI: 10.1109/SENSOR.2009.5285721
90Okamato, T. Mitsui, C. Yamagishi, M. Nakahara, K. et al. (2013) V-Shaped Organic Semiconductors With
Solution Processability, High Mobility, and High Thermal Durability Advanced Mater vol 25(44), pp 6392+
158 Neurons & the Nervous System
Mitsui et al. have published on the same subject91 reporting mobilities up to 16 cm2/V S and thermal
durability of 200C for their dinaphtho[2,3-d :2',3'-d’]benzo[1,2-b:4,5-b’]dithiophene, DNBDT. They also
employed evaporated gold contacts and a “junction” area on the order of 20 microns wide. Values of
mobility of 16 cm2 V–1s–1 are quite low compared to any variant of doped single crystal silicon. Their figure
3d does suggest the drain current does saturate at or near the gate voltage. The gate structure is unusual.
“Using the prepared single-crystal fi lm, TFT was fabricated by evaporation of strong acceptors such as
F4–TCNQ and the Au electrodes through a patterned shadow mask to construct the bottom-gate-top-contact
architecture (Figure 3 a).
“Finally, the Hall effect measurement of the C10–DNBDT–NW solution-crystallized FET was performed to
unveil whether an electronic state of carriers delocalizes over molecules or localizes in each molecule. The
resultant inverse Hall coeffi cient 1/RH was plotted as a function of VG in Figure 3f, suggesting that 1/RH
agreed with the charge density, C ( VG – Vth ), where C is the capacitance of the gate dielectrics. This
agreement indicate that an electronic state of carriers delocalizes over molecules in the C10 -DNBDT–NW fi
lm, which shows the mobility values as high as 16 cm2 V–1s–1 by the band-like transport mechanism.”
These are very low mobility values compared to the 300K mobilities of electrons and holes in single crystal
silicon and germanium semiconductor devices. These are n = 1,300 and p = 500 cm2/V-s for silicon and n
= 3,800 and p = 1,800 cm2/V-s for silicon.
Dong et al92. have asserted much higher mobilities in organic FET’s, “approaching the values for
polycrystalline silicon devices.
The numbers presented the above papers, are not similar to those of single crystal silicon. It can be
questioned whether their devices are actually OFET devices or only dopant dependent resistors , DDR’s, as
in the case of Tybrandt et al. On initial reading, these papers did not provide enough information to
demonstrate the presence of “transistor action,” typified by amplification and/or, in the junction variety of
device, signal injection into the collector space against an opposing electrical bias.
2.2.7.5 “Active” semiconductor devices
of See et al.
See et al93. have described a gas sensitive device.
They describe their device as an organic FET, an
OFET). It is unusual in several ways as indicated
by their figure 7.26, shown here as Figure 2.2.7-5.
The channel of the device consists of a
polycrystalline organic semiconductor, OSC, It is
designed to allow gas molecules (the analyte) to
impact the boundaries between the grains. There
is no diffusion of material into the channel from
the vacuum deposited source and drain electrodes.
The gate electrode is separated from the channel
by a dielectric. The device can be described as an
analyte dependent resistor, ADR, with an auxiliary
control gate. The OSC is described as a thin film
but no actual dimensions were associated with this
figure.
Figure 2.2.7-5 Schematic of an OFET with
polycrystalline channel. The gas (analyte
molecules) enter from the top. The gate is
arranged at the bottom. The channel
consists of an organic polycrystalline
semiconductor. From See et al., 2008.
91Mitsui, C. Okamoto, T. Yamagishi, M. Tsurumi, J. (2014) High-Performance Solution-Processable N-Shaped
Organic Semiconducting Materials with Stabilized Crystal Phase Advanced Mater vol 26(26), pp 4546–4551
92Dong, H. Fu, X. Liu, J. et al. (2013) 25th Anniversary Article: Key Points for High-Mobility Organic
Field-Effect Transistors Adv Mater vol 25(43), pp 6158-6183
93See, K. Huang, J. Becknell, A. & Katz, H. (2008) Performance requirements and mechanisitic analysis of
organic transistor-based phophonate gas sensors In Bernards, D. Owens, R. & Malliaras, G. eds. (2006) Organic
Semiconductors in Sensor Applications NY: Springer Chapter 7
The Neuron 2- 159
2.2.7.6 “Active” graphene semiconductor devices of Tsai & Willner ADD
Tsai & Willner have described a thin film device they describe as a graphene field effect transistor, GFET.
The paper was presented on a manufacturers website94.
The paper appears to be the work of two physical chemists. They focus on the goals of inexpensive
manufacturing and great conceptual potential without demonstrating the actual performance of their device
in any application. They do stress the monomolecular form of their graphene film on a substrate and discuss
the (yet to be demonstrated) functionalization of their configuration by attaching proteins, chemical
compounds and DNA molecules to the graphene film in order to make sensors for various applications.
Reading their paper raises several questions. First, is their proposed device an active semiconductor device,
or more likely a stimulant dependent resistor, SDR, a member of the DDR family defined above? If it is an
active semiconductor device, what is the achievable signal amplification of their current device? What
characteristic of their device qualifies it to be labeled a graphene channel Field Effect Transistor, GFET, and
thereby belong to the FET family of semiconductor devices? Second, how do they account for the
symmetrical character of their “Source Drain Current” as a function of the “Gate Voltage” in volts? They
define no chemical dopant within the graphene structure or any pn junction tending to introduce a
asymmetrical characteristic to the action of the gate voltage.
2.2.7.7 “Active” semiconductor devices of Dumitru et al.
Dumitru et al95. have provided a paper discussing an OFET very similar to the solid state semiconductor
MOSFET. Their introduction highlights the features they are seeking,
In an OFET structure, a dielectric between the thin organic semiconductor (OSC) layer and the gate
electrode is needed to capacitively induce charges at the interface between the OSC and dielectric itself, and
different chemical systems, such as inorganic oxides, polymers, or an ultrathin self-assembled monolayer,
have been proposed. Among the others, polymeric dielectrics are promising candidates for the fabrication of
flexible electronic devices because they can combine high-k and conformability.
An interesting alternative is the use of an electrolyte interface to gate an OFET, exploiting the
Debye-Helmholtz double layer to achieve high capacitance. This is not a new concept because studies in
which an electrolyte was employed to modulate the surface potentials of a germanium semiconductor were
already proposed 60 years ago at Bell Labs. Unless exploited on purpose and in controlled conditions, such
as, for example, in electrochemically gated transistors, one of the drawbacks of this approach is the
occurrence, upon gate biasing, of ion penetration into the OSC layer. The presence of ions inside the OSC
can lead to undesired effects such as increases of the gate leakage and off-current, very low switching speed,
and high hysteresis. This inconvenience can be overcome by using polyelectrolyte films composed of large
anions that are almost immobile because of their steric hindrance. This occurrence prevents OSC doping
when the OFET is operated in accumulation mode.
Even though the polarization mechanisms of electrolyte media under the gating potential are not yet fully
understood, electrolyte gated OFETs (EGOFETs) can exhibit very good performances and hold promise for
low-cost printed organic electronics also because their fabrication procedures.”
Figure 2.2.7-6 shows the excellent, and statistically relevant, performance of their initial devices. PAA;
polyanionic proton conductor, poly(acrylic acid), pBTTT–C14; poly[2,5-bis(3-tetradecylthiophen-2-
yl)thieno[3,2-b]thiophene]. The black squares are the double-run plot of ID versus VG, while the red
circles indicate the gate leakage; the blue squares are ID1/2 versus VG. All data are taken at a fixed drain
voltage of VD = -0.4 V. Note the equal spacing of the VG curves in (a). “The transfer characteristics of
Figure 3b reveal the actual linear trend of ID1/2 versus VG, in agreement with eq 1 with a threshold voltage
(VT) as low as -0.53 V. The best measured on/off current ratio (Ion/Ioff) is 3100, while an average of ca. 900
was computed over 10 different devices.”
94Tsai, V. & Willner, B. (very recent) Graphene field effect transistors for biological and chemical sensors
h t t p : / / w w w . s i g m a a l d r i c h . c o m / t e c h n i c a l - d o c u m e n t s / a r t i c l e s / m a t e r i a l s -
science/graphene-field-effect-transistors.html
95Dumitru, L Manoli, K. Magliulo, M. et al. ( 2013) Plain Poly(acrylic acid) Gated Organic Field-Effect
Transistors on a Flexible Substrate ACS Appl Mater Interfaces vol 5, pp 10819-10823
dx.doi.org/10.1021/am403008b
160 Neurons & the Nervous System
“The output characteristics show significant current modulation at a source-drain voltage (VD) lower than
-0.4 V, with this being among the lowest source and drain bias reported so far for an OFET.” They speak of
their device as operating in the accumulation mode, whereas this mode is labeled enhancement mode in an
earlier figure from Dumitru et al.
The Neuron 2- 161
162 Neurons & the Nervous System
Figure 2.2.7-6 PAA-gated pBTTT-C14 OFET performance curves. (a) output
characteristics and (b) transfer curves. Note the very low drain and gate voltages
employed. See text. From Dumitru et al., 2013.
The Neuron 2- 163
2.2.7.8 Potential FET semiconductor devices of Sigworth
Sigworth, in 2003, published a brief philosophical discussion suggesting field-effect type of transistors occur
within the neural system96. He describes himself as one of the proponents of the ion-channel approach to
explaining the neuron. His thesis was all-encompassing when he says the putative “Voltage gated ion
channels control electrical activity in nerve, muscle and many other cell types.” He did not provide any
quantitative performance data that showed how such a field effect device actually works in the electrolytic
environment of the neural system. He does present an interesting rhetorical question.
“What structural design would allow so many charges to move so far, crossing the 30 Angstrom thick,
electrostatically hostile interior of a cell membrane?”
While potentially hostile to the transfer of ions, the membrane is well known to form a diode that is quite
amenable to electron transport–in one direction. Sigworth concludes with a list of fundamental questions
that need to be answered before the concept of an ion gate can be described as a field-effect transistor, FET.
2.3 The electrical characteristics of the dynamic (second order) neuron
The structural characteristics of the static (first order) and dynamic (second order) neurons are largely the
same. However, the electrical characteristics are spectacularly different. This is partly due to the
introduction of unique configurations of circuit elements within an individual conexus.
When the independent electrical conduits of the neuron are brought into a unique juxtaposition (spacing of
less than 100 Angstrom between type 2 lemma areas) and electrically biased in a specific way (axoplasm
negative, and dendroplasm positive with respect to the podaplasm), they exhibit properties uniquely related
to their juxtaposition. The resulting inter-coupled structures exhibit “transistor action.” Through this
mechanism, the neuron is found to contain an active electrolytic semiconductor device, named an Activa. It
is this Activa that is key to the dynamic operation of the entire neural system.
2.3.1 Background drawn from electrical circuit theory
With recognition of the electrolytic character of the neuron, many additional tools become available for
understanding the operations of the neural system. Some of the ideas introduced in this section will be
expanded upon later.
2.3.1.1 The interconnection of neural circuits
Electrical engineers have encountered two elementary problems in developing electrical circuits. First how
are multiple circuits provided electrical power economically. Second, if multiple circuits are directly
coupled, how do you overcome the tendency of the output signal of the last circuit to approach the voltage
extremes defined by the power supply capability (the walk-off problem). In early electrical circuits (1910-
1920), circuits were frequently provided with individual battery-based power supplies. This became
unwieldy and efforts were made to consolidate the power supplies. This complicated the second problem;
how to minimize the tendency of the quiescent signal levels to approach the limits set by the common power
supply and severely limit the dynamic range of the circuit. This was solved by introducing one or more
capacitors or transformers between selected pairs of circuits to electrically isolate their quiescent potentials.
The neural system encounters the same two situations but treats them differently. First, it does employ
individual chemically-based power supplies for each neuron. Although it maintains direct circuit coupling
among the analog circuits used throughout the system, it takes advantage of the phasic properties of stage 3
neural amplifiers interspersed strategically throughout the system, to overcome the walk-off problem
associated with multiple direct coupled stages.
Figure 2.3.1-1 illustrates the result. A nominal potential is an elusive concept in the neural system. The
figure shows the quiescent point and operating range varies widely among neurons depending on their
assigned task. The reason for the different quiescent points is to simplify the transfer of a signal from one
neuron to the next. As noted above, quiescent potential and the dynamic signal voltage at the output of a
96Sigworth, F. (2003) Life’s transistors Nature vol. 423 pp 21-22
164 Neurons & the Nervous System
Figure 2.3.1-1 Typical quiescent point and
operating range of various neurons. See text..
neuron affects the quiescent potential
and signal voltage applied to the next
neuron via the synapse. In fact, if the
correct potentials are not maintained
at the collector of a neuron, the
subsequent synapse may fail to exhibit
“transistor action” and the signal may
not pass through the synapse at all.
Abnormal collector (axoplasm)
potentials (even among only a few
neurons out of groups of millions)
lead to a wide range of neurological
disorders (diseases).
The figure provides the correlation
between the historical
electrophysiological terminology and
a broader terminology consistent with
the actual situation and normal
electronic circuitry. Frame D of the
figure is based on a figure from
The Neuron 2- 165
Ottoson97. It is clearly a composite figure. The left-hand scale of this frame makes it clear that it is the
voltage of the surrounding interneural matrix, INM, that is actually used as the reference in most
physiological work.
The most frequent nomenclature is defined in terms of the commonly defined “resting membrane potential.”
This potential is actually the quiescent axoplasm potential. The most negative potential associated with a
cell is actually the intrinsic electrostenolytic potential, VCC. While this potential is closely associated with
the axoplasm, it is distinctly different from the intrinsic potential of the membrane. The intrinsic membrane
potential is measurable in a Langmuir apparatus and tend to be less than 10 mV. The intrinsic
electrostenolytic potential is usually considerably more negative than the intrinsic membrane potential. It is
also generally more negative than the quiescent axoplasm potential unless the Activa associated with the
plasma is in the cutoff condition.
The resting axoplasm potential of a neuron need not be at or near –70 mV. It can vary significantly
determined by three circuit parameters. The intrinsic electrostenolytic potential is determined by the
reactants participating in the electrostenolytic process on the surface of the axolemma. The quiescent or
resting axoplasm potential is reduced by the currents flowing in the circuit. This reduction is due to these
currents flowing through the source impedance of the electrostenolytic process. The magnitude of these
currents is determined primarily by the collector current of the Activa associated with this plasma. It is also
a function of any current being injected into the next dendrite at the synapse. The resting potential of the
neuron is unrelated to the Nernst Equation, even as modified by Donnan and eventually Goodman.
Frames A, B & C of the figure present an expanded terminology and nominal potential profile applicable to
the different types of functional neurons. These three profiles discriminate between the ground potential of
the INM and the circuit ground of the individual type of neuron. In many cases, the circuit ground is a few
millivolts more negative than the INM ground due to the intrinsic membrane potential of the poditic
membrane and the impedance of the INM. Frame A represents the typical sensory receptor neuron. Its
dynamic range, of only about 35 millivolts, is less than most other cells. The distribution Activa of the cell
has a quiescent current in the dark which is defined as the dark adapted set point. It also exhibits an average
current in response to illumination that is shown as the resting axoplasm potential. Frame B describes the
potentials found in the signal processing type of neuron. The resting axoplasm potential is near the intrinsic
electrostenolytic potential of the photoreceptor cells. The large signal voltage swing capability of the signal
processing cell is shown by the vertical bar.
Frame C represents the typical signal projection neuron (including the hybrid neurons such as the ganglion
cells of stage 3). Under resting conditions, the Activa within these cells is in cutoff. The resting axoplasm
potential closely approaches the intrinsic electrostenolytic potential under the cutoff condition. The critical
threshold condition of the emitter to base circuit is shown transposed to the output circuit and labeled the
threshold for impulse initiation. The large signal voltage swing associated with action potential generation is
shown by the vertical bar. The collector current of the Activa reaches saturation at the peak of the action
potential. Saturation usually occurs at about +20 mV from the interneuron matrix surrounding the neuron.
20 mV is the typical saturation voltage of the Activa within the neuron.
The intrinsic electrostenolytic potential for the signal processing and signal projection neurons is normally in
the region of –142 to –154 mV relative to the interneural matrix. A broader discussion of this figure will be
found in Chapter 3. As an aside, the resting plasma potential in a cell from the algae, Nitella, was measured
as –138 mV at 20 C. This value would suggest the intrinsic potential of a wide variety of animal and plant
cells was in the –138 to –150 mV range at 20 C. As the chemistry involved appears to be fixed, the variation
is more likely due to experimental technique than differences in the actual intrinsic value.
The data in the literature requires careful interpretation. It is not normally associated with a specific type of
neuron and it generally uses the old, less precise, terminology. Neumcke et. al. have provided a number of
potentials with respect to temperature. The resting axoplasmic potential in myelinated frog neuron is given
as –71 mV @ 17 C and –50 mV @ 21 C98. In a separate paper, a resting potential of –78 mV was assumed
and used as a clamp voltage. The so-called, but misleading , Na equilibrium potential is given as –152 mV
@ 20 C and –144 mV @ 37 C99. These latter values are clearly the intrinsic electrostenolytic potential of the
97Ottoson, D. (1983) Physiology of the nervous system NY: Oxford University Press. pg.. 56
98Neumcke, B. (1983) The myelinated nerve: Some unsolved problems, Experientia, vol. 39, pp. 976-979
99Neumcke, B.& Stampfli, R. (1982) Sodium currents and sodium-dependent fluctuations in rat myelinated
nerve fibres. J. Physiol. vol. 329, pp. 163-184
166 Neurons & the Nervous System
axolemma of a neuron biased for action potential generation. Schwarz & Eikhof100 have provided additional
numerical data concerning the transient performance of such neurons. However the model used to explain
their data is in conflict with the model of this work. They discuss the “run down” that occurred within a
period of 30-50 minutes. This run-down is to be expected if the reactants required by the electrostenolytic
process (see Chapter 3) are not supplied by diffusion within the cardiovascular system supporting the
neurons (or the in-vitro bath).
By comparing these frames, it is seen that only the signal processing neurons exhibit hyperpolarization, the
movement of the axoplasm potential to a more negative voltage than its quiescent or resting value. This
hyperpolarization is the result of a positive signal applied to the poditic (inverting) input to the neuron.
Depolarization is a common occurrence in all three neuron types. The reversal of the axolemma potential
relative to the INM is unusual. Its observation is usually caused by the capacitance introduced by the test set
rather than by the in-vivo neuron. It is sometimes cause by the test set reference ground not corresponding to
the extra neural matrix near the neuron.
The voltage of the dendroplasm and podaplasm must also be addressed briefly although very little data
appears in the literature. Segev & London have recently provided data related to the potentials of the
dendrites and the soma (?) that will be addressed more fully in Chapter 6 (Sections 6.3.2 & 6.3.10). The
instantaneous difference in potential between the dendroplasm and the podaplasm (both measured at the
Activa) determines the emitter to base voltage of the Activa within the neuron. The quiescent value of this
difference determines the operating mode of the Activa, whether it operates electrotonically or generates
action potentials.
2.3.1.2 Analog (electrotonic) versus pulse (phasic) operation
Any active device when supported by other electrical elements is intrinsically unstable. The definition of an
active device is one that converts part of a constant source of power into a varying output signal that
exhibits more power than the original input signal. If a sample of this output power is transferred back to the
input circuit (in the correct phase), the output signal will be increased even more by the amplifier until a
nonlinearity limits the signal growth. This growth in output can occur even if the original input signal is
removed. Increases in output power by this means is described as oscillatory if it becomes continuous. If it
terminates after a single pulse of energy, it is called phasic. The conexus within a neuron qualifies as an
intrinsically unstable circuit.
The intrinsic instability of the conexus within a neuron results in three distinct conditions. The first
condition is a normally stable circuit exhibiting amplification but no oscillation. This is described as analog
or electrotonic operation. The second condition is a normally oscillatory circuit resulting from amplification.
It can be described as oscillatory (continuous output pulses) or phasic (individual output pulses in response
to an input signal). The third condition is also important. It is caused by the instrumentation of a
investigator changing the operation of the conexus from the first or second condition. This change is
frequently caused by the addition of capacitance to the circuit due to the capacitance of the probe.
All three of the above circuit operating conditions are commonly found in neuroscience research.
2.3.1.3 Types of oscillators found in the neural system
The neural system uses a number of different oscillator circuits in order to efficiently transmit signals over
relatively long distances, a few millimeters from a device with dimensions of a few microns. These
oscillators are of the relaxation oscillator class. Oscillators can be described based on the types of electrical
elements used to form them. Every simple (lumped parameter or lumped constant) oscillator employs two
types of electrical elements, a dissipative (resistive) element and a reactive element. The reactive element
can be either a capacitance or an inductance. More stable and precise lumped constant oscillators can be
formed using all three of the above elements but these are not found in neural systems. The expression
lumped parameter refers to the fact that all of the individual impedance is concentrated at one location and
can be described by one parameter.
In addition to lumped parameter oscillators, one type of distributed parameter oscillator has been attributed
to the neural system conceptually. This is the delay line type of oscillator. In the biological literature, this
type of oscillator has been occasionally been described as a syncytium (sin-sish’-e-um). This oscillator
100Schwarz, J. & Eikhof, G. (1987) Na currents and action potentials in rat myelinated nerve fibres at 20 and
37 C. Pflugers Archive--European Journal of Physiology. vol. 409, pp. 569-577
The Neuron 2- 167
employs a repetitive series of reactive and resistive elements to achieve a significant delay in a sample of the
output signal that is fed back to the input terminal of the Activa(s).
The predominant form of neural oscillator is the relaxation oscillator formed from resistive and capacitive
elements in lumped parameter form.
2.3.1.4 Electrical feedback as a powerful (but poorly understood) neural mechanism
The neuroscience literature contains occasional references to feedback, but primarily in a conceptual context.
Randall et al. illustrate external feedback in a manner that is difficult for the uninitiated to understand (page
12). A simpler presentation shows the input to a circuit on the left and the output on the right with the
feedback shown as an overlay passing a sample of the output back to be summed (positive feedback) or
differenced (negative feedback) with the input signal..
Feedback is the technique of extracting a sample of the signal at the output of one or more circuit stages and
returning it to an earlier stage. The sample need not be electrical in form at all points. In larger scale
feedback loops (such as that involved in imaging the exterior world by redirecting the eyes) it is not even
necessary for the feedback loop to be physically closed. The sample need not be delivered by an external
circuit. It can be delivered by an internal circuit even at the elementary three-terminal neuron level.
Two distinct forms of feedback are found within electrical circuits. Two similar implementations of the
concept are found in chemistry.
The presence of reaction products in the vicinity of a reaction site frequently limits the reaction rate in a
chemical reaction. This is a form of external feedback.
Similarly, in a two step chemical reaction, the concentration of a necessary intermediary within the reaction
volume is a controlling factor on the reaction rate. The requirement for an intermediary is a form of internal
feedback. Remove or change the concentration of the intermediary and the overall reaction rate changes
regardless of the concentrations of the original reactants or of the reaction products.
Both internal and external feedback play major roles in the operation of the neural system. External
feedback rarely involves an exclusively electrical feedback path. Randall et al. have described external
feedback to the exclusion of internal feedback101. Except for some paths associated with the muscles,
external feedback is a global phenomenon with the feedback path involving one of the sensory modalities;
the physical disturbance of a hair after an arm is moved, an acoustic vibration generated by the mouth and
sensed auditorially, the movement of an object within a visual scene caused by the motion of the head, etc.
Internal feedback is far more common than external feedback. It is associated with the finite impedance of
the poditic circuit of virtually every conexus. Since any poditic impedance is shared between the collector-
to-ground and the emitter-to-ground circuits, it creates an internal feedback signal routinely. Any collector
current passing through the poditic impedance necessarily generates a voltage that is inserted into the
emitter- to-ground circuit. This voltage will cause a change in the emitter current causing the collector
current in the first place. It will be shown below that the character of this poditic impedance frequently
determines the overall character of the conexus circuit.
The results associated with internal feedback depend strongly on the character of the feedback impedance.
The use of a pure resistance generally affects only the overall gain (output signal level divided by input
signal level) of the circuit. However, the introduction of a reactive component in parallel with the resistive
element can cause many other useful changes in the output signal relative to the input signal. The use
internal feedback dominated by the reactive component is generally required to achieve oscillation.
2.3.2 The three-terminal Activa provides great circuit flexibility
Transistor-action associated with the Activa within the conexus of a neuron introduces previously
undocumented performance capabilities into the neural system. As incorporated into a conexus, the three-
terminal Activa provides all of the capabilities associated with the equivalent man-made transistor. This
section will describe some of the basic circuits that can be recognized in neurological systems and explain
the basis of their operation.
The three-terminal form of the Activa leads to the description of the conexus and the neuron as
fundamentally three-terminal, not two-terminal, devices. In many cases, it will be appropriate to separate
101Randall, D. Burggren, W. & French, K. (1997) Eckert Animal Physiology, 4th Ed. NY: Freeman page 12
168 Neurons & the Nervous System
Figure 2.3.2-1 A circuit diagram showing
the separation of signal and bias
terminals along with the impedances
associated with both the power supplies
and the plasma conduits. Two distinct
signal inputs are shown. The poditic
input is functionally an inverting input
teminal. The dendritic input is a non-
inverting input of limited voltage gain.
each of the three terminals into two sub-terminals related to the signaling function and the power supply
function. In a few complex neurons, additional or alternate terminals can be defined based on multiple
conexuses occurring within one neuron. Figure 2.3.2-1 annotates these additional terminals. The supply
potentials are shown in their normal relationships to support transistor- action. Vds is more positive than Vps,
and Vas is more negative than Vps. The signal inputs and outputs are shown undefined. The input signals are
usually derived from the collector terminals of synapses. The output characteristics of these synapses define
the voltage and impedance that should be shown connected to these points. The output signal normally goes
to the emitter terminal of one or more synapses. The input characteristics of these synapses (combined into a
single equivalent circuit using Kirchoff’s laws if required) define the voltage and impedance that should be
shown connected to this point.
The complication of showing the input and output characteristics of the adjacent (frequently
multiple) circuits is an unfortunate feature of directly connected circuits. It is usually
eliminated in man-made circuits by introducing a capacitance into each of these paths. The
capacitance effectively isolates the absolute (or average) voltages related to one stage from the
adjacent stages. Only the dynamic voltage (or current) representing the signal is passed
between the stages.
By combining the properties of these circuit
elements discussed in Sections 2.2 & 2.3.1,
with available laboratory measurements, the
operational characteristics of complete
individual neurons emerge. However, two
major classes of neurons need to be
distinguished based on the complexity of the
electrical network forming the conexus around
the Activa. As introduced in [Figure 2.2.5.2],
these classes differ in the relative value of the
impedance found between the base terminal of
the internal Activa and the surrounding INM
(local ground in electrical engineering
language). If this impedance is negligible, the
resulting neuron forms a simple amplifier. The
form of the signal component of its output is
generally a copy of the signal applied to its
input. However, if the value of this impedance
is significant, a world of new opportunities
arises. These opportunities include the option
of introducing a second signal into the circuit
via the poditic terminal. It also includes the
opportunity to convert the circuit into an
oscillator.
The following discussion first addresses
operation of the simple amplifier using only
resistive circuit elements (predominantly the local dynamic impedances of diodes). These circuits are
frequency independent. The discussion then addresses frequency selective circuits by introducing reactive
circuit elements. These frequency selective circuits provide an initial capability in interpretation of the
sensory information. However, frequency selectivity is only the simplest of the many techniques available in
a conexus. The circuit elements discussed below can be assembled into an endless variety of overall circuits.
Many of these combinations will be discussed in connection with specific neural signaling functions and
paths in the second half of this work.
2.3.2.1 Small signal versus large signal operation
Because of the fundamental nonlinearity of the Activa, most of its parameters are exponential in character.
However, if the signal amplitudes are sufficiently small, the parameters of the Activa, and the conexus it
supports, can be considered linear within some tolerance. This tolerance level separates what are called the
small signal and large signal modes of operation. The large signal mode of operation can result in significant
nonlinearities and even major waveform distortions. Large signals frequently lead to oscillations within the
conexus. These conditions will be explored in this Section. Chapter 8 will show most signals within the
neural system (following the initial amplification provided by the sensory neurons) are large signals under a
broad range of conditions.
The Neuron 2- 169
Small signal conditions can be useful in the laboratory for evaluating the performance of the neural system.
It is important for investigators to recognize and document the signal conditions they are exploring.
Conversely, large signals introduced artificially can result in unexpected, and frequently pathological circuit
operation.
2.3.2.2 General operating characteristics of a simple neuron
170 Neurons & the Nervous System
Figure 2.3.2-2 Operating characteristics of
typical conexus in grounded base
configuration. Operational regions, based
on Ecc = –80 mV, are shaded. A, two
presentations of the same input
characteristic of the Activa. Dashed line
represents saturation in the output circuit.
B, the output characteristic of the Activa
in electrical terms. C, the output
characteristic of an Activa showing the
output voltage relative to the INM and the
nomenclature of biology. See text.
Figure 2.3.2-2 is an expansion of an earlier figure. It focuses on the nonlinearities of a typical Activa and
the fact that many impedances associated with the collector circuit of the device are themselves nonlinear.
The gray areas represent normal operating areas for the analog (electrotonic) Activa. The output signal is
always directly traceable to the input signal in an analog Activa used in an analog conexus circuit. This is
not true for an analog Activa used in a phasic conexus.
Frame A shows the input characteristic of the
device from two different perspectives The two
versions represent the same data. The left frame
plots the input current as a function of the applied
voltage. The right frame plots the observed voltage
as a function of the applied input current. Both
demonstrate that the input characteristic is that of a
diode.
The operating range of the input circuit is shown by
the shaded area and is limited primarily by the
thermal breakdown of the diode at high currents.
As a general rule, the useful operating region of the
input circuit of an Activa is limited further by the
box formed between 0,0 and the dashed line due to
saturation in the collector circuit as discussed
below.
Frame B illustrates the output characteristic
developed earlier. It is the characteristic of an
Activa with no impedance in the circuit between
the base and the ground point. The output load is
due to the combination of the electrostenolytic
supply impedance and any impedance connected to
the output signal terminal of the circuit. In this
simple circuit, the capacitance of the axolemma is
assumed to be negligible. In typical man-made
electronic circuits, the load consists of a pure
resistance; the corresponding load line is a straight
line (shown dashed). However, in the biological
case, the load is normally a forward biased diode
representing the input circuit of the next neuron.
The corresponding graphical representation is
exponential (also shown dashed). The straight load
line represents a real resistor of 1.5 megohms. The
curved load line represents a diode input
characteristic. It exhibits a dynamic impedance of
only about 0.3 megohms at 30 pA current, but a
much higher value at 10 pA.
The intersection of the load line and the output
characteristic (frequently called the operating
characteristic), in the absence of an input signal,
defines the quiescent point, Q.
For the –80 mV potential of the electrostenolytic
supply and either load impedance shown, the
Activa is driven into saturation for input currents
exceeding about 30 pA. For these supply and load
characteristics, the Activa cannot support collector
currents exceeding 30 pA.
The transfer characteristic showing the current out as a function of the current in is usually not plotted for a
junction transistor since the relationship is very nearly 1:1 over its entire operating range. The same is true
for an Activa, as shown in frame B.
The Neuron 2- 171
The output current and the output voltage are both shown as negative quantities in frame C. This is the
convention for active devices of the pnp-type.
Frame C also shows the output characteristic using the vernacular of the neuroscience community. From a
quiescent operating point, Q, an increase in the negative value of the collector (axoplasm) potential is
described as hyperpolarization. For a reduction in the negative value, the change is described as
depolarizing.
For an applied input voltage of arbitrary wave shape, but less than 10 millivolts amplitude, the resulting
input current will be a reasonable copy of that waveform (from frame A). As a result, the current generated
in the output circuit will also be a reasonable copy of the input waveform. However, if the applied input
voltage signal is considerably larger than 10 millivolts, significant distortion can be expected in the output
current waveform.
Since the current out is equal to the current in to the Activa, frame C can also be used to describe the output
voltage as a function of the current into the Activa (with due attention to the sign conventions used and the
limits of the operating range).
It is very important to note that the axoplasm is always biased to a negative value with respect to the INM
when the circuit is functional. This means that the potential of the axoplasm causes negligible leakage of
current into the INM through any reverse-biased type 2 axolemma wall.
If the connection to the subsequent neuron is removed in a laboratory experiment, the load impedance of the
circuit is profoundly affected. This modified e circuit tends to operate in the mode of a pulse integration
circuit due to the combined capacitance associated with the axon and the capacitance of the test probe. This
situation significantly affects the recorded waveforms.
It is important to analyze these graphs more fully and determine the relationships between the quiescent
operating point of the neuron and its operating points in the presence of an input signal. If the input
conditions are adjusted to cause a current of 20 pA, the output circuit will now operate with an output current
of –20 pA and an output voltage of –33 mV. These three values are spoken of as the quiescent values of the
circuit. If the input conditions are such that the total input voltage generates no current in the input circuit,
the output circuit current will also be essentially zero and the output voltage will be approximately, –80 mV
which is assumed to be the net voltage applied to the collector of the Activa by the electrostenolytic supply.
This is spoken of as the cutoff condition, no current flows in the Activa.
If an additional input current of 5 pA is added to the initial 20 pA, the output will move to the point of –25
pA and –30 mV. Similarly if the input current is reduced by 5 pA relative to the quiescent condition, the
output circuit will be at –15 pA and –37 mV. Notice that if the input current is increased by more than 7 pA,
the saturation limit of the Activa will be reached. The output will remain at -26 mV regardless of further
increases in input current.
The language of the engineering and biological communities can be reconciled with reference to the
quiescent point, Q.. Depolarization is a movement along the curve of frame C toward saturation.
Hyperpolarization is a movement along the curve toward cutoff. In the case of this fundamental neuron, an
increase in input current from its quiescent value will result in depolarization in the output circuit until
saturation is reached. Reducing the input current will hyperpolarize the output until cutoff is reached at zero
output current and maximum output voltage.
2.3.2.2 Dynamic operation of a conexus with transistor-action and a resistive poda
impedance
A large variety of functionally different neural circuits can be formed with only a resistive impedance
between the base terminal of the Activa and the local ground potential. These will be discussed in this
section. Cases where the poda impedance is complex will be discussed in Section 2.3.4.2. The special case
where no electrical connection is made to the base terminal of the Activa will be discussed in the visual
sensor section of Chapter 8.
2.3.2.2.1 Simple amplification
Assume initially that there is no input signal to the circuit shown above, that the poda impedance is equal to
zero, and that Vas is more negative than Vps. Let the dendritic supply be such that Vds is marginally less
positive than Vps. Under this condition, no current will flow in either the emitter or the collector of the
Activa. The quiescent potential, Q, of the axoplasm will approximate the electrostenolytic supply potential.
If a small positive signal should be applied to the input terminal, a current will flow from the emitter to the
172 Neurons & the Nervous System
base of the Activa. This will cause a similar current to flow from the base to the collector and through the
axon impedance and the source impedance, Zas. This current will cause an incremental change in the voltage
across Zas in response to the incremental rise in the input signal. The axoplasm potential will decrease
(depolarize) from Q. The ratio of the incremental change in output voltage to the incremental rise in input
voltage equals the voltage gain of the circuit. This is one description of the transfer characteristic of a
(electrolytically speaking) monopolar amplifier.
Now, let Vds be significantly more positive than Vps. Under this condition, current will pass through the
emitter-to-base circuit and significant current will flow in the collector circuit continuously. The collector
potential will be at a quiescent potential, Q, that is less negative than the intrinsic electrostenolytic potential
of the axon source, Vas. Under this condition, the circuit can respond to either a positive going or a negative
going input voltage signal. The result will be a similarly positive or negative going voltage signal at the
pedicel of the neuron. The ratio of the output signal amplitude to the input signal amplitude is a simple
description of the transfer characteristic of a (electrolytically speaking) bipolar amplifier.
The current gain in a common-base connected Activa is limited to marginally less than 1.0 (as in a transistor
in this configuration). However, it can exhibit significant voltage gain (and a significant power gain)
because of the high collector impedance of the Activa. A typical voltage gain is 131 in the absence of any
external load attached to the collector (axon).
If multiple neurons (employing common-base connected Activa) are connected in series, it is difficult to
achieve significant voltage gain unless each subsequent Activa is a smaller device. This is because the low
emitter input impedance of the Activa significantly loads the collector (axoplasm) circuit of the prior neuron.
Thus larger size Activa (and neurons) are required to effectively stimulate one or more orthodromic neurons
of nominal size.
The trade-off between Activa size and input impedance is an important one in neural circuits.
2.3.2.2.2 Thresholding circuit
If Vds is more negative than Vps, no current will flow in the emitter circuit and no current will flow in the
collector circuit. The collector potential will be at the intrinsic electrostenolytic supply potential, Vas. To
cause current to flow in the collector circuit, a positive input signal will be required that is sufficient to make
the emitter-to-base voltage, Veb positive. For higher signal inputs, an output signal proportional to the input
signal minus the difference, Vds - Vps, will appear at the pedicel of the neuron. Such a thresholding circuit
can be used to eliminate extraneous low level noise from the signal path (Ex., to avoid tinnitus in hearing).
In theory, it can also be used to generate a “dead zone” in neural operation, a condition where nothing
happens until a specific signal level is exceeded. While occasionally referred to in the literature, and
potentially of major value, no documented dead zones have been uncovered among in-vivo analog circuits
within the neural system in the course of developing this work.
2.3.2.2.3 Basic arithmetic functions
One of the major challenges of the neural system is to perform mathematical manipulations in the analog
domain without resorting to transcendental functions (sines, cosines and other higher mathematical
functions). This is particularly important with respect to the complex multi-dimensional information
associated with the visual system, and to stage 5 cognition.. To avoid using these functions, the neural
system uses a variety of simple alternatives involving differentials instead of derivatives, time delays when
processing serial information, addition of the logarithms of arguments in place of multiplication of the same
arguments, computational anatomy and lookup tables. These techniques will be defined as they arise in later
chapters.
Addition and multiplication are both performed using simple diode-based ladder networks of passive
components as shown in Figure 2.3.2-3(A). In the context discussed earlier, these diodes are analog circuit
elements and not unidirectional switches (rectifiers). The left part of the frame illustrates the concept. The
concept relies upon Kirchoff’s Law for summing the currents at a node. Basically, the currents passing
through the diodes on the left must equal the current passing through the diode on the right, without regard to
the individual voltages associated with the different circuit elements. Clearly, if the currents on the left are
proportional to the amplitudes of sensory information, the resulting current will be proportional to the sum of
all of those sensory inputs. This is the condition found in a typical bipolar (summing) neuron of the retina.
Alternately, if the currents on the left are proportional to the logarithms of the amplitudes of the sensory
information, the resulting current will be proportional to the sum of these logarithms. This is a powerful
The Neuron 2- 173
technique, since the sum of the logarithms of a group of arguments is equal to the logarithm of the product of
their arguments.
Whether the circuit performs addition or multiplication is determined by two factors. First the relationship
of the applied currents to the original information. Is the relationship linear, logarithmic or otherwise?
Second, the portions of the operating characteristics of the diodes, in fact Activas, used in the circuit. The
right part of frame A shows how the summing network is actually implemented using synapses wired as
diodes to the left of the node (which is the dendroplasm of the neuron). A simple one-input conexus is
shown to the right of the node.
Subtraction is accomplished using a different technique, it uses the three-terminal Activa in a two-input
circuit as shown in frame B. By adjusting the value of the serial impedance, ZPSR, and the shunt impedance,
ZPSH, of the poda circuit, the output gain associated with the dendritic and poditic input circuits can be
matched. Since a signal applied to the poditic input results in an inverted signal at the axon, the circuit
performs a mathematical subtraction. If the input currents are proportional to the amplitudes of the sensory
information, the resulting current at the collector terminal is the difference between the amplitudes of the two
streams of sensory information.
In analogy to multiplication, if the input currents are proportional to the logarithm of the amplitudes
associated with the sensory information, the output is proportional to the difference in these logarithms. The
difference in the logarithms of two arguments is equal to the ratio of the two arguments. Thus, this circuit
can perform division without relying upon any complex arithmatic or algebraic procedures.
Coefficients can be introduced into the summing and differencing operations by varying the serial
impedances on the left of each figure as desired. This will vary the current in that series channel relative to a
fixed applied voltage. The result will then be an output signal proportional to the weighted sum or
difference of the individual signals.
By combining the circuits of frames A and B, the product or quotient, or the sums or differences of any
group of sensory signals can be computed without resorting to any transcendental algebra. The impedances,
ZDSR & ZPSR in frame B can simply be replaced by the ladder networks on the left o f the node in frame A.
The number of terms that can be summed using a linear ladder network is usually limited by cross talk, the
interaction of the input paths due to their electrical symmetry. The key to the successful operation of these
networks is to make the impedances on the right of the node lower than the impedances associated with any
channel on the left. As a result the common node appears to be a “virtual ground” relative to the inputs on
the left. This problem is aided further by the use of diodes as impedances. Their unidirectional character
limits the electrical interaction between the input channels. These isolation techniques make the extensive
number of inputs associated with the typical dendritic and poditic circuits shown in Chapter 5 practical.
2.3.2.2.4 Threshold and pulse integration circuits
Frame C of the figure shows the threshold circuit discussed above with a graphical component. If a sine
wave is applied to the non-inverting (dendrite) input while Vds is equal or more negative than Vps, the
positive going part of the sine wave will be reproduced at the axon (collector) output but the negative going
part will not be. By biasing the dendrite slightly with respect to the base terminal, the threshold level within
the sine wave can be adjusted as desired.
Frame D of the figure shows a threshold circuit modified further. In this case, the impedance ZC consists of
a capacitance and resistive element in parallel, where the impedance of the capacitance is much lower than
that of the resistive element. In this case, each part of the sine wave applied to the emitter (dendrite)
terminal causes a pulse of current in the collector (axon) circuit, shown dotted. This current flows onto the
capacitor and builds up a charge on the capacitor. The resultant charge leaks off slowly via the resistive
element. As a result, the circuit acts as a pulse integrator as shown by the voltage waveform at VC.
The capacitance of ZC is usually formed by the unmyelinated surface of the axolemma. This type of circuit is
used extensively in the signal transmission circuits of the neural system. It is associated with what are
labeled stage 3 stellite neurons in this work. These neurons act as decoders of information encoded by an
associated ganglion cells of the system. (see Chapter 9).
The muscle tissue of the organism, in conjunction with the stage 7 neuro-effectors, also operates like a pulse
integrator circuit, which gives it a low pass frequency characteristic as discussed in Chapter 16.
174 Neurons & the Nervous System
Figure 2.3.2-3 Addition and multiplication
in ladder networks. A, left; generic
summing network using diodes. A, right;
biological summing network using active
diodes summing to an Activa. B; generic
differencing circuit. C; generic
thresholding circuit. D; generic
integrating amplifier (shown thresholding
and then integrating the segments above
threshold using a long time constant
impedance ZC. See text.
2.3.2.3 Individual
temporal/frequency selective neural
circuits
This paragraph will introduce frequency
selectivity within individual neurons based on
the presence of lumped capacitances
(capacitance that can be associated with a
specific location in a circuit topology). Other
techniques are used within the sensory
modalities to create frequency selective
responses and frequency selective filtering
prior to further interpretation and perception.
These techniques will be introduced as they
occur in the system architecture.
2.3.2.3.1 The common low pass
characteristic of neurons
Except for frame D above, the circuits
described in the previous paragraphs contain
no reactive elements. They will perform their
function faithfully without regard to the
frequency components associated with the
input waveform. However, if one or more of
the input impedances shown in A, B or C
contain reactive components, the overall
performance of the circuit may be changed
significantly. The most common situation
relates to the large shunt capacitances
(capacitances between the individual plasmas
and the INM) associated with the lemma of the
individual conduits. These capacitances are
frequently large relative to the series
impedance of the conduit. As a result, a low-
pass electrical circuit is formed that will
significantly reduce the amplitude of frequency
components higher than its characteristic upper
frequency. For many neurons, this frequency is less than 200 Hertz. The highest frequency passed by a
neural circuit (even within the auditory modality) is believed to be less than 1000 Hertz. This maximum
high frequency capability has been associated with neurons within the thalamus.
2.3.2.3.2 The capabilities of a lead-lag network
A situation is easily implemented wherein, the circuit associated with the dendrite, the podite or the axon
consists of four electrical elements in a simple arrangement. Consider two changes to any of these branches
of the above figure. Replace the series impedance with a pair of elements in parallel (one resistive and one
reactive). Replace the shunt impedance, with a similar pair of elements in parallel. The resulting four
element network is called a lead-lag network because of the characteristics of the signals at its output relative
to the input. Relative to a nominal delay associated with signals traveling through such a network, certain
frequency components of the input signal will appear earlier (leading) or later (lagging) than nominal. By
adjusting the values of these components, it is possible to shape the overall frequency transfer characteristic
of the overall circuit over wide limits. This results in emphasizing or de-emphasizing certain portions of the
frequency spectrum passed within the overall limit set by the low pass characteristic described above. This
type of frequency band manipulation is frequently observed with respect to ganglion cells (introduced in
Section 2.6 and discussed in Chapter 9.
2.3.2.3.3 Interference, an alternate frequency selective technique
The lead-lag network offers limited frequency selectivity (the narrowness of the selected frequency range
relative to the middle of the range is limited. A more selective (albeit more complicated) network can be
The Neuron 2- 175
obtained by relying upon a different characteristic of networks. As suggested above, every network exhibits
a finite time delay for a signal to be transferred from its input to its output. This time delay can be expressed
in terms of a phase shift for each of the frequency components of the signal. The phase shift can be defined
by the time delay associated with that frequency multiplied by the velocity of that frequency component as it
travels through the network (expressed in angular measure). If two networks of different electrical length
are excited by the same signal, and the output of these networks are then summed, certain frequency
components will either be accentuated or suppressed based on their relative phase shift at the point of
summation. This technique appears to be common in the stage 4 signal manipulation circuits designed to
selectively filter certain sounds in the aural system and certain parallel line structures in the visual system of
animals (more effectively in some species and individuals within a species than in others).
2.3.2.4 Multipoint probing of pyramid neurons
The need for the ability to capture neural data from multiple probes simultaneously has long been sought in
neuron research. Prior to the 1990's, the technology to support this desire was not available. Williams &
Stuart began reporting that three probes could be used to collect such data. See Section 2.10.2.1 for a
review of their work. The capability is now on the threshold of general use.
2.3.3 Dynamic operation of a conexus with Transistor Action and feedback
Figure 2.3.3-1(A) introduces the effect of the feedback impedance in the poda circuit connected to the base
of the Activa. Designing common-base amplifiers requires care because of the inherent positive internal
feedback. If the poda impedance is too large, instability is intrinsic. However, this feature can be used to
advantage. The poda impedance between the base and the common ground terminal (n) may be the purely
resistive component of the diode associated with a power supply or it may be augmented by other resistive or
capacitive elements.
Recall that any current passing through the collector-base circuit path induces a voltage into the emitter to
ground circuit. This inducement of a change in the input circuit due to a change in the output circuit is a
fundamental definition of electrical feedback. This circuit configuration forms the heart of all hybrid and
projection neurons associated with the generation and regeneration of action potentials.
2.3.3.1 The nature of feedback
A clear distinction is required between the concept of inhibition of psychology and the concept of feedback
in signaling. The building blocks used in the neural system of animals are analog electrical circuits. They
can be modified to provide a variety of amplifier, comparator and pulse generating functions. However, they
are inherently analog. If, as outlined above, a sample of a change in the output of a circuit is introduced into
the input of that same circuit, the effect is known as feedback. The method of introducing this sample need
not involve a separate and distinct (external) signal path. It may involve a shared impedance between the
two circuits. The sample of the output returned to the input is normally not sufficient to block or inhibit the
operation of the circuit. Its effect is determined by the amplitude and phase of the sample. The sample need
not be “in” or “out” of phase with the output signal. The sample may have any phase relationship with the
output signal.
To appreciate this section completely, the reader must be familiar with the variety of techniques described in
Maddock102, or some other book on circuit analysis in electrical engineering. Techniques will be found in
these books to predict the sensitivity of a conexus to oscillation when it is desired, and the safety margin
before undesired oscillation begins when it is not..
If the poda impedance has a complex value defined by the resistive and capacitive components of the
impedance, its phase angle will be intermediate between the above values.
Because of the importance of the phase angle of the sample returned to the input circuit, it is not appropriate
to speak of positive or negative feedback except in the general sense.
Frame B illustrates the effect on the collector voltage of an Activa as a function of the collector current for
different values of the common impedance, ZP. Assuming the potential due to the poda membrane does not
102Maddock, R. (1982) Poles and Zeroes in electrical and control engineering. NY: Holt, Rinehart & Winston
176 Neurons & the Nervous System
disturb the basic biasing of the overall Activa so that the Activa remains in the transistor mode, the input
current to voltage characteristic of the Activa becomes distorted due to the feedback process as the value of
the poda impedance increases as indicated. Since the output circuit shares the same poda impedance, the
output current to voltage characteristic is similarly distorted. The degree of distortion is shown relative to a
nominal poda impedance.
Note the effect of changing the value of the poda impedance; for low values of resistance only, the circuit
operates as a common (well behaved) amplifier but with reduced gain. If the load impedance includes a
shunt capacitance, it will operate with some distortion compared to a circuit with a resistor load but no
instability. As the poda impedance rises, the amplification varies with signal level until the point is reached
where the output current is bistable as a function of the input voltage.
The distortion in these two characteristics is unusual and extremely important. The portion of the input
characteristic sloping downward to the right represents an area of negative (dynamic) resistance. Such a
negative dynamic resistance over even a limited region is indicative of instability and leads to two stable
states (or an oscillatory condition if a reactive element is present such as a capacitor).
2.3.3.2 Internal feedback in the circuit of a fundamental neuron
The explanation of internal feedback as found in frame B needs expansion. The mathematics of this process
involve complex algebra if the capacitances of the circuit are considered. Even for pure resistances, the
mathematics are relatively difficult. This is because of the mode switching that is involved in the operation
of the circuit. Mode switching typically occurs whenever a given current can be associated with two
different voltages in the same circuit. Which voltage is assumed by the circuit frequently depends on
secondary or parasitic circuit elements within the circuit. These are most often capacitances.
To alleviate this problem, a graphical analysis or computer program is usually used to determine the overall
characteristic. However, the typical result can be shown here.
Frame C presents a four segment nomograph. It illustrates the input characteristic of the Activa at lower left,
a fold line at upper left directing the process into the output characteristic at upper right, and finally, a
temporal response transferred from the output characteristic. The lower left is more detailed than in Frame B
so the actual operation of the circuit can be tracked. A load line has also been introduced, and labeled
Ven(Is). The symbol n is used here as a synonym for the common electrical ground point of the circuit. The
fold line at upper left is used to connect the common current axis of the two sets of axes. The upper right-
hand segment represents the collector current versus the collector voltage for the Activa where the two
currents are identical in the absence of any capacitance in the circuit.
The Neuron 2- 177
Figure 2.3.3-1 Operating characteristics of the Activa with internal feedback. A;
the Activa with a significant poda impedance. B; the effective input characteristic
based on the value of this impedance. C; the overall operating characteristic of
the conexus based on this impedance. See text.
The operation of this circuit is best understood by following the numbers next to the curves. Begin at point 1.
At this point, the operating curve labeled Ven(Ie) intersects the static load line, Ven(Is). However, at this point
the operating curve has a negative slope. It represents a negative impedance. This causes the circuit to be
178 Neurons & the Nervous System
unstable. As a result, the operating point will proceed to point 2. At this point, the voltage Ven(Ie) is
compatible with two different emitter currents. The circuit will jump to point 3 and then proceed in an
orderly way to point 4. At point 4, the operating curve can support two different emitter currents. The
operating point will jump to point 5. At point 5, the operating point will proceed toward point 2. When it
reaches point 2, the cycle will begin again. Note however, the waveform never returns to the initial point, 1.
The lower right segment demonstrates the circuit generates an action potential. The value of the capacitance
and the internal impedance of the Activa at different times during the operating cycle determines the pulse
rate of the output action potential very precisely. Note the voltage can not be maintained at point 3 without
changing circuit element parameters. The circuit is not bistable. It is oscillatory. It can be made monostable
at a low axoplasm potential by adjusting the impedance of the load line shown or by changing the dendrite
source potential, Vee, so that the intersection defined by point 1 is along the line between points 2 and 5. It
can also be made monostable at a high axoplasm potential if the load line crosses the circuit impedance
between points 3 and 4..
The circuit just described is the fundamental relaxation oscillator of the neural system. Its utility within the
neural system will be discussed further in Section 2.6 and in detail in Chapter 9
2.3.3.3 Evidence supporting the relaxation oscillator description
Burke, et. al103. have described the clinical characteristics described in the above figure in section 6 of their
paper. It is interesting how closely their description of the refractory portion of the operating cycle agrees
with the intervals associated with the paths between points defined above.
Baker & Wood104 have presented a measured response similar to the output characteristic of frame C.
However, they did not discuss it or even cite it in the same paper.
Nonner105 has provided a static characteristic (with data points) for a membrane of an axolemma near a Node
of Ranvier. The characteristic is virtually identical to the output characteristic of frame C, labeling the
current in mA/cm2, the “sodium current” through the axolemma as opposed to the net current into the
axoplasm. The negative resistance region is clearly identifiable, with peak current density at a nominal 55
mV.
Avenet & Lindeman106 have provided a measured response from a gustatory sensory neuron of a frog (R.
ridibunda) that is remarkably similar to the theoretical output characteristic of frame C above. Figure 2.3.3-
2 shows their “whole cell patch clamp” recording which is actually from just the axoplasm of the cell. They
provided little description of their exact test configuration or protocol. However, the curve marked “peak
in” shows a region of negative resistance on the order of –60 megohms between a voltage of –30 mV and
zero mV from their holding potential of –80 mV. This would correspond to the active region (the region
exhibiting amplification) of the Activa within the neuron. Sections 13.1.2 & 13.1.3 develop the patch-clamp
technique and its variants.
103Burke, D. Kiernan, M. & Bostock, H. (2001) Excitability of human axons Clin Neurophysiol vol. 112, pp
1575-1585
104Baker, M. & Wood, J. (2001) Involvement of Na+ channels in pain pathways Trends Pharma Sci vol. 22, no.
1, pp 27-31
105Nonner, W. (1969) A new voltage clamp method for Ranvier nodes Pfluger Arch vol 309, pp 176-192
106Avenet, P. & Lindemann, B. (1987) Patch-Clamp Study of Isolated Taste Receptor Cells of the Frog J
Membrane Biol vol 97, pp 223-240
The Neuron 2- 179
Comparing figures 3A & 3B and 5A & 5B of their
paper is instructive because they show the cell
operates nominally whether any sodium ions are
present in the external bath or not. They
demonstrate again that it is not sodium ions that
are flowing into the axoplasm from the bath that
constitutes the inward flowing current (the so-
called “sodium current” labeled by Hodgkin &
Huxley).
2.3.4 Emulation and simulation of
Activa and Activa circuits
In this section, emulation will refer to the use of
physical circuit elements to represent the electrical
performance of another physical element or
elements. Simulation, on the other hand will refer
to the use of a mathematical construct (frequently
via a digital computer) to represent the electrical
performance of a physical element or circuit.
Care must be taken in both emulations and
simulations to recognize the significant impact of
temperature on the neuron. The sensitivity to
temperature is much higher in electrolytic circuits
and BLMs than in metallic circuits.
The Activas of the neural system vary in size and
capacity according to their function. They are all
made up of a large number of unit Activas
arranged within a finite area (the synaptic disk in
the case of a synapse). The characteristics of many Activa circuits are catalogued in Chapter 9.
2.3.4.1 Emulations
This section will differentiate between the emulation of an Activa alone, the simpler task, and the emulation
of a complete Activa circuit (including its electrical circuit configuration, associated components, output
load and input signal).
Selection of a man-made transistor to emulate a biological Activa requires close attention to detail.
Similarly, simulation by digital computer, using a variant of SPICE or similar programs, also requires close
attention to the selection of a template from the available library.
Emulation of the adaptation amplifier within the sensory neurons is more complex than for other Activa and
neurons. The unique characteristics of the adaptation amplifier conexus developed in Chapter 8 must be
introduced into the emulation or simulation of this component.
2.3.4.1.1 Emulation of the first order Activa
Biological semiconductors operate in a current-voltage regime much different than current man-made
devices. This will change in the near future as man-made devices leave the realm of silicon and germanium
and move to substrates of binary chemical composition. However, at this time, the current-voltage
characteristic of an Activa cannot be approximated by a man-made transistor without employing parameter
scaling.
To emulate an Activa using silicon or germanium transistors, it is necessary to scale the currents and
voltages properly to account for this difference in operating range. In general, this scaling requires that the
voltages used reflect the ratio between the offset parameters of the two technologies.
The offset parameter of the biological Activa is known with considerable precision from the graph of Yau107.
The offset parameter of transistors is less well known and was originally derived empirically from test data.
Figure 2.3.3-2 Axoplasm patch-clamp
potential measured using parametric
stimulation Bath:
NaCI-Ringer's with 3.5 mM K. Pipette:
standard filling solution with 110 mM KCI,
no ATP. Pipette resistance not
c o m pe n s a t e d . . P ea k - i n w ar d ,
peak-outward and steady-state-outward
currents as a function of command pulse
voltage. See text. From Avenet &
Lindemann, 1987
107Yau, K. (1994) Op. Cit.
180 Neurons & the Nervous System
Under those conditions, it became common to use the values of 0.2 volts for germanium and 0.6 volts for
silicon. Looking more closely at these materials, the so-called photovoltaic potential is given as 0.1 volts for
germanium and 0.5 volts for silicon. An alternate example for silicon is the parameter called the base cutoff
parameter by Motorola108. The value of this parameter is very close to 0.31 volts at 298 Kelvin and a
collector to emitter voltage of 30 volts. It appears that this last value best represents the theoretical offset
parameter of silicon.
Using 0.31 Volts as the offset parameter of Silicon, an Activa operating with a collector potential of -150
mV would be emulated by a silicon pnp transistor with a collector potential of minus 4.5 volts. If a
germanium transistor is used, a collector potential of about minus 3.1 volts would be appropriate.
If it is preferred to use a npn type of man-made transistor, the investigator must remember to reverse the
polarity of all potentials applied to the circuit relative to those in the biological circuit (and note this fact
carefully in any published report of the investigation).
Similarly, scaling of the current regime requires scaling the impedance level of the emulation circuit to
reflect the ratio between the reverse current saturation parameters of the two technologies. The reverse
saturation current of man-made devices vary significantly between silicon and germanium. Those of silicon
are generally in the nanoampere range and those of germanium are in the microampere range. The reverse
saturation current of most biological Activas appear to be in the range of picoamperes or lower. The data of
Luttgau discussed above, indicates a reverse saturation current of 18-25 picoamperes for a biological diode
of unspecified (but undoubtedly large) cross-sectional area.
In the case of the typical photoreceptor cell, the in-vivo output Activa is only capable of a forward collector
current on the order of 25 picoamperes, the reverse saturation current under this condition is probably
measured in tenths to hundredths of a picoampere.
The result of the scaling process requires the emulation circuit to operate at very high impedance levels. At
these levels, the shunt capacitances of the emulation circuit become quite important. They may control the
bandwidth of the resultant circuit. The investigator should evaluate the desirability of using germanium
versus silicon in emulations because of this impact.
While it is formally correct to base the above scaling on the reverse saturation current of the Activa and the
selected man-made component, the low values for the reverse saturation current associated with silicon are
frequently not documented in conventional transistor data sheets because they are trivial in many
applications. Similarly, biological researchers seldom record the reverse saturation currents associated with
the conduits of a neuron. This complicates the scaling process. The alternative is to employ a totally
empirical method of scaling. In this method, the collector voltage is chosen first to properly emulate the
biological collector potential based on the ratio of offset parameters as described above. The emitter current
is then scaled by overlaying the current-voltage characteristics of the Activa and the chosen emulation
transistor to determine the current scaling factor. These scalings will determine the scaling factor applicable
to the current on the collector current to collector voltage characteristic of the emulation device.
2.3.4.1.2 Emulation of the second order Activa circuit
After developing the proper emulation of the desired Activa at the first order level, it is possible to emulate
the entire circuit for a given neuron. Most of the circuits within neurons employ Activa in the common base
(or grounded base) configuration. However, the adaptation amplifier of the photoreceptor cell employs the
common emitter (or grounded emitter) configuration and the lateral cells (horizontal and apparently most
amercine cells) employ a hybrid circuit where input signals are applied to both the emitter and base signal
leads.
After the configuration to be emulated is chosen, the appropriate load line can be drawn on the output
characteristic of the circuit based on the scaling parameters developed above. This output characteristic is
usually the collector current versus collector to ground voltage characteristic. This characteristic varies
considerably depending on whether the common base or common emitter configuration is used.
While a resistive impedance may be used to approximate the load line over a limited range, it should be
remembered that the load is generally a diode and the Activa circuit is operated under large signal
108Motorola (1974) Semiconductor Data Library, Series A, Volume 1. Figure 13 on pg 2-399
The Neuron 2- 181
conditions. The use of a resistive load may be deceiving under these conditions and mask non linearities that
occur in the real circuit.
2.3.4.2 Simulations
Simulations via digital computer can be performed by implementing a set of differential equations or by
calling upon a library of preprogramed transistor characteristics. The later approach generally involves more
parameters and provides a more accurate result. However, the choice of a template from the library of
available transistors should follow the procedure described in the previous section. In the selection of a
preprogramed template, it is important to confirm that the offset parameter appropriate to the base material
has been included in the template, and the program is capable of operating at the impedance levels required.
The computer simulation known as NEURON implements a large set of (unsolved) differential equations
following the empirical concept of Hodgkin & Huxley. It numerical integration to describe the solution of
this set. It does not provide a closed form general or particular solution to the set. It is primarily concerned
with the phasic operation of a putative neuron and is archaic from the scientific persective. This simulation
is much more complex and much less related to the underlying mechanisms than the closed form description
of the neuron provided here. Before using the simulation program known as NEURON, the investigator
should at least assure himself that the program properly reflects the effect of temperature on the operation of
the neuron.
2.3.4.2.1 Large Sale Simulation of Brain using digital circuitry–Modha, ca. 2013
In a Modha interview, as documented by A. Piore109, has been working on a large scale model of the human
brain based on conventional computer circuitry but significant optimization of the architecture. Piore quotes,
Geoff Hinton, “the hardware is useless without the proper “learning algorithm.” Piore then notes, “But
Modha and his team [at IBM] are undeterred.” The problem is more serious, they are trying to simulate an
analogue computer of unknown architecture and fundamental rules of operation using a digital computer
architecture.
The article composed by Piore, does not suggest Modha et al. have a firm understanding of how the brain
operates and that it is fundamentally an analog computer based on unknown operating principles.
Ananthanarayanan et al110., a member of the Modha team, provided an extensive paper on their simulation
strategy.
They cite an entry level text on Neural Science published in 2000 and spend a full page on what they
describe as Neuroscience 101 (presumably for the benefit of their audience). They restrict their model to
neurons generating action potentials for cumulative stimuli exceeding a threshold in intensity; in actual fact,
95% of the neurons operate in the analog signal mode. They also indicate they set the number of input
channels to 1000 synapses per dendritic input to a neuron; without addressing why so many individual
channels are needed. They speak of their model as “biologically-inspired.” Their reference to the thalamus
as a small body that serves as a center to disttribute signals appears as a better description of the thalamic
reticular nucleus, TRN. The effort seems to be focused on getting their corporate team up to speed in a new
technological area. No realistic model was produced. By marrying the software program to a super-
computer, the number of nodes that could be handled in a reasonable time could be greatly increased, hence
the numbers in the title. However, their simulation had no connection to an actual biological situation.
They did provide an interesting table giving the nominal number of neurons and synapses used within the
biological community as a standard, Figure 2.3.4-1(Top). The following year, Modha et al111. provided a
similar table, Bottom, using different units for the neurons and adding a monkey (of unspecified size).
109Modha, D. (2013) Mind in the Machine Discover, June, pp 52-59
110Ananthanarayanan, R. Esser, S. Simon, H. & Modha, D. (2009) The cat is out of the Bag: Cortical
Simulations with 109 Neurons, 1013 Synapses. SC09 Conf (an ACM event), Portland, OR
111Modha, D. Ananthanarayanan, R. Esser, S. et al. (2011) Cognitive Computing Comm ACM vol 54(8), pp 62-
71
182 Neurons & the Nervous System
2.4 The synapse– Concept versus functional reality
The literature contains many conceptual discussions related to the synapse, generally without providing a
testable null hypothesis. The term synapse was introduced long ago to describe the generic connection
between neurons and/or neurons and other biological tissue.
The literature is also conflicted with regards to the concept of a gap junction. Some texts insist they are
fundamentally limited to electrical (electrolytic) junctions. Others show complex caricatures of the
“chemical junctions” as gap junctions with endless varieties of neurotransmitters crossing the gap. In this
work, all neuron to neuron and neuron to muscle connections involve distinct gap junctions. The former
involve electron transfers to support signaling while the latter involve the release of a variety of chemicals
tailored to specific tasks. With respect to the glandular system, it is the terminals of the stage 7 neurons that
release chemicals known to be effective from a glandular perspective.
Section 1.2 provided an overview of many of the features involved in this determination. That section notes,
there are two major functional roles for synapses;
the transfer of information from an axon or axon segment to the next orthodromic axon segment or neurite
of the neural modality and of the electrolytic type or,
the transfer of commands to activate a muscle or gland from a stage 6 neuron to a muscle or gland and of
the chemical type.
This work makes it perfectly clear, the vast majority of all synapses are of the electrolytic type;
over 99% of all synapses are of the electrolytic type and do not release any chemicals within the synaptic
junction related to signal transfer and,
less than 1% of all synapses are of the chemical type releasing chemicals into the synaptic junction between
a neuron and muscle tissue at the skeletal-muscular interface or into the blood stream as part of the
glandular interface.
In a modern context, these two categories are distinctly different.
The transmission of signals between neurons is fundamentally an electrolytic process (involving only
electrons). These electrolytic (gap junction) synapses are the dominant form of synapse (well over 90% of
all synapses within the CNS, outside of the cerebellum). They are used throughout the stage 1 through stage
6 portions of the neural system described in Section 1.1.5 and particularly Figure 1.1.5-3. This synapse
style 1 is discussed in depth in Section 2.4.3.
The connection between neurons and other biological (non-neural) tissue is fundamentally a chemical
process. In this work, the chemical synapse is limited to the output stage 7 neuro-effectors. Chemical
Figure 2.3.4-1 Nominal # of neurons & synapses in mouse, rat, cat, monkey &
human CNS. The units for neurons differ between the two frames. The two
sources are from Modha’s laboratory. TOP; from Ananthanarayanan et al., 2010.
Bottom; from Modha et al., 2011.
The Neuron 2- 183
synapses form the gateway connection between the neural and glandular systems. This gateway is discussed
in Section 16.9. This synapse style 3 is discussed in Section 2.4.6.
The chemical synapse is also the key interface between the neural and muscular (myocytic) systems. The
myocytic system is only addressed peripherally in this work (Section 16.5). It consists of three types of
muscle, striated, smooth and cardiac. The striated muscle is frequently described as skeletal muscle. The
cardiac muscle tissue is actually a hybrid, neural/muscular tissue. (Chapter 20). The striated muscle occurs
in two forms; what is described as red muscle which responds relatively slowly to the neural system (and is
described as slow muscle), and white muscle (fast muscle) that responds rapidly and is frequently described
using the term, twitch.
There is a synapse style 2 that is introduced in this work for the first time. The synapse style 2 is an
elaboration of the electrolytic synapse style 1; it is the long sought key to the memory storage in the
cerebellum and other memory storage locations. The style 2 synapse is a four layer semiconductor stack of
the form PNPN. The number of synapse style 2 is equivalent to the number of synapses of style 1 within the
CNS but they are concentrated in the cerebellum. This synapse style 2 is discussed, as a component, in
Section 2.4.5 and discussed in its operating environment in Section 17.6.
Unfortunately, the majority of past empirical work has focused on the chemical synapse at the pedicle of
stage 7 neurons (at a muscle interface and as the origination of glandular substances) while much of the early
theoretical work used these empirical results to describe the more general synapse (at the neuron to neuron
interface) that is electrolytic.
All known morphologically defined Nodes of Ranvier (found within stage 3, 6 and 7 signal projection
neurons) involve the transfer of signals between axon segments without involving any chemicals directly in
the transfer. They are all of the electrolytic type.
All of the electrolytic neurons transfer signals between two neural elements with temporal delays measured
in microseconds, not milliseconds. The instrumentations used by biological investigators have not generally
been capable of measuring these short time intervals. As a result, most of the reported measurements have
include the time required for the transfer of signals through portions of axonal or neuritic tissue.
The following material will address and support these assertions in detail.
2.4.1 Historical aspects: the electrolytic vs chemical neurotransmitter
Shepherd discussed a variety of synapse features in 1998 but without a substantive framework to support the
discussion112. This work will separate the electrolytic synapse from the chemical synapse on functional
grounds.
The vast majority, probably exceeding 99% of neurons are involved in signal transfer within the neural
modality and are of the electrolytic type. Less than 1% of neurons are involved in the release of chemical
substances at the neural-muscular or neural-glandular interface and are therefore of the chemical type.
Section 1.1.5 and particularly Figure 1.1.5-3 describes the myriad locations where synapses are found.
Electrolytic synapses connect all neurons within stages 1 through the inputs to stage 7 neurons. It is only at
the outputs of the stage 7 neurons (primarily at the neuron-muscle and neuron-glandular interfaces that
chemical synapses) are actually found (Section 4.2.3).
Pannese provides a recent, but brief, background on the synapse. It is followed by a broader discussion
heavily weighted toward the chemical concept of a synapse. Fonnum provides a more systematic discussion
of the requirements on a synapse113.
112Shepherd, G. (1988) Neurobiology. NY: Oxford University Press
113Fonnum, F. (1984) Glutamate: a neurotransmitter in mammalian brain J. Neurochem. vol. 42, pp 1-11
184 Neurons & the Nervous System
The concept of a chemical neurotransmitter began in 1904 with a hypothesis by a student. McGeer, et. al.
review the early discussions based on analogy with the action of pharmaceutical preparations114. It remains
largely based on this analogy to this day. However, rather than the injection of a pharmaceutical, the
evidence now is largely based on topical application to tissue. The fact that the presumed neurotransmitters
have such a potent impact on the metabolic activity of the neuron when applied to non-synaptic areas has
caused a significant problem. McGeer, et. al. have divided chemical neurotransmitters into two classes to
meet this challenge. They speak of the metabotropic function of neurotransmitters as well as the
conventional ionotropic function. This work will associate their metabotropic function with the hormonal
system and their “ionotropic” function with the actual transmission of signals between neurons, by electrons
and holes. It will show that most materials labeled neurotransmitters, or inhibitors, in the literature relate
exclusively to the metabotropic function. McGeer, et. al. conclude their introductory material with the
statement, “It has turned out that chemical transmission is a much more complicated biological process than
Dale (circa 1938) had supposed.”
Lambert & Kinsley115 have provided the most recent tabulation of the putative neurochemical categories and
neurotransmitters. The labels are largely conceptual, due to the rapidly evolving terminology.
Example; they speak of the catecholines, dopamine, epinepherine, norepinepherine, as containing the
omnipresent benzene ring. The actual participant in a DACB is actually the phenol group, benzene
hydroxide (Section 18.5.2.5 in Appendix ZD of “Processes in Biological Vision”).
They can be read to largely support the more specific categorizations defined in this work (although the
tabulations do not include the word electron anywhere). Their table 5.1 describes dopamine and 5-HT as
neuromodulators rather than neurotransmitters. Their table 5.3 describes dopamine and its putative
receptors, D1 through D5 as effecting, “movement, olfaction, reinforcement, mood, concentration, hormone
control.” They provide no details beond this simple conceptual list.
Ottoson, a very much more hands-on and experienced researcher addressed the question in 1983116.
The introduction of the technique for intracellular recording and the discovery of excitatory postsynaptic
potentials led to the abandonment of the earlier generally accepted idea that synaptic transmission occurred
by direct electrical contacts between neurons. It therefore came as a surprise when it was found that
transmission in some invertebrate synapses does in fact occur by current spread. The recorded delay in
conduction was negligible so that the postsynaptic potential was concurrent with the rising phase of the
impulse in the presynaptic neerve fibre; thsi finding precluded a chemical link in the transmission. These
observations demonstrated that there war specialized synapses for electrical coupling between neurons. An
extensive search soon disclosed regions where the membrane of neighboring neurons appeared to be fused.
These so-called gap junctions apparently provided for low resistance electrical contacts between cells. .
.These junctions allow electrical activity to be transmitted form one cell to another without the mediation of
neurotransmitters.” He goes on in the following paragraph, “It is interesting to see how the notion of
synaptic transmission in the nervous system has changed in the past few decades. From a position of
universal acceptance for almost a century, the electrical hypothesis was ousted in the early 1950s and the
chemical hypothesis was greeted with great acclaim. Today, abundant evidence for both modes of
transmission exists.”
This work will separate the electrolytic junction, used universally within the neural system from the
chemical synapse used as the neuro-effector controlling the hormonal system and most of the
neural/motor interface.
In the following paragraph, McGeer, et. al. are clearly referring to neuron-to-myocyte synapse. They say,
“These chemically transmitting synapses were designed to compensate for electrical mismatch between the
presynaptic and post synaptic components of the synapse, e. g., the very small nerve terminal and the large
area of the muscle fiber membrane with its high capacity.” Section 2.7.1 will show that more than
compensation is involved. An alternate operating protocol is involved.
114McGeer, P. Eccles, J. & McGeer, E. (1987) Molecular Neurobiology of the Mammalian Brain. NY: Plenum
Press. pg 80-174
115Lambert, K. & Kinsley, C. (2011) Clinical Neuroscience, 2nd Ed. NY: Oxford University Press pp 130-131
116Ottoson, D. (1983) Physiology of the nervous system. NY: Oxford University Press page 191
The Neuron 2- 185
Pannese has confirmed, the subject of electrolytic versus chemical neurotransmitters was a hot topic during
the 1930-40s. It was supposedly settled in favor of the chemical neurotransmitter, using the technical base
available at that time. More recently, the debate has gained new life with the demonstration of electrical
synapses in a long list of animals (pp 108-116). While he continues to suggest the primacy of chemical
neurotransmitters, he recognizes the legitimacy of electrolytic synapses in specialized situations and the
presence of both types of synapses in many animals.
Following the debate in the 1930-40s, it became necessary to isolate one or more putative neurotransmitters.
Fonnum noted; “Electrophysiological studies focused early on the powerful and excitatory action of
glutamate on spinal cord neurons. Since the action was widespread and effected by both the D- and L-forms,
it was at first difficult to believe that glutamate could be a neurotransmitter.” Fonnum provides a variety of
evidence concerning glutamate as a neurotransmitter. It is largely conceptual and involves topical
application of the material, generally in bulk, and not to a specific neuron or portion of a neuron.
McGeer, et. al. assert “Highly convincing evidence that L-glutamate and L-aspartate should be
neurotransmitters comes from their iontophoretic actions. Both of these dicarboxylic amino acids powerfully
excite virtually all neurons with which they come in contact. (Page 186)” Such topical application of a
chemical does not relate to its role as a neurotransmitter. It relates to its role as a fuel source, particularly
when its concentration exceeds the normal 2-5% at the site of electrostenolysis. Just prior to the above
quote, McGeer, et. al. say “While the anatomical data at this stage must still be regarded as highly tentative,
it can be said that glutamate and aspartate meet many of the generally accepted anatomical criteria for
neurotransmitter status.” The words “should be” and “highly tentative” are important in the above
quotations. Chapter 3 will develop the role of glutamate and aspartate as the primary fuels, neuro-
facilitators, of the neural system.
Still earlier, McGeer, et. al. said “Nevertheless, it must be recognized that truly definitive markers that can
be applied at the cellular level do not exist for glutamate and asparate as they do for several other
neurotransmitters. Therefore, evidence for neuronal identification and for pathways involving these amino
acids must in all cases be considered as tentative.” Their chapter 6 describes the role of glutamate and
aspartate primarily in metabotropic terms which are completely consistent with the above sections of this
work. Their table of metaboloid concentrations by location within the nervous system is very useful. They
also note the ubiquitous ability of glutamate and aspartate to excite multiple neural “receptors” in response to
topical application. The problem of markers has been overcome through nuclear chemistry and other
techniques as discussed in Sections 3.2.2.
Additional experimental effort needs to be expended on identifying the microscopic portions
of a single cell that are sensitive to the topical application of so-called neurotransmitters. It is
predicted that these areas will be found to be chemically asymmetrical membranes segments
and the applied chemical will form a stereochemical union with the membrane at these
locations.
Lam threw down a gauntlet in 1978117. At the conclusion of a comprehensive program studying the
photoreceptor, he asserted, “In conclusion, our chemical studies so far indicate that none of the known
putative transmitters appears to be a likely candidate for the photoreceptor transmitter.” and
“The possibility that an as yet unsuspected or unknown substance may be the transmitter for vertebrate
photoreceptors has to be seriously considered.”
Brown noted in 1991, “The classical view of chemical transmission was that an individual nerve cell only
released a single transmitter substance and that the effects of that substance depended on the particular
receptor on the post synaptic cell.”
Greenfield discussed current problems with the concept of a chemical neurotransmitter in 1998118. Her
frustration is couched in such expressions as “I shall consider some of the principal anomalies arising from
current findings, specifically why; (a) there are many diverse transmitter substances; (b) transmitters are
released from sites outside of the classical synapse; (c) some well-known transmitters have surprising
‘modulatory’ actions; (d) synaptic mechanisms themselves have no obvious or direct one-to-one relationship
with functions such as movement, mood and memory; and (e) it is difficult to extrapolate from drug-induced
modification of synaptic mechanisms to the effects of those same drugs. . .” and “No doubt the forthcoming
years will herald the discovery of still further surprising transmitter-like molecules that strain the accepted
117Lam, D. (1978) Identified cells in the vertebrate retina In Osborne, N. ed. Biochemistry of Characterised
Neurons. NY: Pergamon Press pp 250
118Greenfield, S. (1998) Future Developments. In Higgins, S. ed. Essays in Biochem. vol. 33, chap. 14, pp 179
186 Neurons & the Nervous System
concept of how transmitters behave.” She concludes with “We are about to enter an exciting phase in brain
research, where there is a shift in emphasis away from the all-pervasive paradigm of classical synaptic
transmission.” This work provides the basis for that shift and provides a rationale for each of the above
problems. Unfortunately, the new paradigm is completely contrary to the concept of a chemical
neurotransmitter.
Baars, writing in Baars & Gage, has made a major statement that is best introduced by an allegory;
The academic neuroscience community has just placed its toe in the waters of real neuroscience when Baars
noted (page 62, 2007), “It is now known that electrical synapses, which use no neurotransmitter al all, are
much more common than was previously believed. Even the dendrites of a single nerve cell may be able to
compute useful information. . . Other surprises keep coming.”
As a matter of fact, virtually all synapses (greater than 95%) are electrolytic (the precise form of electronic)
synapses. Furthermore they are three-terminal electrolytic devices (like the Activa within the neuron) that
are sometimes wired to emulate an active diode (a two-terminal device). And, the role of the
“neurotransmitters” glutamic acid and GABA is to power the neuron or synapse. They act as neuro-
facilatator and neuro-inhibitor respectively.
Although Baars reverts nearly instantly to the common wisdom, his including the above statement shows the
winds are changing.
This paragraph was presented earlier in Section 2.1.2. of the general introduction to the neuron.
Deutch & Roberts119, writing in Byrne & Roberts, have reviewed the rapidly changing character of the
conventionally defined, and more recently unconventional, neurotransmitters to include various peptides, a
few gases and potentially all electronic synapses. “Why have so many transmitters” is the provocative title
of an introductory section of their work. They noted (page 287), “The designation of a substance as a
neurotransmitter rests on the fulfillment of certain criteria, which were discussed in Chapter 9. However,
these criteria were formulated early in the modern neuroscience era, and are based mainly on studies of
peripheral sites, particularly the neuromuscular junction and superior cervical ganglion.” They also note
(page295), “The use of the terms conventional and unconventional transmitters reflects our current unease
with the expanding definition of transmitters.” Their focus on the neuromuscular junction is key, to satisfy
the need for specificity, a variety of neurotransmitters are employed at the pedicles of stage 7 neurons.
Spray et al120, also writing in Byrne & Roberts, have introduced the same sense of the change under way
when they note, “Electrical synapses do some things that chemical synapses cannot.” Unfortunately, they
continue to interpret these electrical synapse within the putative chemical theory of the neuron that is not
supported here.
Chapter 4 of Quinn has once more reviewed the problems with the chemical theory of the neuron related to
synapses, inorganic flow of ions through biological membranes, the character of the lemma within synapses
and potential neurotransmitters. The situation has not changed since the time of Hodgkin & Huxley (ca
1945). The chemical synapse is an archaic concept.
Randall et al. have provided a cartoon of an electrical (more specifically an electrolytic) junction being
interrogated electrophysiologically. Figure 2.4.1-1 shows their cartoon. The cartoon suffers from two
significant shortcomings. First, the lemma of neural cells is a perfect insulator except in the areas modified
at the molecular level to support electrical interaction. Second, they failed to recognize that the milieu
between their presynaptic and post synaptic neurons was in fact at electrically ground potential as shown by
the alternate representation. This modification makes the junction an active electrical junction employing
semiconductor physics to explain its operation. The cartoon also shows how an electrolytic synapse can be
made reversible by simply changing the polarity of the applied potentials (a characteristic of devices
employing semiconductor physics but difficult to explain using chemical principles). This capability has
been well documented (Section 2.4.2.2).
119Deutch, A. & Roberts, J. (2004) Nonclassical signaling in the brain In Byrne, J. & Roberts, J. eds. From
Molecules to Networks, NY: Academic Press Chapter 10
120Spray, D. Scemes, E. Rozental, R. & Dermietzel, R. (2004) Cell-cell comunications: an overview
emphasizing gap junctions In Byrne, J. & Roberts, J. eds. From Molecules to Networks, NY: Academic Press
Chapter 15
The Neuron 2- 187
Note also that the synapse is operating in the
analog mode. Randall et al. showed its
performance when excited by pseudo action
potentials but their calibration is open to question
if they did not recognize the condition of the fluid
environment between their cell walls. While
recognizing the much faster operation of the
electrolytic synapse, the rest of their text suffers
from not appreciating the actual active electrolytic
character of their conceptual synapse (Section
2.4.3).
As will be shown below, the transmission of a
signal across a synapse is extremely simple when
the signal remains in electrical form. In this case,
the physical structure of the synapse forms an
active electrolytic device, an Activa, virtually
identical in characteristics to the man-made
transistor. When the Activa is properly biased
electrically, an electron can pass from the pre-
synaptic to the post synaptic terminal of such a
device with an efficiency of greater than 99%.
On the other hand, the chemical synapse requires
what is generally described as the translation of the
signal from an electrical form in an axoplasm to a
chemical form in the synaptic gap and then a
reconversion from the chemical form back to an
electrical form in the post synaptic neuroplasm.
How such a translation would be achieved remains
largely conceptual to this day.
Ramachandran (page 602) provides material
concerning a large number of chemicals believed
to be released at the pedicles of stage 7 neurons.
The open question is how many of these (if any)
are neurotransmitters and how many are neuro-
effectors?
Chapter 3 will review the chemical characteristics
of various pharmaceuticals (including their stereo-
chemistry) and how these characteristics determine
whether the materials are neuro-facilitators or
neuro-inhibitors.
2.4.1.1 Requirement on a chemical neurotransmitter
The detailed description of a chemical neurotransmitter and its mode of operation (in equation form) have
not yet appeared in the literature. However, a spirited debate raged during the 1980's.
Ottoson, in a chapter labeled “putative transmitters121,” asserted, “Despite arduous efforts, only a few
compounds have been identified which can with various degrees of certainty be considered as
neurotransmitters. To be identified as a transmitter, a substance should fulfil certain criteria. The main
properties to be establish are the presence of the substance in the presynaptic terminals and its release during
presynaptic activity. Furthermore, there should be a correlation between its release and the amount of
presynaptic activity; local administration of the compound should produce the same effect as presynaptic
activity and substances antagonistic to the putative transmitter should block synaptic transmission. Actually,
none of the compounds generally considered to be transmitters in the central nervous system fulfils all these
criteria. Because of the complexity of the central nervous system, it is technically difficult to prove the
release of a putative transmitter or to administer it locally at the synapse. The rigorous criteria which are
applied to the peripheral system therefore cannot be easily satisfied within the central nervous system.”
Figure 2.4.1-1 Early and updated
electrolytic synapse. A cartoon from
Randall et al. shown with the addition of
an alternate representation. The curved
arrows shown exiting the lemma of the
neuron are superfluous. The lemma is a
perfect insulator except in the junction
areas. The alternate representation is a
better cartoon of the actual in-vivo
situation that was unknown to the
investigators. It constitutes the third
terminal of the electrolytic neuron. See
text. Modified from Randall et al., 1997.
121Ottoson, D. (1983) Physiology of the nervous system. NY: Oxford University Press Chapter 8
188 Neurons & the Nervous System
Fonnum describes “the four main criteria for the classification of a chemical as a neurotransmitter:
1. it is presynapticaly localized in specific neurones;
2. it is specifically released by physiological stimuli in concentrations high enough to elicit postsynaptic
response;
3. it demonstrates identity of action with the naturally occurring transmitter, including response to
antagonists; and
4. mechanisms exist that will terminate transmitter action rapidly.”
He then attempts to show that glutamate meets most of these requirements. He does raise one concern;
“There is a poor correlation between the pharmacological activity of the agonist and antagonist and the
binding to glutamate sites in several studies.”
Each of Fonnum’s criteria are global in concept. They lack specificity with respect to the mechanisms
involved in meeting these criteria. Item 3 appears to be the catchall item. It includes the requirement that
the chemical neurotransmitter somehow cause the generation of a change in electrical potential within the
post-synaptic neuroplasm. The mechanism used to accomplished this transition has not been described in
detail in the literature.
McIlwain & Bachelard gave a similar list of five criteria122;
1. the transmitter must be stored specifically pre-synaptically and enzymes for its synthesis should be found
there.
2. pre-synaptic stimulation (usually but not necessarily electrical) should result in release of the transmitter.
3. controlled application of the transmitter should elicit the same post-synaptic response observed on pre-
synaptic stimulation.
4. specific agents should be found which block the post-synaptic response to the transmitter
5. specific mechanisms for termination of action should be demonstrable.
Similar to Fonnum’s set of criteria, item 3 appears to be a catchall lacking specificity. The requirement
should call for the generation of a change in potential within the post synaptic neuroplasm that is
proportional to the change in potential of item 2.
While these lists are similar, as noted by Ottoson specifically, the ability of most of the putative
neurotransmitters found in the literature to satisfy them is in considerable doubt, particularly with respect to
neuron-to-neuron signaling and within the CNS in general.
Ottoson proceeds to discuss the role of various chemicals in the CNS based primarily on their physical
presence rather than their function importance. He does note (page 198) the “potent depolarizing role of
glutamic acid and aspartic acid on neurons throughout the central nervous system, which makes it difficult to
discriminate between a non-specific action of these compound and their possible role as transmitters.” The
non-specific action is in fact the powering of all neurons through their neuro-facilitator role in the glutamate
to GABA (or aspartate to glycine) conversion with the release of an electron. Ottoson even asserts, “Glycine
is evidently a major inhibitory neurotransmitter in the spinal cord and brain stem, while GABA plays that
part in the cerebral cortex.” These chemicals are neuro-inhibitors in the terminology used in Chapter 3.
2.4.1.2 Requirement on an electrolytic neurotransmitter
The requirements on an electrolytic neurotransmitter are much simpler than those listed above. The
requirement is for a change in the potential of the axoplasm of a neuron to be reproduced in the neuroplasm
of one or more orthodromic neurons. As defined in this work, the electrolytic neurotransmitter is an
electron. The challenge is to define how the change in the number of electrons on the capacitance
representing the change in the axoplasm potential can cause a similar change in the potential of the
orthodromic neurite. Section 2.4.3 will explain this mechanism in detail. The same mechanism is used
between both analog and phasic neurons.
2.4.1.3 The neurotransmitters, neuro-facilitators & neuro-effectors
122McIlwain, H. & Bachelard, H. (1985) Biochemistry and the Central Nervous System. NY: Churchill &
Livingstone. Pg 414
The Neuron 2- 189
Furness & Costa123 struggled in 1987 to define the basic functionality of the enteric system by addressing the
definition of neurotransmitters. They used the highly conceptual definition that, “Any substance that is
released from a neuron and has an effect on that neuron or on a cell near the site of release can be regarded
as a neurotransmitter.” They ended their discussion with the observation that, “In practice, the criteria used
in transmitter identification are empirical.” This broad conceptual definition does not address how a signal
is relayed from one neuron to one or more orthodromic neurons. Nor does it address the difference between
neurotransmission between neurons and neurotransmission designed to affect muscle and other non-neural
tissue.
Karczmar, Koketsu & Nishi124 reviewed the history of the chemical versus electrolytic neurotransmitter in
1986. While they remain proponents of the chemical theory (page 13), their text presents extensive electrical
data on the function, including excellent evidence for the unique operating characteristic of the neuron and
synapse clearly describing an internal electrical diode (pages 87, 112, 165 & 166). They also develop the
difference between a neurotransmitter and a “modulator” (page 65), discriminating between a modulator as
an endogenous substance and exogenous toxins and pharmaceuticals. This work extends their concept of a
modulator to either a neuro-facilitator or a neuron-inhibitor.
In his fourth edition in 2008 (which largely repeated the 2nd Ed and 3rd Ed.), Fuster wrote extensively about
“chemical neurotransmission.” While he asserted again that “Communications between neurons takes place
by electrochemical transaction at synaptic junctions,” his material does not support a fundamental synaptic
mechanism. In fact, his figure 3.1 provides a smorgasbord of proposed mechanisms (in cartoon form) and
relevant chemical constituents (over forty are named). The figure asserts there are six fundamental types of
chemical synapse. Unfortunately, the material does not demonstrate in detail that any of the mechanisms and
necessary chemicals are present within the in-vivo synaptic junction. It does not address the role of nitrogen
oxide (NO) as a neuro-effector. Fuster groups the above chemicals into chemical families and describes
their importance as neurotransmitters. This work will use his families to demonstrate these chemicals are
either primary neuro-facilitators, primary neuro-inhibitors, secondary neuro-inhibitors or neuro effectors that
play no direct role in the transmission of signals between neurons (Section 3.2.2).
Fuster notes the much greater prevalence (200x-1000x) of GABA in the brain than any of the first four
“neurotransmitters” he discusses; norepinephrine, dopamine, serotonin and acetylcholine. He also
characterizes GABA as a neuro-inhibitor while glutamic acid and aspartic acid are characterized as neuro-
facilitators (his term excitatory neurotransmitters) in agreement with this work.
By 1990, the argument over chemical versus electrolytic neurotransmission was reversing again. Brown125
noted, “Many examples of excitatory electrical synaptic transmission are now recognized, not only in
invertebrate species but also in vertebrate species, including mammals. The essence of excitatory electrical
transmission is that current flow generated in one cell (the presynaptic cell), for example by an action
potential, passes across a synapse and leads to a depolarization in the post synaptic cell.” And, ”The gap
junction provides a low resistance path for current flow between the two cells, and therefore there is little
delay, since it is the speed of electronic transmission that matters.”
See Section 3.5.4 for the definitions used in The Electrolytic Theory of the Neuron.
2.4.2 Detailed history of the electrolytic and chemical synapses
Sherrington, the student, set the stage for understanding the synapse during the last of the 19th Century.. He
deduced that neurons somehow communicate information, one to the next, by a mechanism that is
fundamentally different from the way that they conduct signals along their axons. His contemporary, Ramon
y Cajal continued to define the synapse. He proposed that neurons were distinct entities, fundamental units
of the nervous system, that were discontinuous with each other. The synapse, a specialized apposition
between cells, mediated the signals. The word “synapse” implies “contiguity,” not continuity: between
neurons, as Cajal himself explained it. As Boron & Boulpaep note (page 295), “Neurons come very close
together at chemical synapses but their membranes and cytoplasm remain distinct. At electrical synapses,
the membranes remain distinct, but ions and other small solutes can diffuse through the gap junction.” The
wording in the last sentence is a stretch, and he did not document such movement. It will be seen that only
electrons pass through electrical synapses.
123Furness, J. & Costa, M. (1987) The Enteric Nervous System. London: Churchill Livingstone, pg 55
124Karczmar, A. Koketsu, K. & Nishi, S. (1986) Autonomic and Enteric Ganglia. NY: Plenum Press
125Brown, A. (1991) Nerve Cells and Nervous Systems. NY: Springer-Verlag pg 53
190 Neurons & the Nervous System
Cole126 provides a very early discussion of a unique property of the synapse. Speaking in 1968 of two
membranes in close proximity, he said:
“The idea that a pair of unit membranes might have a negligible resistance–perhaps less than that of a micron
thickness of electrolyte was so contrary to past experiences as to be quite unbelievable. Yet in a flurry of a
few years of intense competition and cooperation, electrophysiology and electron microscopy forced us to
believe that two membranes not only can but frequently do join to become essentially perfectly ion-
permeable connections between cells. . . . Electrically these were usually known as electrotonic junctions,
with resistances from 1 Ohm-cm2 on down to practically nothing. . .”
The last line is indicative of an active device with a high transconductance (a negligible apparent series
resistance). Although the semantics appear awkward now, Cole went on:
“In contrast to the primitive use of an axon as a passive cable, these electrotonic junctions are highly
developed structural elements which allow much the same electrical performance. As both these and
apparent chemical transmitter connections appeared side by side we had an answer to yet another
controversy; that of ‘sparks vs. soup’ of three decades before. From all of the lines of physical and chemical
evidence we are led to a bimolecular membrane model with a hydrocarbon central layer about 25-50
Angstrom thick and a polar and protein layer of about the same thickness or less on each side, . . .”
It will become clear below that his reference to ions passing through a synapse should have been limited to
the negative charged particle, the electron and his “a hydrocarbon central layer about 25-50 Angstrom thick”
can be identified as liquid crystalline water (Section 1.3.2). Such liquid crystalline water has been labeled
EZ-water by Pollack127,128. Cole’s reference to the vanishingly small impedance of the synapse to charge
transfer is a characteristic of the “active diode” configuration of an Activa, developed below.
Hayashi & Stuar129 t inadvertently displayed the difficulty of explaining the operation of the synapse on
chemical grounds in 1993. Their specimen was a barnacle, Balanus nubilus. They found difficulty
explaining the phenomenon they defined as synaptic adaptation using chemical models. The phenomenon is
easily explained as the transient performance of an active non-linear electrolytic circuit. Their concluding
sentence falsifies their premise that Ca2+ is the mechanism controlling the phenomenon.
Barnes130 continued to display the difficulty with the chemical hypothesis in an extended commentary in
1994. He chose to define a myriad of individual channels. His figure 4 is explained on entirely different
electrolytic grounds in this work.
As noted in Pannese, it has only been in recent times that the biological community has accepted Cole’s
ideas and begun to consider the possibility that the junction between two neurons might have an electrical
aspect. They are now speaking more frequently of a “gap junction” which is electrical in nature. This work
differentiates between the electrolytic synapse, found between neurons, and the paracrine chemical synapse,
found between a neuron and other tissue, primarily myocytes.
Sherman & Guillery131 have recently re-opened the discussion of the conventional wisdom related to the
synapse. Unfortunately, they parrot the conventional wisdom with a new twist. They focus on the putative
ionotropic versus metabotropic forms of receptors. These complex explanations of the operation of a
synapse are not supported here.
126Cole, K. (1968) Membranes, Ions and Impulses. Berkeley, CA: University of California Press pg 517
127Ho M. (2004) Water forms massive exclusion zones. Science in Society vol 23, pp 50-51,
128Pollack G. (2008) Water, energy and life: Fresh views from the water’s edge. 32nd Annual Faculty Lecture,
University of Washington at Seattle, Washington, USA http://uwtv.org/programs/displayevent.aspx?rID=22222
129Hayashi, J. & Stuart, A. (1993) Currents in the presynaptic terminal arbors of barnacle photoreceptors Visual
Neurosci vol. 10, pp 261-270
130Barnes, S. (1994) After transduction: response shaping and control of transmission by ion channels of the
photoreceptor inner segment Neurosci vol. 58, no. 3, pp 447-459
131Sherman, S. & Guillery, R. (2001) Exploring the Thalamus. NY: Academic Press, pg 143.
The Neuron 2- 191
Pappas132 provided a good discussion of the junctions between cells in 1975 that can be expanded into a
figure embracing more recent information. Figure 2.4.2-1 is modified from Pappas. It expands the concept
of the chemical neuromodulator while accepting his variant of the electrolytic synapse. Although he asserted
that the electrolytic synapse was bidirectional; when properly biased, it is a unidirectional “active diode”
(Section 2.4.2 and Section 2.4.3).
Beginning on the right, the electrolytic synapse (used in both tonic and phasic situations).is shown
interconnecting two neurons via a gap junction of 20–30 Angstrom spacing. Pappas did not describe what
features of the two lemma were used to determine this dimension. It may have been the centerline of the two
dark lines in an electron micrograph, or it may have been the edges of those two dark features. A nominal
value of 45 Angstrom is used in this work. Regardless of the spacing, the arrow associated with the
electrolytic synapse represents the direction of the signal that is passed under the nominal in-vivo bias
conditions (the axoplasm of cell 1 becoming more positive than the base of the synapse and the
dendroplasm, or podaplasm of cell 2 remaining more negative than that base ). The broader gap usually
observed under light microscopy is shown to the left of the gap junction. As Pappas noted, the gap junction
is always of the punctate form, with a typical diameter of 0.1 to 10 microns. On closer examination, it is
found to consist of small individual regions in an orderly matrix. The diameters of these punctate structures
is typically on the order of a hundred Angstrom or less. Each of these punctate structures is formed by EZ
Water in a liquid-crystalline lattice (Section 2.4.3.6).
Figure 2.4.2-1 Caricatures of the chemical and electrolytic junctions. Right; the
nominal electrolytic synapse showing the conventional electrolytic signal, the
electron or hole (arrow), crossing the gap junction. No chemical species is
involved in this transition, only a solute-free liquid-crystalline lattice of EZ Water
is needed to support this transition. Center, right; the paracrine chemical
junction typically associated with muscle tissue as cell 2. The area between the
two cells is typically confined by other tissue (not shown). The double bars
represent a stereo-chemical site with release controlled by the axoplasm
potential. Center, left; a basic caricature that can represent the endocrine
chemical junction with no upper limit on the spacing between cells. Cell 2 can
be far removed from cell 1. Left; A nominal exocrine situation with a duct
through tissue to the external environment. See text. Modified from Pappas,
1975.
132Pappas, G. (1975) Junctions between cells In Weissmann, G. & Claiborne, R. ed. Cell Membranes;
Biochemistry, Cell Biology & Pathology. NY: HP Publishing Co. Chapter 9
192 Neurons & the Nervous System
The chemically mediated signal transmission originating at a neuron appears to be more complicated (three
left frames of figure). As noted here, the chemicals released by the stage 7 neurons can be used under at
least three different conditions. They can be released in a very confined (paracrine) space, typically
associated with muscle tissue, or released in a less confined (endocrine) space within the organism, or into
the external (exocrine) space.
The paracrine situation is believed to involve the stereochemical capture of a progenitor of the chemical
actually released as a muscle stimulant. Prior to the establishment of an axoplasm potential conducive to
such release, the progenitor is stored on the surface of cell 1. When the axoplasm becomes more positive
than its resting potential (typically –140 to –154 mV), the progenitor reacts to form two substances, one of
which is the major stimulant for the type of muscle involved. The 200 Angstrom gap can be considered the
nominal minimum, the effectiveness of the agent is controlled more by its degree of confinement which
controls its mean time to chemical deactivation by other chemicals in the local matrix..
The more complex endocrine situation is shown in one of its forms. The conventional wisdom is that a
chemical prepared within cell 1 and stored in the vesicles can be released into the surround under neural
control. In the simplest case, the agent is released into a confined space and affects only one or a few
orthodromic cells. However, the endocrine situation applies to a wide variety of agents (hormones) that can
affect a wide range of cells at significant distances (meters) from the release point. Thus the chemical
junction should be described as greater than 200 Angstrom (frequently much greater).
For completeness, the exocrine situation is shown on the left. The mechanism of hormone creation and
release is similar to the endocrine case, except the agent is released into the external environment (which
includes the digestive tract). In this case, cell 2 can be a receptor in a separate organism, or a food that is to
be digested.
2.4.2.1 Definition of the neural synapses
A precise definition of a neural synapse is difficult to locate. The concept of such a synapse has generally
evolved from similar terms used when studying non-neural tissue, such as epithelial cells. This slow
evolution began in the 1970's. At low magnification, ~5000X, the two juxaposed lemma forming the
synapse cannot be resolved. Therefore, the axon is shown as continous between the two paranodes (figure 3-
11B &3-12B of Berthold et al.). At higher magnification, >35000X, the individual lemma are easily
resolved.
Figure 2.4.2-2 illustrates these two situation from one paper. Figure 3-8 shows a caricature of the low
magnification situation without detailing the NoR region. It is frequently reproduced erroroneously in the
literature (Section 9.4.1.1). Figure 3-11C shows a similar figure to 2-11B, frequently published without
noting, “where the sectioning plane is outside of the nodal gap.”
The Neuron 2- 193
Figure 2.4.2-2 Comparing synapses at different magnification of adult cat. Top;
low magnification, ~5000X, “Electron micrograph of longitudinal section through
a highly segregated CON segment and its proximal (P) and distal (D) intemodal
end regions; alpha motor nerve fiber, L7 ventral spinal root, adult cat. Dense
lamellar bodies (DLBs), multivesicular bodies (MVBs), filled vesiculotubular
profiles, and some mitochondria occupy the clear axoplasm distal to the nodal
midlevel. Note the bulging contour of the proximal paranodal segment (Para).
ASN = axon-Schwann cell network. Bar: 2 pm.” Bottom; high magnification,
>35000X. “Electron micrograph of transversely sectioned nodal axon segment;
alpha motor nerve fiber, L7 ventral spinal root, [of same] adult cat. Two
arrowheads indicate the axolemma. The axoplasmic cortex is particularly well
developed (white bar) and measures 60 to 100 nm. Arrows mark out crosscut AR
profiles. MTs are encircled. Asterisks are in organelles of the vesiculotubular
type. Ng = node gap.” Bar: 0.1 microns.” From Berthold et al., 2005.
2.4.2.1.1 Junctions in non-neural, epithelium, tissue–Gilula
194 Neurons & the Nervous System
Gilula133 provided the definition of the gap junction and the tight junction applied to non-neural tissue in
1975. These were accompanied by high magnification electron-micrographs of the two. In the paper, he
offered an alternate label for the gap junction, the electrotonic junction.
Gap Junction
“In thin sections, the gap junction can be resolved as a septilaminar (seven-layered) structure that is
comprised of two 75-Angstrom-thick unit membranes separated by a 20- to 40-Angstrom space or gap. The
width of the structure is 150 to 190 Angstrom, or a maximum of 40 Angstrom greater than the combined
thickness of two unit membranes.
When electron-opaque tracers, such as colloidal lanthanum hydroxide, are used, the 20- to 40- Angstrom gap
is penetrated by the electron dense material. A polygonal lattice of 70- to 80- Angstrom subunits can be
resolved in en face views of lanthanum-impregnated gap junctions.”
Tight Junction
“In thin sections, the structure is characterized by a true fusion of the membranes of adjacent cells (fig. 8).
The junctions is about 140-150 Angstrom thick at the site of the fusion. A series of interconnected fusions
effectively provides a complete belt-like (zonula) element that is capable of occluding the diffusion of large
molecules between cells (four citations) Tracer substances, such as lanthanum, are not capable of penetrating
the points of fusion in the tight junctional structure.”
Figure 8 is reproduced here as Figure 2.4.2-3 to support the wording above.
While appearing in a recognized and authoritative text on Neuroscience of the time, this image from Gulila
does not appear to be the definition and image of a tight junction as used by most investigators examining
the chemical synapse of the nervous system, with a cleft between the pre and post synapse surfaces. See the
next subsection.
Figure 2.4.2-3 “Thin section of the tight junction between rat hepatocytes. The
point of fusion (arrows) between the plasma membranes of adjacent cells are
interconnected to form a complete belt or zonula around the cells. x247,500.”
Note the lack of electronic charge on either side of the tight junction. From
Gilula, 1975.
133Gilula, N. (1975) Junctional membrane structure In Tower, D. ed. The Nervous System, vol 1, The Basic
Neurosciences. NY: Raven Press figure 6
The Neuron 2- 195
Friend & Gilula134 expanded on their range of investigation in their 1972 Abstract,
“The fine structure and distribution of tight (zonula occludens) and gap junctions in epithelia of the rat
pancreas, liver, adrenal cortex, epididymis, and duodenum, and in smooth muscle were examined in
paraformaldehyde-glutaraldehyde-fixed, tracer-permeated (K-pyroantimonate and lanthanum), preparations.”
Raviola & Gilula135 expanded on their concept to include contacts (potential junctions) between
photoreceptors in a 1973 paper. It did not achieve a wide following. The charge accumulation on the
internal side of each lemma between the arrows in their figure 6 is more suggestive of separate
electrostenolytic process (Section 3.2) on each lemma than a junction between the two photoreceptors.
2.4.2.1.2 Junctions between neurons
Gilula’s precise definition of a gap junction given above fits the definition of a synapse between two neurons
very well,
Gap Junction
“In thin sections the gap junction can be resolved as a septilaminar (seven-layered) structure that is
comprised of two 75-Angstrom-thick unit membranes separated by a 20- to 40-Angstrom space or gap. The
width of the structure is 150 to 190 Angstrom, or a maximum of 40 Angstrom greater than the combined
thickness of two unit membranes.
When electron-opaque tracers, such as colloidal lanthanum hydroxide, are used, the 20- to 40- Angstrom gap
is penetrated by the electron dense material. A polygonal lattice of 70- to 80- Angstrom subunits can be
resolved in en face views of lanthanum-impregnated gap junctions.”
In fact, Gilula described the gap junction by the alternate name, electrotonic junction. However, the gap
junction is also used for the Nodes of Ranvier and other synapses projecting pulse signals.
2.4.2.1.3 Junctions between neurons according to chemical theory
The concept of a gap junction, under the chemical theory of the neuron, has become more complex as the
prior concept has encountered barriers. The concept of Rudy, page 29 in 2008, is the currently most
complex concept proposed. It implies electrical transmission within the pre- and post-synapse neurons with
a confusingly complex conversion to a chemical mechanism to cross the synaptic cleft. His figure 2.9 is
reproduced as Figure 2.4.2-4 illustrates the problem before encountering the state of matter within the cleft
described in the next subsection.
If the cleft, and all similar concepts of a chemical synapse as a gap junction, consists of chemically
impermeable (solute-free) liquid-crystalline EZ Water (Section 2.4.3.6), the illustrated concept of a
chemical synapse COLLAPSES. The collapse of the chemical synapse also puts in danger of falsification
the concept of a “second messenger.” The collapse of the chemical synapse also puts in danger of
falsification the concept of a “pores.”
134Friend, D. & Gilula, N. (1972) Variations in Tight and Gap Junctions In Mammalian Tissues J Cell Biol vol
53, pp 758-776
135Raviola, E. & Gilula, N. (1973) Gap Junctions between Photoreceptor Cells in the Vertebrate Retina Proc.
Nat. Acad. Sci. USA vol 70(6), pp 1677-1681
196 Neurons & the Nervous System
Figure 2.4.2-4 Chemical theory representation of a gap junction synapse. Note
step 2, “An action potential invades the presynaptic terminal.” Note step 9,
“Postsynaptic current causes excitatory or inhibitory postsynaptic potential . . .
Only the intervening steps are based on chemistry. The porosity of the lemma
to Ca2+ in a timely manner has not been demonstrated. The opening or closing
of channels has yet to be demonstrated. If the cleft consists of chemically
impermeable liquid-crystalline water, the illustrated concept collapses. From
Rudy, 2008.
The rate of Ca2+ ions traveling through the lemma must exceed a rate of change of 1.0 Amperes/second, steps
3 & 4, based on the measured current profile for the active region in Section 2.4.2.4, to satisfy the
requirement of step 9, not including the time required to open the vesicles and pores of steps 5, 6, 7 & 8.
This is a very high current per unit area of a material not known to readily conduct such ions, especially in
their hydrated (much larger diameter) form, especially if part of the area of the lemma is of type 1 and known
to be a near perfect insulator.
The Neuron 2- 197
2.4.2.1.4 Junctions between neurons and non-neural material
The junctions between neurons and either muscle or glandular material are known to involve the emission of
chemicals from the pre-junction axon and the receiving tissue. This type of chemical junction is associated
with stage 7 neurons of this work (Section 2.7).
The gap junction as defined between neurons cannot be used between the axon of a neuron and non-neural
tissue. The gap region consists of a special form of liquid crystalline water that is impervious to molecular
flow (Section 2.2.2.7.1). Pollack136 has also reported on new knowledge concerning structured water, liquid
crystalline water or what he likes to call EZ (exclusion zone) water.
This zone of EZ water has major implications regarding the formation of any active semiconductor liquid
crystalline device such as an Activa, synapse, Node of Ranvier, etc. The existence of this zone of EZ
water is totally inconsistent with the concept of a chemical synapse developed during the 20th Century.
Such a synapse involved a multitude of chemical moieties, neurotransmitters, moving through the region of
the EZ water from the presynaptic to the post synaptic lemmas (Section 9.4 of Processes in Biological
Vision) and in the previous subsection.
2.4.2.2 Recent studies of the chemical synapse concept
At the end of the 20th Century, a group of pharmacologists, led by Danbolt provided a different definition
than that of Gilula.
Danbolt and his associates have continued to rationalize the chemically dominated synapse but with little
success137,138,139,140. Their focus was on a set of proteins labeled “Excitatory amino acid transporters
(EAATs).”
Danbolt et al. published a paper in Bloom that described attempts to determine how glutamate levels within a
chemical synapse were controlled. As the title indicated, the thesis was purely exploratory but focused on
potential proteins in this task.
After extensive investigation of the physical presence of a number of proteins suggested to control glutamate
concentration near and removal from a synaptic gap, Dehnes et al. close with the observation, “The findings
described here give further support to the idea that the tasks of the glutamate transporters are more
sophisticated than simple transmitter removal.” In essence, they did not find their proteins adequate to the
task of removing glutamate from a chemical synapse in a timely manner.
Lehre & Danbolt reach a similar conclusion to Dehnes et al. They open their abstract with the assuertion,
“The role of transporters in shaping the glutamate concentration in the extracellular space after synaptic
release is controversial because of their slow cycling and because diffusion alone gives a rapid removal.”
Their Introduction begins, “The glutamate uptake system (Danbolt et al., 1998) consists of at least five
different transporter proteins (GLAST/EAAT1, GLT/EAAT2, EAAC/EAAT3, EAAT4, and EAAT5) and
represents the only [known] mechanism for removal of excitatory amino acids from the extracellular fluid in
the brain.” They go on, “The roles of these transporters during the first millisecond after synaptic release of
glutamate, however, is currently being debated.” They do discuss an alternative, “the glutamate transporters
[a cycling time of
136Pollack, G. (2001) Cells, Gels and the Engines of Life. Seattle, WA: Ebner & Sons Publishers QH631 .P65
2001 in UCI Library
137Danbolt, N. Storm-Mathisen, J. & Ottersen, O. (1994) Sodium/potassium-coupled glutamate transporters,
a “new” family of eukaryotic proteins: do they have “new” physiological roles and could they be new targets
for pharmacological intervention? in Bloom, F. ed. Progress in Brain Research, vol 100, chapter 7, pp 53+
138Dehnes, Y. Chaudhry, F. Ullensvang, K. et al. (1998) The Glutamate Transporter EAAT4 in Rat Cerebellar
Purkinje Cells: A Glutamate-Gated Chloride Channel Concentrated near the Synapse in Parts of the Dendritic
Membrane Facing Astroglia J Neurosci vol 18(10), pp 3606-3619
139Lehre, K. & Danbolt, N. (1998) The Number of Glutamate Transporter Subtype Molecules at Glutamatergic
Synapses: Chemical and Stereological Quantification in Young Adult Rat Brain J Neurosci vol 18(21), pp
8751-8757
140Danbolt, N. (2001) Glutamate uptake Prog Neurobio vol 65(1), pp 1-105
198 Neurons & the Nervous System
50–100 msec (Wadiche et al., 1995)], it has been argued (Otis et al., 1996) that glutamate uptake is
important only for the slow components of glutamate removal and for the ambient glutamate levels.
However, the glutamate transporters could buffer glutamate on a submillisecond time scale by binding rather
than by transport if they are present in sufficient numbers close to the release sites (Tong and Jahr, 1994).”
Lehre & Danbolt struggled to satisfy the time requirement for a synapse to complete an action potential
generation cycle within one millisecond by binding.
“Binding and transport capacities compared with release capacity
Stevens and Tsujimoto (1995) estimated that each average central synapse has approximately 20 release
sites, each of which needs ~10 sec to refill. Thus, each terminal can release a total of approximately 20
vesicles within a 10 sec period. This implies a maximum average release rate of two vesicles/sec. The
average densities of glutamatergic synapses in the stratum radiatum of hippocampus CA1 and the cerebellar
molecular layer are 0.9 –1.3 m–3 (Woolley and McEwen, 1992) and 0.8 m–3 (Harvey and Napper, 1991),
respectively. If one synaptic vesicle contains 4000–5000 molecules (Clements, 1996; Barbour and Hausser,
1997), it follows that the binding capacity of the known transporters (15,000 and 23,000 m–3) is significant
compared with the release capacity. A transporter cycling time of 70 msec implies that the theoretical Vmax
of 20,000 glutamate transporters is 290,000 glutamate molecules/sec.”
They do not assert a satisfactory conclusion to binding as a timely solution to the glutamate concentration
problem.
Danbolt provided an extensive summary of the teams work in 2001. It is all based on the concepts of the
chemically defined synapse. It failed to address the specific function of a series of proteins in removing, or
controlling the concentration of glutamate in the region adjacent to or in the synaptic cleft of a chemical-
based synapse. His abstract opens with, “Brain tissue has a remarkable ability to accumulate glutamate.”
This is certainly true based on its role in powering every neuron of the 100billion neurons in the CNS
(Chapter 3). He goes on, “The transporter proteins represent the only (significant) mechanism for removal
of glutamate from the extracellular fluid and their importance for the long-term maintenance of low and
non-toxic concentrations of glutamate is now well documented.” This observation is not accepted or
supported here. See the reconstitution of glutamate in Section 3.1.3 via the extended acid cycle of Krebs,
also known as the Tri-Carboxylic-Acid (TCA) cycle, Danbolt then echoes the conclusion of Dehnes et al.
“In addition to this simple, but essential glutamate removal role, the glutamate transporters appear to have
more sophisticated functions in the modulation of neurotransmission.” His abstract concludes with the
rationale, “ Like glutamate itself, glutamate transporters are somehow involved in almost all aspects of
normal and abnormal brain activity.” “Somehow” is not a strong term when used in a major academic paper.
His data does not support the rapid removal of glutamate from the synaptic cleft at a rate sufficient to
support the sub-millisecond operation of the synapse, and Node of Ranvier, in signaling. His Section 3
onwards focuses on the proteins labeled excitatory amino acid transporters (EAATs) above. While
providing extensive narratives of what might be going on, the paper provides several “paradoxical effects of
high transporter densities.” He concludes his section3.2.6 with the observation, “In conclusion, the roles of
glutamate transporters in synaptic transmission are far from being fully understood and their importance in
the control of extrasynaptic and intersynaptic glutamate diffusion is likely to vary considerably between
different synapses.” His section 4.2.4, and its subsections, describe a variety of opposing evidence
concerning the presence of glutamate in nerve terminal endings. Section 5 is focused on potential transport
of glutamate across neuronal lemma. Section 5.3 provides some basic information about the total currents
encountered in electrophysiological experiments. “Electrophysiological measurements typically monitor the
sum of the anion current and the glutamate translocation current (often referred to as the stoichiometric
current).” Section 9.1 describes “Missing information and methodological comments” related to the
chemical theses of Danbolt. The remainder of the paper veers off into territory unrelated to glutamate within
or adjacent to a synapse cleft.
Danbolt has stated, “The glutamate transporters appear to cycle slowly. The time required for one complete
transport cycle is believed to be in the order of 60–80 ms (Wadiche et al., 1995b; Otis and Jahr, 1998;
Wadiche and Kavanaugh, 1998; Auger and Attwell, 2000) although a cycle time of 11.6 ms at 36°C has also
been reported (Bergles and Jahr, 1998). Bergles and Jahr (1998) state that their results either indicate that the
turnover rate is faster or that the efficiency of transport is low (incomplete transport cycles).” These are very
long intervals relative to the required clearance times for action potential generation!
The Neuron 2- 199
Fontana et al141. have presented a paper in 2007 that approaches the study of glutamate and the chemical
synapse from a different perspective. In general, they discuss the bulk transport of glutamate and not
specifically within the chemical synaptic cleft. The analysis and conclusions say little about the role of
glutamate in normal neuron operation.
2.4.2.3 Summary framework of the electrolytic synapse
The primary, and exclusive, (ionotropic?) neurotransmitter, between the neurons of stages 1 through 7, is the
electronic charge (or its saltatory surrogate, the hole). This charge traverses the active electrolytic junction
known as the “gap junction” as demonstrated in Section 2.4.3.
No neuro-effector substances are associated with the electrolytic gap junction. While other chemicals may
be present in the vicinity, the only biological chemicals associated with the gap junction are the neuro-
facilitators, glutamic acid, its backup, aspartic acid and their residues GABA or BAPA (Section 3.4.2).
They are used in a metabotropic process, specifically not in signaling.
This work has defined a new class of neuron that is designed to affect non-neural tissue, the neuro-effector
neuron. Such a neuron may release a chemical material to support this action within a paracrine chemical
junction. Alternately, the material may be released into a wider environment. This material will be called a
neuro-effector substance. As noted above, the range of neuro-effector substances is quite large, and includes
the hormones released by the hypothalamus and hypophysis.
The paracrine neuro-effector substances are typically acetylcholine and nitric oxide. They are typically
released by one neuro-effector and stimulate one myocyte within a confined space generally described as an
end-plate. The end-plate involves a larger gap between the neuron and the myocyte than does a gap
junction. It is also designed to contain the neuro-effector substance for a finite period to optimize the
tradeoff between maximizing the effectiveness of the stimulation and timely termination of the stimulation
(believed to be by hydrolysis)..
The electrolytic synapse employing a gap junction, and the paracrine chemical synapse employing an end-
plate appear to be the only forms of synapse required within the neural system.
In the evolution of this work, the similarity between the structural form of the Nodes of Ranvier and the so-
called gap junction cannot be ignored. Close study indicates the functional part of the Node of Ranvier is a
gap junction. The Node of Ranvier incorporates additional elements associated with homeostasis (Section
2.6.3).
In the electrolytic synapse, there is no requirement for a translation mechanism between the axoplasm
potential and the release of a specific chemical substance. Nor is there a requirement for the release of a
given number of molecules of the substance within the synaptic gap that is proportional to the change in
electrical voltage generated in the axoplasm. Nor is there a need for the substance to cause the generation of
an electrical potential within the orthodromic dendroplasm or podaplasm.
There is no requirement for the conexus forming an electrolytic synapse to be functionally different from the
conexus found within a neuron.
In the paracrine chemical synapse, there is a requirement for a mechanism releasing the neuro-effector
substance in proportion to the change in axoplasm potential. This stereochemical process appears to be
straightforward, as introduced in Section 2.7.1.2 and addressed more fully in Chapter 16.
Within the cardiac system, the synapses are primarily electrolytic and the form of the myocyte is unique to
that system (Chapter 20).
A broader discussion of the variety of concepts proposed for the synapse can be found in Section 3.6.5 of
“Processes in Biological Hearing142.”
2.4.2.4 A reversible synapse challenges the chemical theory
141Fontana, A. Beleboni, R. Wojewodzic, M. et al. (2007) Enhancing Glutamate Transport: Mechanism of
Action of Parawixin1, a Neuroprotective Compound from Parawixia bistriata Spider Venom Molecular
Pharmacol vol. 72(5), pp 1228-1237; DOI: https://doi.org/10.1124/mol.107.037127
142http://neuronresearch.net/hearing/pdf/3Electrolytic.pdf#page=40
200 Neurons & the Nervous System
Figure 2.4.2-5 The ortho- (normal) and
anti-dromic operation of a synapse. a;
currents recorded at a post synaptic
plasma under voltage patch-clamp
conditions. Voltages are original holding
potential before a step change. Numbers
on right indicate number of waveforms
averaged to obtain the trace. Eliminating
the trace at –94 mV improves the
symmetry of the graph. b; the transfer
function of the synapse obtained by
varying the collector potential of the
Activa forming the synapse. Extended
from Glowatzki & Fuchs, 2002.
The measured data from Glowatzki & Fuchs introduces a very significant problem for any chemical theory
of the synapse. The chemical theory of the synapse implicitly assumes the synapse is unidirectional with at
least one chemical released by the presynaptic terminal. The chemical theory normally does not concern
itself with any mechanism involved in creating a change in the electrical potential of the post synaptic
terminal. The concept of the process being reversed doesn’t appear. However, the experimental record is
clear. The flow of current through the synapse is easily reversed by reversing the electrical biases applied to
it. As expected by the Electrolytic Theory of the Neuron, the synapse is actually a three terminal device
whose performance should be reversible by simply reversing the electrical potentials on the terminals. On
the other hand, the chemical theory must either assume chemicals are released by the post synaptic terminal
and collected by receptors at the presynaptic terminal, or postulate additional chemicals that can have the
opposite effect of normal neurotransmitters when the electrolytic bias conditions are reversed. Neither of
these situations is supported, or addressed, by the current chemical theory.
Within its operating range, a synapse can be
represented by an active diode (a specifically
wired three-terminal device). However, if its
operating potentials are reversed while the base
(interneural matrix connection) remains most
positive, the three-terminal device will operate like
an active diode in the opposite direction. This
phenomenon is frequently encountered during
patch-clamp experiments as reported in the
literature. This is clearly represented in figure 3 of
Glowatzki & Fuchs143. Figure 2.4.2-5 redraws
their figure slightly to show this situation. The
current is shown as an excitatory post-synaptic
current (ESPC) measured in-vivo at the synapse on
the surface of a rat (AF #5) auditory sensory
neuron. The current resulted from a tight-seal
patch-clamp configuration. The location and
character of their reference potential were not
specified. As a result, their holding potentials are
most likely relative to the resting potential of the
dendroplasm contacted. They did not report the
axoplasm potential of the sensory neuron or the
steady state current through the synapse associated
with their holding potentials. The randomly
occurring waveforms have been aligned in time,
and displaced in quiescent current for purposes of
presentation. The temperature of the animal was
not specified. Their exploratory experiments
should be repeated under more controlled
conditions in order to support future applied
research. The typical operating range of a synapse
is 20-30 mV with its output terminal, the
neuroplasm contacted in this case, more negative
than its input terminal, the axon of the hair cell in
this case.
Glowatzki & Fuchs chose to draw a single straight
diagonal line through their data points. This line
represents a transimpedance of about 230,000
Ohms (transconductance of 4 micro-mhos) for the
synapse. This is a very low impedance relative to
most neural circuits and explains why some of the
literature describes the synapse as of zero
impedance. The range of their data at zero current
was large, ±11 mV (n=4). This range is suggestive
of the change in mode occurring in that region.
143Glowatzki, E. & Fuchs, P. (2002) Transmitter release at the hair cell ribbon synapse Nat Neurosci vol. 5(2),
pp 147-154
The Neuron 2- 201
Two recent events have cause additional problems for the chemical theory of the synapse. Ottersen et al.
have found a lack of glutamate (and a low ratio of glutamate to glutamine) in the vesicles associated with the
synaptic body of auditory sensory neurons144. Siegel has also noted the growing evidence that the putative
synaptic vesicle binding protein, synapsin, is absent from a number of synaptic bodies (ribbons) in the
sensory neurons145.
2.4.3 The Electrolytic (gap junction), Synapse style 1
The synapse of interest in neural signaling is a very specific structure. It is often labeled a gap junction
morphologically and synapse style 1 in signaling.. The morphological label is frequently shared with other
non-signaling structures as discussed in the next few paragraphs. In this work relating to the neural system,
the label tight junction will be reserved for a passive lap joint between lemma. Additional clarity will be
developed in Chapter 5 based on Vardi et al. The recent work in electron microscopy, documented by
Pannese146 and presented in detail by Vardi147 and others, when combined with the physical chemistry
associated with a gap of between two and four nm (20 & 40 Angstrom) between the axon and a neurite,
demands the electrolytic mode of signal transmission be recognized.
The gap junction synapses of stage 1 through stage 6 have been shown to be electrically reversible. This
capability is easily demonstrated by Eliasof et al148 using multiple probe techniques. This capability places a
serious impediment in the interpretation of the generic synapse as a chemically dependent functional
structure. It is easy to cause the reversal of the diode characteristic exhibited by the gap junction synapse by
simply interchanging the three potentials at its terminals. The diode characteristic can be reversed within
microseconds. Under the chemical theory of the neuron, this reversal requires the interchange of
positions between the vesicles of the axon and the receptor sites of the neurites as well as their attaining
functional normality within microseconds. The time requirement is needed to correctly exhibit the diode
reversal property. It is proposed this interchange is impossible via the chemical theory of the neuron and
the chemical theory of the interneuron synapse is invalid.
If one places two of the fundamental neurons of Section 2.2.5 in series, the configuration between the axon
and dendritic conduits appears remarkably similar to that between the dendritic and axonal conduits of either
of the individual neurons. The only difference is the fact that the region between the two juxtaposed
conduits is in contact with the interneural matrix instead of being enclosed by a podaplasm as shown in
Figure 2.4.3-1. If the two conduits are juxtaposed with the necessary spacing, this configuration has the
potential for exhibiting “transistor action.” It is only necessary to provide the required electrolytic
potentials. The nominal junction dimensions are lemma thicknesses, 75 Angstrom and base thickness of 45
Angstrom.
The label neurite has been used instead of the more familiar dendrite to support the general case. A neurite
can be either a dendrite or a podite. The similarity to the conexus within a neuron is not coincidental.
Whether the conduit on the left is labeled an axon or a neurite (or later an axon segment) is a formalism.
The basic electrical configuration of frame A is the same. As seen in frame B, the only potential difference
is in the physical location of the power sources. As will be developed later for the case of long axon
segments, additional power sources may be associated with a single conduit. These additional power
sources, and other chemical transfer activities may be found within the synaptic gap but outside of the 280
Angstrom wide area of the gap junction (discussed below). Another characteristic of a synapse is shown
conceptually in frame C. It is typically biased to form an “active diode,” a three-terminal device wired to act
as a two-terminal device. The pre-synaptic axon is supported by a soma and nucleus as shown. The post
synaptic neurite is supported by a separate soma and nucleus (not shown). Hence, the conexus related to a
synapse is not located within a specific neuron. The electrolytic synapse represents a fundamental
144Ottersen, O. Takumi, Y. et al. (1998) Molecular organization of a type of peripheral glutamate synapse: the
afferent synapse of hair cells in the inner ear Prog Neurbiol vol 54, pp 127-148
145Siegel, J. (1992) Spontaneous synaptic potentials from afferent terminals in the guinea pig cochlea Hear Res
vol 59, pp 85-92
146Pannese, E. (1994) Neurocytology. NY: Thieme, pp 5 & 80-116
147Vardi, N. Morigiwa, K. Wang, Y. Shi, Y-J. & Sterling, P. (1998) Neurochemistry of the mammalian cone
‘synaptic complex’ Vision Res. vol. 38, pp 1359-1369
148Eliasof, S. et. al. (1998) Localization and function of five glutamate transporters cloned from the salamander
retina. Vision Res. vol. 38, pp 1443-1454
202 Neurons & the Nervous System
Figure 2.4.3-1 Overlay of electronic circuitry of a fundamental synapse on its
topography. Note the similarity to figure 2.2.5-2( C). Only the labels have been
changed. The overall synapse lies within the dashed boxes. See text.
physiological unit of the neural system that is extra-neural. Such a conexus typically exhibits an area of
charge concentration on one side of the junction under the electron microscope.
The Neuron 2- 203
By application of appropriate voltages to the plasmas on each side of these juxtaposed cell walls relative to
the material in the space between the walls, transistor action will occur149. .
To achieve this result, the transistor formed is employed in what is conventionally called the common base
configuration. This configuration does not normally exhibit any voltage amplification and the ratio of the
output current to the input current is greater than 0.99. A conexus containing an Activa used in this “gap
junction” role (with a gap of between 40 and 100 Angstrom) will be defined as a Type BS with the S derived
from the name synapse.
Section 2.3 has introduced the problem of selecting the potential(s) associated with each conduit power
supply in order to maintain the required bias conditions for a group of conexuses connected in series. The
potential of the neural matrix is not necessarily uniform throughout this figure. This problem will be
addressed further in Chapters 4 & 6.
When two conduits of separate neurons are brought into close proximity without meeting the above
operational considerations, the situation is just en passant; the conduits do not pass a signal between them.
In some cases, type 2 lemma of two neurons are found in close proximity, separated by a pool of extra-neural
material associated with the electrostenolytic mechanism powering each conduit. This close relationship is
readily identified by electron microscopy where both lemma show a concentration of charge in their type 2
areas. The overall area does not represent a synapse
Within the central nervous system (CNS), 1000 synapses are typically associated with the axon of each
neuron. In the peripheral nervous system (PNS), the number is lower but probably still exceeds 100 on
average, counting both synapses and the specialized Nodes of Ranvier. The number of Nodes of Ranvier is
large but generally less than 100 for any given stage 3 signal projection neuron.
- - -
The style 1 and style 2 synapses cannot be explained under the chemical theory of the neuron; they are
intrinsically liquid crystalline semiconductor devices explainable only under The Electrolytic Theory
of the Neuron . See Section 2.2 and Section 2.3.
The proposition that the synapse is an electrical connection between two neurons does not eliminate the role
of chemistry in the vicinity of the junction. Chemistry is seen to play the same role at the external Activa
found at a synapse that it plays in supporting the internal Activas of the neural system. The main purpose of
these chemicals are two; to provide the source of energy that powers the active device (Section 3.2) and to
act as hormonal neuromodulators to the signaling neurons (Section 2.7.1). Dopamine is a prime example of
a paracrine neuromodulator (Section 3.5.5.4.1)
2.4.3.1 Introduction EDIT
The conditions described above for “transistor action” does not require that the action occur within a single
cell membrane. It can occur between two adjacent cells under the prescribed conditions, i. e:
+ each membrane “system” must be operational; that is the membrane must be of the right
molecular constituency and be contacted on each side by an appropriate electrolyte.
+ the input membrane must be forward biased so as to conduct current relatively easily
and the output membrane must be reverse biased so that it does not easily conduct current.
+ the distance between the adjacent membrane walls must be less than the distance
required for transistor action, i.e., a charge passing through the input membrane will
continue on and pass through the output membrane regardless of the polarity of the output
membrane.
These conditions are easily met at many places within the retina. It appears an Activa can be created at any
point where a cell wall enclosing a region of axoplasm is brought within the appropriate distance of a cell
wall enclosing a region of dendroplasm (and the above electronic conditions are met). There is no
requirement that the cell walls be especially modified to achieve “transistor action” as long as they present
the impedance of a diode. The contact areas can be quite small or can be extended depending on the overall
current carrying capacity required. The synapse between two neurons is the site of an active electrolytic
semiconductor device, an Activa.
149U.S. Patent --Fulton, J. (1998) Active Electrolytic Semiconductor Device
204 Neurons & the Nervous System
Under the above conditions, it is possible for a dendrite to form gap junctions exhibiting “transistor action”
with as many axons as desired. It is only necessary for the dendrite areas of type 2 lemma to “grow” to
within the appropriate gap spacing of similar type 2 lemma of each of the target axons. By this means, the
dendrite collects a current from each axon with a magnitude proportional to the voltage difference between
the axoplasm and the dendroplasm, the area of the contact and the diode characteristic. The total current
collected can then be passed to the axon of this cell through its internal Activa.
2.4.3.2 Recent empirical data
Pannese has provided a recent description of the so-called electrotonic or gap junction that is in excellent
agreement with the above description except for one point150. He describes (this) mode of transmission via a
gap junction as distinguishable “from chemically mediated transmission since (a) it is basically reciprocal, . .
.” (Emphasis added). He gives no reference for this assertion that is in opposition to the position of this
work. Under in-vivo conditions, the transmission mode across a gap junction is asymmetrical to the
point of being unilateral. One of the simplest representation of “transistor action” occurs at such a
junction, and the forward transfer characteristic of the Activa, is that of an electrical diode.
It may be that Pannese collected data under non-operational conditions. If the potentials of the emitter (axon
) and collector (neurite) of a synapse are interchanged, the conexus will operate as an active diode in the
opposite direction. All Activa, and in fact all junction transistors, are reversible in this way.
Pannese provides a long list of the locations of gap or electrotonic junctions within various species of
animals. This type of junction is obviously common (if not, as proposed here dominant) in the neural
system. Pannese also provides a caricature of the possible forms and locations of synapses between neurons
based exclusively on the exterior morphology of the cells. The functional names resulting from that analyses
are a bit fanciful. If the internal cytology of the cells is studied, it is found that all of his designations are
represented by a synapse between an axon conduit and a subsequent neurite conduit in the orthodromic
signal path.
The electron micrograph in his figure VI.1, at about 90,000X, provides an excellent cross-section of a
synapse at high resolution. It clearly demonstrates the bilayer character of each membrane, the close spacing
associated with the liquid crystal lattice of semi-metallic water between the axon and the neurite, and the
variety of inclusions found within the respective plasmas. These inclusions include the reticulum that has
formed a hydraulic delta, similar to that of a river, as it approaches its termination at the surface of the
conduit. His figure VI.2, at 44,000X, is more complex. It shows multiple synapses between four axons and
three neurites (there being no definitive way of determining whether these structures are dendrites or
podites). Some degree of darkening can be seen in the figures at locations where that effect is usually related
to concentrations of electronic charge.
This work has developed the fact that the coupling between neurons (an external coupling) is not
fundamentally different from the coupling between the various internal conduits of a neuron. These internal
coupling include both the Nodes of Ranvier and the previously undefined Activa at the junction of the
dendrites, podites and axon. This section will develop the detailed characteristics of such external couplings,
synapses.
2.4.3.3 The schematic of the electrolytic synapse
While the morphology of the electrolytic synapse is discussed in greater detail in Chapter 5, it is useful to
complete this discussion with a caricature of the fundamental synapse. The literature provides many copies
of a simple concept of the synapse as a chemical interface between two neurons. A more advanced cricature
is shown in Figure 2.4.3-2. Frame A shows an interface with a relatively wide gap easily discernable by
light microscopy and a much narrower gap only observable by electron-microscopy. This gap-junction is
between 50 and 100 Angstrom wide, depending on how the imprecise edges of the lemma are defined.
Frame A of the figure is divided into two major zones. Those activities below the center line related to
signaling, and those above the line related to support functions. While illustrated as asymmetrical, the
functional representation is nominally symmetrical about the center of the gap-junction (cylindrically
symmetrical about the arrow). The overall gap-junction frequently consists of an array of smaller diameter
individual gap-junctions, or unit Activa, described in the next paragraph.
150Pannese, E. (1994) Neurocytology. NY: Thieme Medical Publishers pg. 88-116
The Neuron 2- 205
Figure 2.4.3-2 The electrolytic synapse
showing signaling and support functions.
A; while the support area (above
centerline) includes a variety of
chemicals, these are not involved in
signal transmission. The electrostenolytic
process powering the axoplasm is shown
explicitly below the centerline The cleft
between the two lemma is filled with
solute-free EZ Water. The biasing of the
synapse limits the direction of signal flow
to that of the arrow. B; The schematic of
the three-terminal Activa with a high
impedance in the podalemma circuit. C;
the equivalent “active diode.” See text.
The The electrostenolytic process powering the
axon is shown explicitly. The biasing of the
neurite is not shown because it may take several
forms. Like in the Activa within the neurons, there
is no transfer of ions or molecules between the two
sides of the gap-junction. The gap between the
presynaptic and post synaptic membranes is only
50-100 Angstrom and is filled with an impervious
liquid crystal of semi-metallic water (EZ Water,
Section 2.4.3.6.1).
It is important to note that electron-
microscopists frequently complain, when
preparing a sample of a synapse for
examination by freeze-fracture
techniques, that it is necessary to fully
remove a small amount of water on the
surface of the axolemma to avoid
problems with their vacuum system.
The upper part of frame A shows the presence of a
variety of elements, and many caricatures show a
variety of free chemicals as well in support of
neural operation. In general, the presence of these
element s and chemicals are related to homeostasis
rather than signaling. Although the concentration
of these chemical constituents change slightly with
signal operations, this is a secondary effect due to
electrostenolysis and other local processes.
Although the literature generally equates these
chemical changes to the signaling function and
defines some of the chemicals as
neurotransmitters, this association is not required
in this work.
The lower portion of frame A shows a typical
synaptic junction, or synaptic disk, supporting the
transfer of an electrical signal from an axon on the
left to a neurite on the right. The signal is
unidirectional as indicated by the arrow. The large
open circle is an early representation of the
vesicles associated with the synapse. See below.
2.4.3.3.1 The cytology of the synaptic
disks
From a structural perspective, it is virtually
impossible to maintain a constant spacing between
two parallel membranes as shown in the above
figure. A different fundamental architecture is
needed at the detailed level. The proposed detailed structure is shown in Figure 2.4.3-3. This configuration
solves the structural problem of maintaining planarity and introduces scalability. The size of the overall
synaptic disk depends primarily on the current carrying capacity required of the connection. As indicated in
the previous section, each synapse of the pedicle synaptic complex employs a group of synaptic disks as the
connection between an axon and a neurite (dendrite or podite). Each of these synaptic disks has a diameter
of 0.3-0.5 microns and consists of an array of “unit Activa.” The sizes shown are in Angstrom and these
features can only be resolved by high magnification electron microscopy. The structure can be compared to
that visualized by the group led by Robertson151.
151Zampighi, G. & Robertson, J. (1973) Fine structure of the synaptic discs separated from the goldfish medulla
oblongata. J. Cell Biol. vol. 56, pp92-105
206 Neurons & the Nervous System
Figure 2.4.3-3 Fundamental structure of a
synaptic disk of a photoreceptor pedicel.
Dimensions are in Angstrom. Open
circles are vesicles on each side of the
junction. Upper bifurcated bar is the
axolemma of the photoreceptor cell.
Lower bar is the post synaptic lemma.
Hatched areas are the active regions
between the two lemma. Cutaway shows
the configuration of these active regions.
From Zampighi & Robertson, 1973.
The disks within the gap between the two lemma
are islands of liquid-crystalline EZ Water that are
solute-free zones according to the ETN. .
Groups of unit Activas are frequently observed
forming disk shaped arrays within the gap
junctions of synapses. These arrays should not be
confused with vesicles or gates forming pores in
either of the membranes.
The details of this structure have been addressed
by Vardi et al. (Chapter 5 ). The vesicles shown
along the upper edge by open circles correspond
to those of the previous drawing. They are
connected to the reticulum of the axon through the
synaptic ribbon. A similar row of vesicles is
shown along the bottom edge. In fact, both of
these arrays are two-dimensional as shown in the
cutaway view at lower left. The vesicles place
structural pressure on the two bilayer membranes
so as to establish a fixed spacing between the
membranes. In the regions between the upper and
lower vesicles, this space is so small that only
water molecules can fill it. These molecules
assume an impervious liquid crystalline structure
in these areas known as semi-metallic water.
2.4.3.3.2 The electrolytic synapse as an
“active” diode
Frame B of [Figure 2.4.6-1] shows the synapse schematically as a conexus containing an Activa. The cross-
hatched impedances are complex. The podaplasm impedance is shown as a high resistivity impedance.
Such an impedance insures the Activa is always biased into the conductive region when a signal is applied to
it. As a result, the current out of the Activa is a precise copy of the current into the device.
Frame C of the figure shows the simplified equivalent circuit of such a conexus. Note, whenever the axon of
the junction is positive, this diode is always biased into its conducting mode. As a result, it does not
“rectify” any signal applied at the axoplasm terminal. The signal at its output is a true replica of the signal at
its input. As noted in Section 2.2.2.9, the current transfer efficiency of an Activa is very high, with typical
measured values near 99.5%. While these transfer efficiencies have been measured in the electro-
physiological laboratory, researchers have had difficulty describing the results based on a two-terminal
model. Series resistances as low as 0.01 Ohms have been reported but these values have seldom been
confirmed by independent tests, usually because of differences in laboratory instrumentation. Using a three
terminal model makes the task simple. Rather than speak of a series impedance between the input and output
terminals, the correct representation is to define the current transfer efficiency of the active diode device.
The I-V characteristic of the normal synapse is as shown in Figure 2.4.3-4. When biased to the right of the
zero-crossing, the circuit acts as a thresholding device suppressing noise associated with the quiescent
condition. Under this condition, it can be considered an “Active” diode. It is used in this mode when
summing signals at the input to a signal processing neuron. It is also valuable in the transfer of monopulse
signals between stage 3 signal projection neurons. When biased to the left of the zero-crossing, it acts as a
very high efficiency linear signal transfer device, the conventional analog synapse.
The Neuron 2- 207
2.4.3.4 Powering the electrolytic
synapse
Under static and dynamic conditions, the electrical
potentials of the presynaptic axoplasm and post
synaptic dendro– or poda– plasm is provided by
their respective neurons. This is true for both the
analog and phasic electrolytic synapse.
2.4.3.5 The amino acids as neuro-
facilitator, not neurotransmitter
Efforts to define a chemical substance to be passed
across a synaptic junction, for purposes of
signaling, have a long history within those
investigators with a formal education in chemistry.
They have found it extremely difficult to
characterize a neurotransmitter based on
functionality and performance152. In general,
materials have been defined as neurotransmitters
based on their ubiquity near neurons and their
ability to affect neural actions long term (over
periods measured in seconds or more). There has
been little success in quantifying the amount of a
chemical compound released by an axon and
received by a dendrite.
In recent times, beginning in the 1960's, there has been a concerted effort to coopt the well accepted
conceptual role of the glutamates in energy manipulation and hypothesize the use of these materials as
chemical neurotransmitters153. This effort, in support of a function that is not required based on this work,
has been relentless. Brown has hedged his bets by saying “It is likely that the amino acid used as transmitter
is separated from that used in general metabolic pathways, perhaps by its localization in vesicles.” This
position would seem to leave large amounts of glutamates available on the surface of neurons for
electrostenolytic purposes with a much smaller amount confined within vesicles and possibly in the synaptic
space. One of the finding of this work is that the synaptic space within the gap junction is filled with a liquid
crystalline material, semi-metallic water. The low solubility of any amino acid in this liquid crystalline
material and the laws associated with Brownian Motion in such a narrow space suggest that no chemical
neurotransmitter can migrate across this gap.
This work has developed the role of glutamic acid (glutamate), and its backup aspartic acid (aspartate) as the
principle sources of energy in the neural system in detail (Chapter 3).
2.4.3.6 The gap junction is a barrier to ions EDIT to include EZ Water
The synapse, the junction between the axon of one neuron and the neurite of another has been studied for a
long time via light microscopy. A large mass of literature has evolved based on this imagery and the
presumed chemical nature of the signal transmission across this gap. Unfortunately, this literature has been
largely limited to a conceptual foundation. This foundation has not been able to explain the most basic
features of the synapse; how an electrical potential elicits the release of chemicals by the axon or how the
arrival of a chemical at the dendrite elicits a current in the dendrite or a potential between the dendrite and
the surrounding medium. The details of the synapse recently revealed by the electron microscope did not
play a major role in the development of the above literature.
The micrographs produced by the electron microscope have shown a structure for the synapse that is
drastically different from that portrayed by the light microscope. It not only shows the finer structure that
was never available earlier, it also shows the location of charges in these structures. The imagery shows an
uncanny similarity to the imagery of man-made transistor devices. This resemblance applies both to the
Figure 2.4.3-4 The I-V characteristic of a
synapse as an “active” diode. When
biased to the right of the zero crossing
point, the synapse acts as a thresholding
circuit thereby suppressing noise
associated with the quiescent condition.
Data points from Glowatzki, 2002.
152Mandell, A. Spooner, C. (1968) Psychochemical research studies in man. Science, 27 Dec. vol. 166, pp
1442-1452
153Brown, A. (1991) Nerve Cells and Nervous Systems. NY: Springer-Verlag pg 76
208 Neurons & the Nervous System
dimensions of the structures and to the charge distributions. This imagery provides strong support for the
proposition of this work that the synapse is an active electrolytic semiconductor device based on liquid
crystal technology.
Pappas has provided information supporting the position of this work that large molecules do not cross the
synapse in the gap area154. He performed a series of experiments using “certain marker substance–their
molecular weight must be less than 200–are injected intracellularly into one of several cells connected by
gap junctions.” He then noted, “Immediately afterwards, the marker is seen to pass rapidly into adjacent
cells but not into the intercellular spaces.” [emphasis in the original] The next experiment injected
lanthanum, which he says we know cannot cross the plasma membrane, into the fixative associated with the
cells. He says, “it will still penetrate the gap junction insinuating itself between the 20 Å to 40 Å
extracellular space or gap.” He describes the gap saying, “the electron microscope reveals a hexagonally
arranged mosaic of more-or-less circular areas into which the lanthanum has not penetrated. Several
conclusions can be drawn from these experiments. First, molecules with a molecular weight greater than
400, such as the typical putative neurotransmitter, cannot cross the gap junction. Second, a heavy metal can
diffuse into the gap region but cannot diffuse into the actual liquid crystalline lattices of semi-metallic water
forming the active electrolytic junctions critical to the operation of the Activa present and key to the
electrical transmission of neural signals across the gap. Pappas concludes with “Evidently, then, the gap
junction consists of an array of channels, or pores, passing through the cell membrane.” This work prefers
the designation channels to pores and proposes the channels are electronic in nature and incapable of
transporting heavy ions or molecules.
2.4.3.6.1 Liquid-crystalline water–EZ water
Documentation of the liquid–crystalline form of water has matured during the 21st Century. Dellago, Naor &
Hummer have documented “proton conduction”at 40 times the equivalent conduction in aqueous water155.
When read by a semiconductor specialist rather than a theory–oriented physical chemist, it is clear that they
are actually discussing hole conduction in liquid crystalline water confined within their nanotube, a one-
dimensional situation.
The fact that it is holes and not protons that are involved appears in their initial assertion, “Protons can hop
from one water molecule to the next via a Grotthuss mechanism, resulting in transport of charge defects
rather than individual protons. No water molecules are displaced, and the mobility of an excess proton
along chains of hydrogen bonded water molecules is high.” Their figure 1 also supports their assertion
when viewed from a semiconductor perspective. After discussing the types of potential defects in figure 1,
they note further, “Transport of D and L defects, unlike that of an excess proton, requires reorientation of
water molecules and
hence breaking and formation of hydrogen bonds. Orientational defects should thus have a small
diffusion
constant and could form effective barriers for rapid proton conduction.”
A similar position was taken by Dr. Mae-Wan Ho beginning in 1998156. After discussing the hydrogen bond,
she asserted,
“then a ‘jump’ conduction of positive electricity could, in theory, take place. This involves the positive
charge of the hydrogen nucleus - a proton – passing rapidly down the chain by relay, without the proton
actually moving down the chain. The free proton takes over bonding with the oxygen of the first water
molecule in the chain, creating a second free proton that displaces its neighbor down the chain until the last
proton comes off at the other end [1] (Fig. 1). Jump conduction is faster than ordinary electricity passing
through a metal wire, which involves electrons actually moving, and much, much faster than conduction by
154Pappas, G. (1975) Junctions between cells In Weissmann, G. & Claiborne, R. ed. Cell Membranes;
Biochemistry, Cell Biology & Pathology. NY: HP Publishing Co. Chapter 9, pg 89
155Dellago, C. Naor, M. & Hummer, G. (2003) Proton Transport through Water-Filled Carbon Nanotubes Phys
Rev Letters vol 90(10), pp 105902-1 to 105902-4 See also
156Ho M-W. The Rainbow and The Worm, The Physics or Organisms, 2nd ed., World Scientific, Singapore,
1998; reprinted 2000, 2001, 2003 See also http://www.i-sis.org.uk/liquidCrystallineWater.php and
http://www.i-sis.org.uk/PEZTWC.php for additional citations
The Neuron 2- 209
charged ions diffusing through water. But it needs to have chains of water in a sufficiently ordered state and
protein and membrane surfaces may impose that kind of order on water.”
Doctor Ho also presented an intriguing table experiment to demonstrate the capability of structured water at
room temperature157.
“Two identical beakers are almost filled with water and placed next to each other with the rims touching.
The beakers of water are connected to a power pack and a current is passed through a positive electrode
placed in one beaker and the negative electrode in the other. Instantly, a bridge of water forms between the
beakers, looping over the adjoining rims and connecting the two bodies of water. The beakers are then
moved apart slowly, the water bridge stretches and lengthens, but remains intact, even when the beakers are
separated by a gap of several centimeters158. And furthermore, the water bridge is still passing electricity
from one beaker to the other, like a stiff, transparent cable. There is no doubt that water conducts electricity,
as our readers will be aware. But what makes the water stiffen up to make a bridge?”
The mathematical model explored by Dellago et al. was based on non-ionized water consisting of a chain of
six molecules of water and one molecule of H3O+ within a column of square cross-section, 14.28 Angstrom
on a side representing their nanotube. They defined two lattice defects graphically but did not consider the
presence of H3O+ a lattice defect. They did not discuss the lattice constants of crystalline water, which exists
in a variety of forms. They did not justify their choice of lattice or consider the 3-dimensional case. They
did not discuss the potential of oxygen to support two hydrogen bonds (coordinate bonds) besides the two
covalent bonds simultaneously. In general, the appearance of liquid crystalline water in the neural system
requires three-dimensional mathematical modeling.
Pollack has also reported on new knowledge concerning structured water, liquid crystalline water or what he
likes to call EZ (exclusion zone) water159. Quoting Ho again, “Pollack refers to EZ water as “liquid
crystalline water”, and says it was in fact biologist William Bate Hardy who first suggested almost a hundred
years ago that water molecules at the interface could exist in many layers approaching crystalline order. This
is very much in line with the discovery in my laboratory that organisms and cells are liquid crystalline (The
Rainbow And The Worm), and that water is intrinsic to the liquid crystallinity of organisms.” Figure 2.4.3-
5 shows an important relationship. The presence of a region of liquid crystalline water adjacent to a
hydrophilic (water-loving) gels effectively prevents the presence of any solutes. Figure 1(a) in Zheng et al.,
shows a more extended view with an excluded zone on each side of a gel. Quoting Ho,
“The initial discovery that Pollack and his colleague Zheng Jian-ming reported in 2003160 was that water
forms a massive ‘exclusion zone’ (EZ) next to the surface of hydrophilic (water-loving) gels. The EZ is
so-called because it excludes solutes, i.e., substances dissolved in the water. By putting into the water
solutes large enough to be seen under the microscope, or even with the naked eye, the EZ shows up as a
region completely clear of the solute. Thus, when a suspension of microspheres 0.5 to 2 mm in diameter is
put into a chamber with the gel, a clear zone, free of microspheres soon develops next to the gel and
typically ends up hundreds of microns thick (see Fig. 2). This EZ is stable if undisturbed, for days and
weeks once it is formed.”
157Ho, M-W. (2008) New Age of Water: Liquid Crystalline Water at the Interface Science in Society archive
158https://www.jamesedwardhughes.com/science-essays/liquid-crystalline-water
159Pollack, G. (2001) Cells, Gels and the Engines of Life. Seattle, WA: Ebner & Sons Publishers QH631 .P65
2001 in UCI Library
160Ho, M-W. (2004) Water forms massive exclusion zones. Science in Society vol 23, pp 50-51
210 Neurons & the Nervous System
Again quoting Ho,
“The scientific community greeted the initial
discovery with much scepticism. Interfacial water
– water next to surfaces – is generally recognized
as being restricted in motion, relatively ordered,
and having somewhat different properties from
water existing in the bulk. Using sophisticated
techniques and big machines such as NMR
(nuclear magnetic resonance) X-rays, and more
recently, neutron diffraction, researchers have
found no more than one or two layers that have
altered properties compared to bulk water. But the
EZ is so enormous that at least hundreds of
thousands of layers are involved.”
It is proposed that the lemma of a neuron qualifies
as a gel in the sense that Ho and Dellago et al. are
using the term. Zheng et al. (2003) noted,
“Such large exclusion zones were observed in the
vicinity of many types of surface including
artificial and natural hydrogels, biological tissues,
hydrophilic polymers, monolayers, and
ion-exchange beads, as well as with a variety of
solutes.”
It is further proposed that two lemma separated by a minimum of 100 nanometers up to 200 microns of water
between them will force the water into a three-dimensional liquid crystalline form that excludes virtually any
solute from passing between the two lemma (or through the lemma as in the case of a synapse). See the
words of Pollack in this section and Section 9.4.
Figure 2.4.3-6 shows how ubiquitous the phenomenon of liquid-crystalline water is in nature.
Figure 2.4.3-7 shows another important figure
from Pollack and colleagues161. This figure must
be interpreted carefully. Pollack and colleagues
claim this characterization of EZ water shows it
can be used as a battery. In fact, the measurement
was made with a very high input impedance
voltmeter, essentially an electrometer. The
impedance of the EZ water is so high it can not
provide any significant power as a battery. This
condition is described in any text on
semiconductor theory. In the form shown, the EZ
water forms a step-graded potential in the open-
Figure 2.4.3-5 EZ water is liquid
crystalline. “The EZ is so-called because
it excludes solutes, i.e., substances
dissolved in the water. By putting into the
water solutes large enough to be seen
under the microscope, or even with the
naked eye, the EZ shows up as a region
completely clear of the solute. “From
Pollack, 2003.
Figure 2.4.3-6 Glass rod lifts up stiff EZ
layer at water air interface. The
microspheres can be virtually any solute
that enters solution in water. From
Pollack, 2003.
161Zheng, J-M. Chin, W-C. Khijniak, E. Khijniak, E Jr. & Pollack G. (2006) Surfaces and interfacial water:
evidence that hydrophilic surfaces have long-range impact. Adv Colloid Interface Sci vol 127, pp 19-27.
The Neuron 2- 211
circuit condition162. Later, Pollack extended his experiments to include stimulation of his EZ water by light.
He thereby demonstrated it could be considered a photoelectric energy source but not a battery. It is
incapable of storing electrical energy.
When present in a constrained region between two gel surfaces, there is no net potential due to the EZ water
between those surfaces.
Pollack in his 2013 text (pp 51-63) considered, conceptually, the alternative possibilities in the lattice forms
of EZ Water formed in confined spaces. He did not provide any data.
2.4.3.6.2 Test of solute-free phase in confined EZ water
Zheng et al. noted,
“To test whether indeed the solute-free phase is physically distinct from the solute-containing phase, we first
explored possible differences between exclusion and bulk water through the measurement of potential
gradients. Standard 3 M Kcl-filled tapered glass microelectrodes were used to measure the potential profile
in the vicinity of Nafion and polyacrylic-acid-gel surfaces. A reference electrode was positioned remotely,
while the microelectrode tip was advanced with a motor toward the gel surface. With the probe tip
positioned well beyond the exclusion-zone boundary, the potential difference was zero. As the probe
advanced close enough to the surface, negative potentials began to be registered, their magnitude increasing
with increasing proximity of the surface (Fig. 3a and b). In the case of the polyacrylic acid gel (Fig. 3a), the
magnitude just outside the gel was ~120 mV, and remained steady at that value as the probe advanced inside
the gel. In the case Nafion (Fig. 3b–not shown), the magnitude rose to (negative) 160 mV at the gel surface,
and the profile was altered by the addition of various chloride salts (1 mM). In both situations, non-zero
potentials could be detected rather far from the surface: within ~200 μm in the case of the gel, and often
beyond 1 mm in the case of Nafion.”
Nafion (CAS Number: 66796-30-3) is a sulfonated
tetrafluoroethylene based luoropolymer-copolymer
discovered in the late 1960s by Walther Grot of
DuPont. It is the first of a class of synthetic
polymers with ionic properties which they labeled
ionomers
Zheng et al. reported the time to form the EZ water
in a gel-water mixture in the presence of a solute.
“Microspheres immediately and rapidly translated
away from the edges of the Nafion sheet at ~2
μm/s, leaving an exclusion zone of 600 μm within
~10 min. The width of the zone then increased
more slowly, commonly expanding to ~1 mm
within 1 day. The images shown in the figure were
taken during the early phase of the exclusion
process. The results illustrated in panels c, d and e
(Fig. 1) show that the exclusion process does not
require a gel; only a surface with hydrophilic
moieties is necessary. The apparent hydrophilic
requirement implies that the exclusion zone might
be initiated through hydrogen bonding with the
nucleating surface. This hypothesis was further
tested by exposing microsphere suspensions to
surfaces that are unable to hydrogen bond with
water. No exclusion zones were seen at the
interface between silicon rubber and water. Nor were such zones seen adjacent to various metallic wires,
including copper, stainless steel, gold, and silver.”
Figure 2.4.3-7 Electrical potential
measured at different distances from the
gel surface located at 0. Contrary to
Pollack’s claim, this potential is
associated with a very high impedance
source that cannot be considered a
battery. See text. From Pollack, 2003.
Also from Zheng et al., 2006.
162Millman, J. & Halkias, C. (1972) Integrated Electronics: Analog and digital circuits and systems. NY:
McGraw-Hill pp 43-45 and other citations within that volume.
212 Neurons & the Nervous System
The Zheng et al. paper went on to conjecture on the character of the EZ water without referring to the
accepted semiconductor theory of their materials. They provided a variety of results obtained by different
experimental methods that may be useful to future investigators.
In 2008, Pollack & Chin edited a book resulting from a symposium in Poitiers, France a year earlier163.
Other than the one paper by Pollack & Clegg, the papers define the conventional thinking among
bioscientists at the end of the 20th Century. At the end of their Preface, they make the interesting statement,
“Biology, after all, is little more than applied physics and chemistry. Is it not?” It is not “little more than
the physics and chemistry” of the textbooks of the 20th Century. The neural system of biology, as a
minimum, is based on the Electrolytic Theory of the Neuron expressed in this work (Section 8.1.3). Even
the Pollack & Clegg paper only took small steps in their discussion of unstirred layers, USL, of water and
their exclusion zone water, EZ water. They did not define or describe any new phase diagram for water
associated with their studies. The breadth of the paper was much narrower than their earlier papers in the
21st Century.
2.4.4 First documentation of the PNP Activa in a synapse
The first documentation of the Activa within a neuron as a three-terminal active semiconductor device is
presented in Section 10.2.4 and repeated in Section 17. 6.4. When used as a synapse, the three-terminal
active semiconductor device has the base terminal (connected to the thin layer of EZ-water within the
semiconductor sandwich described below) is usually at the same potential as the output of the synapse (the
postsynaptic potential) to form an “an active diode,” effectively a PN diode.
2.4.4.1 Background–summary of facts leading to a PNP designation
Although not obvious that a sandwich of a type 2 (unsymmetrical) bilayer lemmas separated by a thin layer
of liquid-crystalline water should form an active semiconductor device, the first man-made transistor was
discovered under similar circumstances. It was only after-the-fact that the area of semiconductor physics
blossomed into the major field it is today.
P & N, frequently written as p- & n-, describe a materials excess of voids(P)or electrons (N) in the
crystalline (or liquid-crystalline) lattice over the neutral condition. A PNP sandwich separated by a thin
layer of water describes two asymmetrical bilayer lemma (P) materials separated by a thin layer of water (an
N material). When properly biased electrically, such a sandwich exhibits unique semiconductor
properties, including “transistor action”–the ability to exhibit signal amplification.
It was only after 1980 that the electrical properties of lipid materials fell under intense investigation. Now,
almost every home has a TV screen where a liquid-crystalline lipid forms the image on the screen. These
lipids display limited conductivity, but this high resistivity (the reciprocal of conductivity) is entirely
acceptable at the high impedance level of the neural system.
The properties of a thin layer of water in a confined space was only reported by Pollack following the
opening of the 21st Century (Section 2.4.2). His EZ-water forms a thin liquid-crystalline layer after
excluding all other materials from the confined solution space. This unusual property is enshrined in the
name EZ-water, it is a contraction of Exclusionary Zone-water.
The specific properties of a type 2 phospholipid bilayer lemma can form sandwich separated by a thin layer
of EZ-water constitutes a active biological PNP semiconductor device are developed throughout this work
with foci below and in Section 10.2 and in Section 17.6. The capabilities of this sandwich are described in
Section 2.2, Section 2.3 and Section 9.4.
When used as a three-terminal Activa, the output terminal is usually biased to a positive potential in a NPN
device and a negative potential in a PNP device. All known Activa found in biological neural systems are
PNP devices with their axoplasm biased to a negative potential.
163Pollack, G. & Chin, W-C. (2008) Phase Transitions in Cell Biology. NY: Springer
The Neuron 2- 213
2.4.4.2 The synapse as an active device, an ACTIVA
As developed in Section 10.2.4 and Section 17.6.4, Eccles et al. provided a significant and far ranging text
in 1967164. This text included a variety of electron micrographs based on the use of different “staining
agents.” They cited Herndon165 of 1963. Figures 6 & 7 in that paper showing electron micrographs of
axodendritic and axosomatic synapses on the surface of a Purkinje cell “after perfusion fixation with
buffered osmium tetroxide” stain. He cited a paper by Zetterqvist but the staining information is easier to
find in Brandes, Zetterqvist & Sheldon166. This stain highlighted the line/surface between the presynaptic
and post synaptic surfaces of the synapses. It is proposed that the line constitutes the first documentation of
the central or base region of a PNP Activa. This early documentation provides strong confirmation of the
Electrolytic Theory of the Neuron as an electrolytic device, an active liquid crystalline semiconducting
device. This documentation occurred within less than two decades of the discovery of the solid state
semiconductor, the transistor, by man and not long after the introduction of the RCA EMU 3E electron
microscope. It is not surprising the PN “active diode” and its cousin the PNP Activa was not identified prior
to that time.
Figure 2.4.4-1 reproduces the original Herndon figure 6 accompanied by a higher magnification of the
circled area.
164Eccles, J. Ito, M. & Szentagothai, J. (1967) The Cerebellum as a Neuronal Machine. NY: Springer-Verlag
reprinted 2013
165Herndon, R. (1963) The fine structure of the Purkinje cell J Cell Biol vol 18, pp 167-180
166Brandes, D. Zetterqvist, H. & Sheldon, H. (1956) Histochemical techniques for electron microscopy: alkaline
phosphatase Nature vol 177, No. 4504, pp 382-383
214 Neurons & the Nervous System
The Neuron 2- 215
Figure 2.4.4-1 Electron micrograph showing the base region of the PNP
synapses of a Purkinje cell. See text for original caption and discussion.
Copied from Internet Journal. See original publication for higher resolution
imagery. Bottom; higher magnification image of upper frame. From Herndon,
1963.
216 Neurons & the Nervous System
The original captions for the upper frame (Herndon fig 6) and for the following image (Herndon fig 7) were
as follows,
Figure 6–“Near the center of this micrograph is an axodendritic synapse (circled). The terminal axonal
enlargement, which is above, contains numerous synaptic vesicles, and a mitochondrion is readily seen.
Between the presynaptic (axonal) and postsynaptic (dendritic) membranes, a thin dense line (arrow) can be
seen. At the left is a secondary branch of a Purkinje cell dendrite which contains a mitochondrion at m. The
origin of the dendritic spine making synaptic contact is out of the plane of section. X 42,000.”
Figure 7–“This micrograph shows an axosomatic synapse (circled). Near the center of the figure is the
enlarged synaptic terminal (probably of a basket cell) containing two mitochondria and numerous synaptic
vesicles clustered about the presynaptic membrane. To the left is the Purkinje cell cytoplasm. At the far left,
elements of the Golgi apparatus (G) are seen. Mitochondrion, m; synaptic vesicles, sv. X 40,000.”
The chemical theory of the neuron has a difficult challenge explaining a substantial surface inserted
between the pre and post synaptic membranes of a synapse. On the other hand, the Electrolytic Theory of
the Neuron expects such an element to be in that location; it is expected to be a liquid crystalline form of
water that forms an effective barrier against chemicals crossing the barrier while electronic charges move
freely through it.
The axosomatic synapse of Figure 7 is probably an axopoditic synapse providing an inverted waveform at
the output axon of the Purkinje cell.
2.4.5 The PNPN Diode forming a Storage Unit used in Memory Circuits– Synapse
style 2
Figure 2.4.5-1 displays the structure of the style 2 synapse. The operation of the PNP synapse of style 1
when expanded by the addition of a n-type semiconductor element, thereby forming the four layer PNPN
diode of the style 2 synapse (or cruciform synapse), is described in Section 17.7.2.3. The PNPN structure
can be considered a PNP Activa and a NPN Activa in cascade. The fundamental feature of the PNPN
structure is a discontinuity in its transconductance that results in two stable states, a low impedance state and
a high impedance state. The result is the two states can store one bit of information in a write/read
configuration. When created during morphogenesis, it is in the high impedance state; when stimulated with a
greater than the forward blocking voltage, VFB, it reverts to a stable low impedance condition. This
condition is maintained as long as a sensing signal of less than, VFB, is applied to the package. Thus a
reliable long term two-state memory unit is formed. The operation of this PNPN synapse is discussed in the
context of the full Purkinje neuron in other subsections of Section 17.7.2.
The Neuron 2- 217
Figure 2.4.5-1 The physical arrangement of the electrolytic synapse style 2 in
triplicate along the upper edge of the dendritic branchlet of a Purkinje neuron.
The synapse is of the PNPN type semiconductor as labeled on the right of the
triplet and incorporates the type 2 lemma of the parallel fiber (the presynaptic
element), the liquid crystalline filled cleft, the type 2 lemma of the dendritic
branchlet and the liquid crystalline filling the terminal end of the spine. The rest
of the figure is discussed in Section 17.7.3.2.
The style 1 and style 2 synapses cannot be explained under the chemical theory of the neuron; they are
intrinsically liquid crystalline semiconductor devices explainable only under The Electrolytic Theory
of the Neuron . See Section 2.2 and Section 2.3.
2.4.6 The Chemical or Paracrine Junction– Synapse style 3
The paracrine synapse is the easiest to study; it is the easiest to locate (between a neuron and a myocyte of
striate muscle) and it is typically large (compared to an electrolytic synapse). It is the synapse of the popular
press and introductory biology. While stage 7 neuro-effector neurons release a variety of neuro-effector
substances, it is only the paracrine neuro-effector neurons that do so in a confined space. This chemical
synapse will be developed more completely in Section 2.7.1.2.
A related, semi-endocrine synapse is reported to be used in the amygdala to release dopamine into the CNS
on the brain side of the brain/blood barrier (LeDoux in Section 12.5). Ottoson (page 197) quotes
Baldessarini167 showing dopamine is not released by the amygdala but by the tegmentum and S. nigra of the
midbrain.
167Baldessarini, R. (1979) The pathophysiological basis of tardive dyskinesia Trends Neurosci Volume 2, pp
133–135
218 Neurons & the Nervous System
2.4.7 Morphogenesis of a synapse
Tanaka et al. have discussed the formation of synapses from a very conventional concepts of the chemical
theory of the neuron168. Their use of the term “polarization” refers specifically to the morphological
asymmetry of neurons, not their electrical characteristics.
On their page 2089, they discuss the morphogenesis of a morphological bipolar neuron leading to the
formation of a synapse between the axon of one neuron and the dendrite of the next orthodromic neuron,
“Almost 60% of the multipolar, MP, cells first extend the trailing process (future axon) and then generate a
leading process (future dendrite), whereas ~30% of MP cells first generate a leading process and then extend
the trailing process. The remaining 10% of MP cells form both processes simultaneously. We have recently
proposed a novel model of axon initiation in vivo called the ‘Touch & Go’ model. According to this model,
once a minor neurite of a MP cell ‘touches’ the pioneering axons of early born neurons, it extends rapidly
(‘goes’) and develops into an axon.”
“However, the molecular mechanisms underlying the formation of a leading process in 30% of MP cells are
largely unknown.”
“Neuronal polarization is driven by cytoskeletal organization, primarily through microtubule and actin
dynamics. The stabilization of microtubules is crucial for the axon specification in vitro.”
“In contrast to microtubules, actin filaments are more unstable and dynamic in the growing axon than the
growth cones of minor neurites in vitro. The destabilization of actin filaments by severing proteins such as
cofilin allows microtubules to penetrate into the growth cone, thereby leading to axon specification.
Conversely, myosin II and profilin IIa stabilize actin filaments at the minor neurites to prevent the formation
of multiple axons through interfering with the penetration of microtubules.”
They only briefly address how glia might provide a means of “glial-guided neuronal migration.
Tanaka et al. conclude,
“However, despite intensive study, it is still unclear how neurons generate only one axon and multiple
dendrites. In particular, the molecular mechanisms of global inhibition underlying the maintenance of
neuronal polarity remain elusive, and there may be unknown molecular machinery functioning to prevent the
formation of multiple axons and in turn to induce dendritic outgrowth. One reason for this major gap in our
knowledge is the lack of suitable methodologies for investigating the spatiotemporal regulation of the
signaling molecules responsible for negative-feedback signaling. Future challenges will entail exploring
these issues using advances in imaging technology, genetic model systems and innovative experimental
approaches. Despite our incomplete understanding, the molecular mechanisms identified thus far seem to be
widely used and evolutionarily conserved.”
Tanaka et al. do not address what primary mechanism leads to the formation of a synapse through
juxtaposition of an electrically asymmetrical lemma of an axon (generally associated with a bouton on the
axolemma), and an electrically asymmetrical lemma of a dendrite (generally associated with a bouton on the
dendrite). No consideration of the potential growth of the two boutons toward each other by electrophoretic
means was provided.
2.4.7.1 Potential electrophoretic formation of a synapse EMPTY
The means by which a bouton of an axon of one neuron becomes juxtaposed with a bouton of a dendrite of
an orthodromic neuron remains poorly documented. One suggestion that glia form a channel that is then
filled by an expanding axonal spine and/or a dendritic spine. However, this position only transfers the
question to how glia are formed into a similar channel.
See Sections 2.8.6 & 10.2.6.
168Takano, T. Xu, C. Funahashi, Y. (2015) Neuronal polarization Development vol 142, pp 2088-2093
doi:10.1242/dev.114454
The Neuron 2- 219
With respect to neurons who are already closely spaced, the formation of a synapse supporting memory
formation might be by means of electrophoretic means. No substantial evidence of this approach was found
in the literature.
2.4.7.2 Re-examining the initial connection between neurons
Historically, investigators have been trying to develop a null hypothesis of neurogenesis without employing a
realistic model of the physiology involved. They have not distinguished between myelinated and non-
myelinated neurons or neurons present within the embroyonic stage of development versus the mature stage
of the same animal species.
An alternate approach is to recognize that the initial neurogenesis of the neurons and the definition of the
path between the antidromic and orthodromic terminals of a given neuron occur generally before birth and
generally when the distance between the antidromic and orthodromic terminals are less than two millimeters
apart. This small distance negates needing to consider myelinated neurons and generally associates creation
of a pioneer neuron at a totally different stage of morphogenesis of the host animal. As a result, the
consideration of how a stage 3 neuron extends to a length of up to two meters in adult humans over a period
of twenty years after birth is placed in an entirely different context.
2.4.7.3 Re-examining the initial connection between neurons at the molecular level
The details of the input lemma and the solution between the input and output lemma has recently been a
focus of study. It appears that the solution between the two lemma may consist of EZ Water because the
narrow space involved (Section2.4.3.6). If the Electrolytic Theory of the Neuron is appropriate, it appears
the input lemma and the EZ Water may form a semiconductor PN junction with properties of its own, the
tunneling mechanism (Section 2.2.3.3.5). The operational aspects of the mechanism of tunneling will be
discussed further in Section 2.2.4.1.
2.5 Neural applications of electrotonic, or analog, neurons
The vast majority of the neurons within the neural system receive analog signals via their neurite structures,
manipulate those signals algebraically and distribute the resulting signals via the pedicles of their axons to
multiple orthodromic neurons. This section will address the operation of a variety of neuron types labeled
primarily by their morphological designations to avoid confusion.
Over 95% of the neurons in the human nervous system consists of analog neurons; those neurons that do not
generate “action potentials.” Action potentials are single monopolar, positive going monopulses with pulse
widths of 1.0 to 1.5 msec depending on how their duration is measured. Action potentials may occur in
strings. Phillips169, a significant laboratory investigator in his day, made note of the dominance of analog
neurons in his 1956 paper which included his frustration at his major discovery,
“Potentials from cells of other types have been frequently seen, but have not been systematically
investigated. Particularly interesting were cells which were evidently extremely common, in that in
almost every puncture at least one would be encountered. These showed membrane potentials of -60 to
-90 mV. These were free from oscillations, and no natural action potentials were seen in cases in which a
watch was kept for them for half an hour. The potentials were undisturbed by strong pyramidal shocks.
Single rectangular shocks to the cortex (sent through the 0.5 mm. pore in the watchglass) of strength up
to 2.0 mA, and duration 10.0 msec., and causing movement of a limb, had either no effect, or produced a
few declining sinusoidal oscillations of about 5 mV amplitude. The conspicuous occurrence of such idle
cells in every experiment, in contrast to the disappointing infrequency of successful “ cell impalements, is
a most striking phenomenon. Obviously, the existence of these cells as electrical entities would be
undiscoverable without intracellular recording.”
His Betz cell were clearly called Purkinje neurons beginning at that time. In an equally important statement
related to the last line of the quotation above,
Analog neurons can only be interrogated using intracellular probing and recording techniques!!! They
cannot be evaluated by extraneural probes or extracranial probes. Analog neurons are small and not
identifiable using fMRI, PET and other imaging techniques with current resolutions in the cubic mm range.
169Phillips, G. (1956a) Intracellular records from Betz cells in the cat Quart J exp Physiol vol 41, pp 58-69
220 Neurons & the Nervous System
A voxel of one cubic mm typically contains 4-8 million individual analog neurons. Analog neurons can be
counted using microscopy and electron microscopy. Fox and Barnard170 calculated 2.44 million just granule
cells per cubic mm in the molecular layer of the cerebellum of monkey based on an actual count of 2000
cells in their chosen area. Many other types of neurons were present in this layer. They were using oil
immersion light microscopy. Electron microscopy would raise this value at least marginally. Fox and
Barnard provide an immense amount of histological data on the neurons of the cerebellum as of 1957.
Phillips was a colleague of Granit and Eccles, and in communications with Hodgkin, Cole & others of his
day, yet his definitive finding was not publicized or pursued adequately to this day.
In the following discussion, it will be seen that some of the signals are reversed in polarity as they pass along
the signal path. This functional process frequently eliminates any correlation between the nature of the
signal and the concept of hyper- or de-polarization with respect to the signal at a given point.
2.5.1 Morphologically bipolar cells of Stage 2
The bipolar neuron of the retina is probably the best characterized of all neurons. It is the simplest type of
neuron and has been used as the prototype in Section 2.2. As noted there, the morphologically labeled
monopolar and bipolar neurons are functionally the same. The position of the nucleus relative to the neurites
and axon is irrelevant. The bipolar neuron has only one input structure, a dendrite, connected to the emitter
of the Activa within it. While this dendrite may be highly ramified in support of well over 1000 synapses in
some applications, all of the inputs are summed using a diode-based summing network as discussed in
Section 2.3.2.2. The axon structure of the bipolar neuron can also ramify in support of multiple synapses
with orthodromic neurons. However, in some cases, multiple neurites from orthodromic neurons synapse
with pedicles of the axolemma that appear to be integral with the soma just like some of the input synapses.
These are not soma-neuritic synapses, they are functionally axo-neuritic synapses.
2.5.1.1 Topology of the morphologically bipolar cell
The general morphology of the bipolar cell is straight forward although it is sometimes difficult for
investigators to definitively describe the end structures associated with the dendrites and axons. The general
cytology and topology of the bipolar cell is shown in detail in Figure 2.5.1-1(a). This figure can help in
understanding the morphology as well as the topology of the cell. The dendritic conduit of the cell is shown
on the left. The wall of the conduit consists of several zones reflecting different types of BLM. Most of the
wall acts as a simple insulator to the flow of all fundamental charges, ions and large molecules. It is
probably made up of a symmetrical bilayer membrane at the molecular level (type 1 lemma). In areas
juxtaposed to various other neurons, the cell wall consists of a zone(s) of asymmetrical bilayer membrane
exhibiting an electrical characteristic typical of a diode (type 2 lemma). The area of this diode is a parameter
controlling the reverse cutoff current of the diode and therefore its impedance. Two active connections to
other neurons are shown as well as one potential or failed connection. Also shown is a zone of the BLM
associated with the electrostenolytic process establishing the quiescent potential of the dendroplasm with
respect to the surrounding matrix. Finally a zone is shown where the dendritic conduit is juxtaposed to the
axon conduit. This juxtaposition comprises the Activa within the neuron. The axon conduit is shown to
consist of a similar set of zones of BLM. The majority of the BLM is probably symmetrical at the molecular
level and an insulator. One area is shown supporting an electrostenolytic function for biasing the axoplasm.
Two areas are shown as connecting to following neurons via synapses..
The electrostenolytic power supply of the axon is well characterized as discussed in the next Chapter.
The power supply to the dendroplasm is shown as “potential” because the bipolar neuron may be “self-
biasing” in some situation, without requiring an electrostenolytic supply. In that case, the supply shown may
only be a resistive impedance.
The juxtaposition of the two conduits and the associated electrical path to the surrounding matrix through the
podaplasm allows the Activa to function as an active electrical device when it is properly biased. It appears
from the literature that, in the bipolar neuron, the base connection of the internal Activa is connected to the
surrounding fluid environment via a low impedance path. This condition removes internal feedback as a
factor in the operation of the bipolar neuron. However, the poditic electrostenolytic process may be
important in establishing the overall bias structure of the neuron. The dendrite is seen to exhibit one or more
input sectors along its surface and it is conceivable that in certain physical locations the surface of the
170Fox, C. & Barnard, J. (1957) a Quantitative Study of the Purkinje Cell Dendritic Branchlets and Their
Relationship to Afferent Fibres J Anat vol 91(part 3), pp 299-313
The Neuron 2- 221
Figure 2.5.1-1 The topology of the bipolar cell. (A); the topology showing the
interface with the surrounding circuits. (B); the schematic circuit of the bipolar
cell. See text.
dendrite forms a continuous proto-Activa providing synapses anywhere along its length. Such a continuous
or quasi-continuous surface is found among the stage 1 sensory neurons.
2.5.1.2 The Electrolytic Circuit
Figure 2.5.1-1(b) shows the electrical circuit of this cell. This circuit is a non-inverting current repeater for
all input signals. The current delivered by the collector into the axoplasm is essentially identical to the
current entering the emitter of the Activa. However, the delivered current may be at a higher impedance
level, thereby providing power gain.
In the absence of input current, the circuit of the bipolar neuron is usually biased near cutoff by the various
batteries and electrostenolytic processes involved. The axoplasm is therefor at its highest potential under
quiescent conditions, i. e. fully polarized. Upon the application of a signal, the axoplasm becomes
depolarized, the voltage relative to the interneural matrix drops.
The establishment of the quiescent potential between the emitter and the base of the Activa within the
bipolar neuron is highly dependent on its associated neurons (as it is in any direct coupled system).
222 Neurons & the Nervous System
In many cases, the bipolar neuron is basically in cutoff in the absence of any input signal (axoplasm potential
near the intrinsic electrostenolytic supply potential). When a signal is received at one or more of its
dendritic synapses, the net current flowing through the synapses makes the emitter more positive relative to
the base and the net signal waveform is reproduced in the collector (axon) circuit.
In some cases, it may be desirable to operate the axon at a lower quiescent potential and some form of
biasing is employed to accomplish this. This may be by means of an electrostenolytic supply associated with
the dendroplasm or the podaplasm.
The Neuron 2- 223
2.5.2 The lateral (differencing) cells of stages 2 through 6
The morphologically designated lateral neuron is the prototype of the differencing amplifiers used widely in
stage 2 signal processing and in stage 4, 5 & 6 where signal manipulation is a primary function. They
exhibit signal inputs to both the emitter and base terminals of the Activa. These inputs frequently involve
highly ramified dendritic and poditic trees. These neuron have frequently been labeled bi-stratified neurons
(see Chapter 5). The poditic tree has frequently been labeled the basal dendritic tree. When there is only
one dendritic and one poditic tree, the neurons are frequently described as pyramid cells. These pyramid
cells can be and frequently are drawn as triangular in two dimensions. When the cells involve more than two
poditic trees radiating from a disk perpendicular to an axis defined by the root of the dendritic tree and the
root of the axon, they are generally described morphologically as stellate (star-like) neurons.
Other common morphological names for neurons of this functional type are horizontal neurons (in the retina
particularly), amercine (axonless) neurons and sometimes interplexiform neurons. These variations in
morphological names are due more to packaging constraints than to any difference in their functional roles.
They all have an axon formed by an axolemma but the axolemma may not be distinguishable from the
remainder of the neurolemma by optical means. The axon is normally identifiable by electron microscopy,
particularly by the charge distribution along the surface of the neurolemma.
The term interplexiform neuron evolved from studies of the retina at low light microscope magnification
during the 1970's. The retina had been found to contain distinct layers of cell nuclei. The cells associated
with the inner and outer plexiform layers became known as interplexiform neurons in some circles, even
though they were clearly identifiable more specifically as either bipolar, lateral, horizontal or amercine
neurons by other investigators. Thus, interplexiform neuron can be considered a global morphological
designation for either bipolar or lateral functional neurons. No formal definition of this designation could be
found in the literature, except with respect to the plexiform layers.
2.5.2.1 The topography of the lateral cells
The lateral neurons exhibit two independent input structures that are not summed algebraically at the
dendritic input to the Activa. They exhibit two input structures that appear similar to a histologist but enter
the cell at distinctly different locations. One is the conventional dendrite structure normally connected to the
emitter of the Activa. The second neurite, the basal dendrite, pseudo-dendrite or podite, is a similar
structure but it connects to the base structure of the Activa. This characteristic provides a new dimension of
circuit flexibility to the neuron. Shepherd171 shows a good electron-micrograph of a cell of this class which
he credits to his co-workers, Hersch and Peters. Unfortunately, it is imbedded in a surrounding structure
that is not related to the functional aspects of the cell itself. The cell is labeled a pyramidal cell with an
apical dendrite and a basal dendrite (podite) as well as the normal axon hillock and other conventional
structures, Figure 2.5.2-1. The plane of the micrograph does not appear to contain the Activa. However, it
is reasonable to say the dendrite and the axon are separated by structures related to the podite. To
demonstrate the unique functional role of the two arborizations, it is necessary to examine their role in the
cytology of the cell at x50,000 or better under an electron microscope.
171Shepherd, G. (1988) Neurobiology. NY: Oxford University Press pg. 43
224 Neurons & the Nervous System
Figure 2.5.2-1 Electron micrograph of a
pyramid cell. Note the apical dendrite at
the top, the basal dendrite (podite) at
lower right and the axon exiting via the
hillock at the bottom. In Shepherd, 1988,
courtesy of Hersch & Peters.
The above figure can be compared with Figure
2.5.2-2 showing the proposed idealized structure
of the same type of cell at the cytological level
(although at a slightly different orientation).
A key fact is illustrated by this figure: the dendritic
compartment and the dendroplasm extend well
into the interior of this neuron type. As a result,
the morphological designation of a synapse as axo-
somatic refers functionally to an axo-dendritic
synapse. The designation axo-somatic is
meaningless functionally.
The figure is drawn to support the idea of two
distinct areas of poditic input, at E & F. If
location E should be ramified, the figure would
exhibit two poditic trees in the plane of the neuron;
this is the simplest version of the stellate neuron.
The axon of this neuron is not shown in detail.
While the axon may be long and even ramified
near its pedicles, this is not necessary. Many
neurons appear axon-less with their pedicles
located immediately adjacent to the hillock. While
these have been labeled amercine (axon-less)
neurons in the retina, all of the stage 1 sensory
neurons of the auditory modality exhibit this
configuration.
The Neuron 2- 225
Figure 2.5.2-2 The cytological organization
of a pyramid cell. The structure labeled
podite corresponds to the basal dendrite
of the previous figure. The expanded
inset shows the electrical topology of the
active base region separating the
dendritic structure from the axonal
structure in the area of the hillock. A
variety of synapses are shown interfacing
with this cell. Note the synapses labeled
E and F support inverting signal paths.
226 Neurons & the Nervous System
Figure 2.5.2-3 The input topography of a
typical differencing (lateral) cell, as
typified by the neurites of a small bi-
stratified ganglion cell. The cell has two
arborizations which ramify in the inner
and outer plexiform layers respectively.
One arbor is the poditic (inverting) input.
The other is the dendritic (non inverting)
input. From Dacey & Lee, 1994.
2.5.2.1.1 The typical input structure of signal differencing neurons
Many terms used in the study of the neuron have a long legacy in morphology. Often, these terms are not
well suited to the functional description related to specific classes of neurons. This is a particular problem
concerning the various lateral cells found in the signal processing of the retina. Figure 2.5.2-3 develops the
bi-stratified topography of these cells as currently understood.
The differencing mechanism used in neurons
appears to be the same in the horizontal, amercine
and ganglion cells. The electrophysiology of this
mechanism will be addressed in more detail in
Chapters 9 and 13. The signals are all
electrotonic. However, the topography is unique.
It consists of two separate neurite arborizations.
The dendritic arbor collects the signals to be
summed by the cell without polarity inversion.
The poditic arbor collects the signals to be
subtracted from the signals collected by the
dendritic arbor. The detailed topography of these
two arbors is determined by the algorithm
employed by the particular cell. This algorithm
may be aimed at a variety of types of signal
manipulation. These include forming the
chrominance and polarization signals of the
signaling system, performing signal correlation in
the POSS and both temporal and spatial diversity
encoding.
In all of the above applications, the gross
topography of the cell looks the same. There may
be a small difference in the topography of the
soma of the ganglion cells because of the added
capacitance required by the circuit.
In the horizontal, amercine cells, the output
remains electrotonic. However, in the ganglion
cells, the output is phasic as required by their role
as the encoders for the signal projection stage of
the neural system, stage 3.
The inner dendritic tree (presumably the poditic tree) has sometimes been labeled the pseudo dendrite. It is
a distinct morphological and electophysiological element in its own right. It can frequently be identified by
its entry into the “side” of the soma. When ramified as here, it collects signals and provides the inverting
input to any neuron.
2.5.2.1.2 The electrolytic circuit of the lateral neuron
Figure 2.5.2-4(a) illustrates the basic topological design of the lateral neuron. It is similar to a bipolar cell
except the poda region is expanded and includes signal input points. Thus, the podal region has taken on the
same cytological and morphological characteristics as the dendritic portion. The cell frequently appears in
the literature to have two independent dendritic trees which will be differentiated here by describing them as
the dendritic tree and the poditic tree.
The features of the neuron related to the electrostenolytic power supplies are the same as for the bipolar
neuron.
Figure 2.5.2-4(b) presents the circuit diagram of a nominal Lateral Signal Processing Cell. Only its poditic
compartment is modified from the physical configuration of the Bipolar Cell. The main circuit difference
consists of the poditic conduit providing a signal connection on the surface of the podalemma to the base
terminal of the Activa. The functional difference is much greater than the physical difference for a number
of reasons. Whereas the poda impedance in the bipolar neuron is of negligible value and significance, it
plays a significant role in the lateral cell:
The Neuron 2- 227
Figure 2.5.2-4 Topology and circuit diagram of the lateral cell. (A); the topology
of the cell. (B); the circuit diagram of the lateral signal processing cell.
+ The presence of a significant resistive component in the poda impedance introduces negative feedback into
the circuit with respect to any signal applied to the emitter terminal. This feedback normally introduces a
loss in amplification with respect to the input signal at the base terminal over what would otherwise be
obtained.
228 Neurons & the Nervous System
+ The presence of a significant poda impedance allows a signal to be introduced into the base terminal of the
Activa. This alternate input signal can be derived from a voltage divider network between the poda
impedance and the source impedance of this alternate signal. Although this signal does not suffer from any
diminution due to negative feedback, it may be suffer degeneration due to the ratio of the base input
impedance and the emitter input source impedance.
+ The signal introduced through the base terminal is in phase opposition to any signal introduced via the
emitter terminal, e. g., the net output is the difference between these two input signals.
The overall performance of this circuit is highly dependent upon the impedances found in the various circuit
elements, the bias voltages applied and the recognition that the Activas involved are typically operating
under large signal conditions.
2.5.2.3 Operation of the lateral neurons
The fundamental role of the lateral neurons is to perform analog subtraction between two input signals. If
the neurites of the lateral cells exhibit complex arborizations, the signals due to the multiple connections
with preceding cells will be summed within the respective neurite plasma before participating in the signal
subtraction of the lateral cells. As discussed above, the precise value of the output potential of the axoplasm
is complicated because it involves so many circuit variables. However, within the operating range of the
circuit, the output is essentially the algebraic difference between the amplitude of the dendritic signal
amplitude and the poditic signal amplitude, each modified by a fixed coefficient. As best determined from
the literature, it appears that these coefficients provide equal weighting to the aggregated signals from each
neurite
The axoplasm potential represents the difference between the sum of the inputs to each neurite.
The lateral neurons are normally biased to effectuate a nominal quiescent collector current. This results in a
quiescent collector (axoplasm) potential that is near the middle of the operating range of the collector. This
allows the collector potential to rise or fall depending on the net current through the Activa in response to the
differencing process carried out between its emitter and base input circuits.
2.5.3 The sensory neurons of stage 1
The sensory neurons are responsible for the collection of stimuli from the environment and transducing those
stimuli into an electrical signal that can be processed further. The sensory neurons explored to date all
exhibit a generic circuit topology preceded by a particular receptor mechanism characteristic of the sensory
modality. They all exhibit an important feature not found among other analog neurons, the ability to
electrolytically amplify an initial low level signal resulting from transduction. They accomplish this be
introducing a different conexus configuration employing the Activa defined earlier.
2.5.3.1 The functional properties of the generic stage 1 neuron
Figure 2.5.3-1 shows the development of the sensory neuron from the fundamental neuron of Section 2.2.5.
To develop this generic neuron type, portions of the reticular lemma enclosing the space normally labeled
the reticulum are transformed into type 2 lemma. These areas are brought into juxtaposition with similar
areas of type 2 lemma of the dendrolemma. When electrolytically biased, each of these areas forms a
conexus containing an Activa of the type defined earlier (frame A). The other features of the neuron remain
the same as in the fundamental neuron. Frame B shows one conexus in greater detail (shaded area). It
consists of an Activa on the right supported by an additional area of type 2 lemma on the left connected to a
receptor. This receptor is responsible for the actual transduction mechanism. This mechanism creates an
electrical potential that is passed through the type 2 lemma and horizontally in the medium between the two
lemma where it is applied to the Activa. The current passing through this Activa is passed into the
dendroplasm and delivered to the original conexus of the neuron. Frame C shows the schematic for two
conexuses delivering current to the original conexus. The key feature of this type conexus is that the input
signal is applied to the base terminal of the first Activa (as for the inverting signal in the lateral neuron
described in Section 2.5.2).
The Neuron 2- 229
Figure 2.5.3-1 Generic sensory neuron cytology and schematics. A; cytology
showing the reticulum and dendrolemma forming multiple receptor sites. E.S.;
electrostenolytic supply. B; detail showing the regins of type 2 lemma (shaded)
forming an active conexus. All other lemma is type 1. Current through the new
conexus feeds into the existing conexus. C; schematic showing multiple new
conexuses connected electrically to the existing conexus. See text.
230 Neurons & the Nervous System
The operation of the electrostenolytic power supply is addressed comprehensively in Section 3.2. The
process involves an unsymmetrical bilayer lemma of Type 2 (Section 2.1.4.2.1) with the reaction of
glutamate–> GABA+ CO2 plus the injection of an electron into the plasma of the neuron, opposite the
location of the electrostenolytic process on the outside of the lemma (Section 3.2.2).
2.5.3.2 The gain mechanism in a sensory neuron
A major feature of transistor action is the deterministic division of current flowing between its terminals.
Section 2.2.2 noted that the current at the axon terminal was typically greater than 98% of the current
flowing into the dendritic terminal. The equation is a precise one, and is usually written as;
IC = ICO – IE and IB = (1– )IE
where IC is the total collector (axon) current, ICO is the collector current absent any emitter current, IE. and
alpha is defined as the fraction of the emitter current that travels across the Activa to the collector. The base
current is IB.
Using Kirchoff’s current law for a three terminal device;
IB = – (IC + IE)
and combining these two equations leads to an important result;
IC = IB/(1– ) + ICO/(1– )
In a high quality device, the second term is negligible compared to the first and;
IC = IB/(1– = IB
Under the assumption of negligible ICO, the emitter current is also very nearly equal to the collector current.
For an alpha of 0.995, beta is 199 and the change in collector current is 199 times the. change in the base
current of the Activa. This is the source of amplification within the sensory neurons of the neural system.
Beta is labeled the amplification factor in common emitter connected Activa circuits like those of the sensory
neurons. For individual receptors with large capture cross-section or multiple sensory conexuses feeding
into one common output conexus, the change in output current at the axon of the second conexus can be
considerable.
2.5.3.3 The conventional sensory neuron schematic
Figure 2.5.3-2 shows the electrical circuit of the sensory neuron in conventional electrical terms. It is shown
without detailing the input structure associated with the sensory receptor which is modality specific. The
potential of multiple conexus circuits to the left is indicated only by the dashed line. The circuit is
immediately recognized as the common differential pair found in a profusion of electronics circuits.
However, in this application it is an asymmetrical differential pair, a very important specialization. The two
Activa are not matched and generally exhibit different operating characteristics. The impedances shown are
all complex and generally include both capacitor and diode elements. Impedances ZA1 and ZA2 also differ.
The impedance, ZA1, is of particular importance because it defines the dynamics of the left or first conexus of
the differential pair. This impedance causes the effective amplification factor of the circuit to vary from a
maximum of beta as a function of time and input current, by varying the average potential applied to the
collector terminal of the Activa. This is the most prominent property of this conexus and leads to its labeling
as the adaptation amplifier of the differential pair. This adaptability plays a major role in the instantaneous
sensitivity of the organism to most stimuli, regardless of the sensory modality. The impedance, ZA2, plays a
different role. It is designed to minimize the output impedance of the second conexus insuring the potential,
Vout, is stable regardless of the number of orthodromic neurons synapsing with the sensory neuron. This
conexus is labeled the distribution amplifier of the differential pair. The impedance, ZP, is designed to
control the quiescent axoplasm potential of the distribution amplifier. These two amplifiers, the high
amplification factor adaptation amplifier and the unity gain distribution amplifier are found in all stage 1
sensory neurons. While the role of the impedance, ZD, is important in the sensory neurons of some sensory
modalities, that importance will be discussed in Chapter 8.
The Neuron 2- 231
Figure 2.5.3-2 Circuit diagram of generic
sensory neuron. The left conexus can be
replicated as suggested by the dashed
line, or considered an equivalent conexus
representing the sum of these circuits.
The interneural matrix provides a common
“ground” for all sensory neurons. See
text.
i( ),,,,F t j
..
.
.
F
( )1
.
.
F
e
.
.
j KT
1
F
1
6
e
.
.
.
F t KTe
.
KT
t
Figure 2.5.3-3 The complete impulse solution to the E/D Equation for the transduction
process in any sensory receptor for F 1.000
2.5.3.4 The excitation/de-excitation
mechanism of sensory neurons–sources
The excitation/de-excitation (E/D) mechanism has
been studied in detail for the visual, auditory, taste
and smell modalities and is believed to be common
to all sensory modalities. For the complete
derivation of the excitation/de-excitation equation
applicable to stage 1 sensory neurons, see Section
7.2 of “Processes in Biological Vision172” for the
visual modality, where the expression
photoexcitation/de-excitation is used in place of
E/D. For the auditory modality, see Section 5.4 of
“Processes in Biological Hearing173.” For the
gustatory modality (taste), see Section8.5 in
“Processes in Biological Taste174.” Similarly, for
the olfactory modality (smell), see Section 8.6 in
Processes in Biological Smell175.”
2.5.3.5 The E/D mechanism of sensory
neurons–general case
The solution of this equation is the Complete
Excitation/De-excitation (E/D) Equation (derived
in Section 8.10) given by;
In the complete impulse solution to the E/D Equation for F 1.000, i is the current generated by the
piezoelectric process within the cilium, F is the applied stress, is the quiescent sensitivity coefficient, is
the time constant of the net cross link replacement process, t is time, j is the imaginary vector, and KT =
102 e (–T/8).
This equation has been found to apply to any sensory neuron involving a quantum-mechanical mechanism.
All biological sensory modalities involve such a mechanism (where the process of breading a chemical bond
constitutes a quantum-mechanical process.
172Fulton, J. (2004) http://neuronresearch.net/vision/pdf/7Dynamics.pdf#page=29 Section 7.2
173Fulton, J. (2008) http://neuronresearch.net/hearing/pdf/5Generation.pdf#page=40 Section 5.4
174Fulton, J. (2012) http://neuronresearch.net/neuron/pdf/8SignalGenerationPt1.pdf Section 8.5
175Fulton, J. (2012) http://neuronresearch.net/neuronpdf/8SignalGenerationPt2.pdf Section 8.6
232 Neurons & the Nervous System
The ratio of the terms prior to the first exponential is defined as the scale factor of the equation.
The first exponential term contains the imaginary operator, j. It is a pure delay that is intrinsic to the
transduction process ahead of the first amplifier circuit of the sensory neuron. It arises between the initial
stimulation and the initial response of the piezoelectric mechanism. This term has not been accounted for in
most hearing data. It is common to show the relative response starting simultaneously with the stimulus
because of the frequent unmeasured delays associated with the distance between the point of stimulation and
the point of measurement.
The values of 102 and 8 in the expression for KT were derived from the visual responses of a variety of
exothermic animals. It is related to the range of temperature compatible with life. This range is roughly zero
to 40 C. Little equivalent data is available for hearing. Corey & Hudspeth have presented limited data for
the saccules of the bullfrog that might suggest different values for the mechanoreceptors176. Their data is
based on step-response instead of impulse-response experiments. Further experiment is required in this area.
The product of F is critically important in this equation. It causes the time constant in the first
exponential within the brackets to be a function of the applied stimulus and the state of the polymer bundle.
It also causes the overall coefficient to be a complicated function of the stimulus and the state of the polymer
bundle. For the condition, F = 1.000, the solution to the differential equation is quite different. It is
given in a following section.
The term in brackets in the above equation has recently been called a double Boltzmann function in the
hearing literature because of the two exponential terms that they look upon as simple time constants. They
associate the honorarium Boltzmann with a simple exponential decay function with time as the primary
argument. However, the function is more complex than those writers anticipated. The first term is a
function of several variables that can change the total response significantly. Both terms are a function of
temperature. The difference between these two terms forms the apparent decay function in the E/D
Equation. This difference cannot be approximated by a simple exponential function.
Figure 2.5.3-4 illustrates the complete impulse solution to the E/D Equation using two different abscissas.
Both frames assume a decay time constant of 12.5 ms. The products of F are given in reciprocal seconds.
The upper frame shows the shapes of the responses in greater detail. The lower frame shows the intrinsic
delays associated with each response more clearly. The response at the Hodgkin condition is shown by the
dashed line in both figures (See next paragraph).
176Corey, D. & Hudspeth, A. (1983) Kinetics of the receptor current in bullfrog saccular hair cells J Neurosci
vol 3(5), pp 962-976
The Neuron 2- 233
Figure 2.5.3-4 The complete impulse
solution to the E/D Equation presented at
two different scales. Both frames show
the complete solutions, including the
intrinsic time delays. The decay time
constant is 12.5 ms. No noise or band
limiting is present. All curves depart from
the baseline as first order responses. The
dashed line is the degenerate or Hodgkin
Condition, F = 1.00. The curves are
drawn for 37 Celsius and KF = 30. The
time to peak response is clearly the sum
of the intrinsic delay plus the rise time.
234 Neurons & the Nervous System
2.5.3.6 The E/D mechanism of sensory neurons–Hodgkin Condition
The E/D Equation exhibits a discontinuity at F = 1.000. However, it is mathematically well behaved.
Thus, the function can be evaluated at this point by taking its derivative. The resulting equation is
considerably simpler. It is Poisson’s Equation of the second order. This is the equation used (but not
derived) by Hodgkin in the 1960's in an attempt to describe the responses of the photoreceptors of the turtle.
It only applied at one intensity of excitation (that was not used in the Hodgkin & Huxley model).
For F = 1.00, L’Hospital’s Rule must be applied to solve the overall differential equation of the E/D
Process. Interestingly, the solution is simpler and only involves one exponential in the amplitude term. The
absolute delay term is also simpler and the scale factor disappears.
The following equation represents the complete solution at the singularity.
Eq. 2.5.3-2
where is the same intrinsic time constant of the de-excitation process found in the complete equation. KT
remains the thermal coefficient modifying that time constant as a function of temperature. The imaginary
term, describing the physiological latency of the circuit, remains well behaved. The amplitude term is
recognizable as the equation of Poisson’s Distribution of the second kind. The only variable is the time, t.
The peak amplitude of the response always occurs at the same time following the appropriate delay.
The general E/D equation can be reduced to the Hodgkin Condition and then be further reduced to the so-
called alpha function, used in the software program known as NEURON described by Carnevale & Hines177,
by eliminating temperature (by setting KT = 1.000) and setting the delay term to 1.000 (equivalent to their
limiting t to t tact).
Hodgkin first proposed the real part of this mathematical form as the general solution to the E/D Process in
1964. However, he could not fit this equation to most of the data without adopting a piecewise approach.
As shown above, the Poisson Distribution is a special case of the general solution. This special case, for
•F• equal to 1.00, has been previously labeled the Hodgkin Condition by this author.
A set of templates can be prepared for the Hodgkin Condition and different time constants. After overlaying
the templates on the experimental data, the curve best fitting the Hodgkin Condition is easily identified.
Finding the time constants and other factors in the general solution describing other responses is then
straightforward.
2.5.3.7 The E/D mechanism in parametric stimulation
The general E/D mechanism and equation appear to describe the typical operation of all neurons (except
those described separately for the visceral neurons) under parametric stimulation with the possible exception
of some of the delay parameters. The general shape of the predicted E/D response appears to fit the reported
data for the nominal neuron found in the literature quite well.
2.6 The pulse (phasic) and hybrid signaling neurons
Before continuing the discussion, it is important to recognize that phasic, or pulse, generating neurons are a
minority in the neural system of animals. They are estimated to consist of only 5% of all neurons in a given
mammalian neural system. The other 95% are analog neurons discussed in detail in Section 2.5. Phillips178,
177Carnevale, N. & Hines, M. (2006) The NEURON Book. NY: Cambridge Univ Press page 4
178Phillips, G. (1956a) Intracellular records from Betz cells in the cat Quart J exp Physiol vol 41, pp 58-69
The Neuron 2- 235
a significant laboratory investigator in his day, made note of the dominance of analog neurons in his 1956
paper which included his frustration at his major discovery
“Potentials from cells of other types have been frequently seen, but have not been systematically
investigated. Particularly interesting were cells which were evidently extremely common, in that in
almost every puncture at least one would be encountered. These showed membrane potentials of -60 to
-90 mV. These were free from oscillations, and no natural action potentials were seen in cases in which a
watch was kept for them for half an hour. The potentials were undisturbed by strong pyramidal shocks.
Single rectangular shocks to the cortex (sent through the 0.5 mm. pore in the watchglass) of strength up
to 2.0 mA, and duration 10.0 msec., and causing movement of a limb, had either no effect, or produced a
few declining sinusoidal oscillations of about 5 mV amplitude. The conspicuous occurrence of such idle
cells in every experiment, in contrast to the disappointing infrequency of successful Betz cell
impalements, is a most striking phenomenon. Obviously, the existence of these cells as electrical entities
would be undiscoverable without intracellular recording.”
As indicated by the last line above, analog neurons are essentially quiet, even in living tissue. On the other
hand, they are the dominant form of stage 2 signal processing and stage 4 information extraction neurons
within the neural system. They are also the dominant neuron form in stage 1 signal generation and stage 5
cognition neurons. See Section 1.1.5 for the definition and description of the above stages. Analog neurons
can only be interrogated using intracellular probing and recording techniques!!!
In the past, the conventional wisdom was that the axon of most neurons consisted of a continuous core with
the signal propagated along the axon in a continuously decaying manner similar to an electrical cable. The
purpose of the Nodes of Ranvier was essentially unknown and the purpose of the myelin sheath was usually
related in vague language to the insulation surrounding an electrical cable. More recently, it has been
recognized that the signal along an axon is regenerated at each Node (with the mode of signal transmission
described as salutatory) and that the axon actually consists of semi-independent regions connected at the
nodes; in the fashion of a string of sausages.
As noted earlier, neurons are capable of acting as monostable or astable oscillators if positive internal
feedback is present. This capability is exploited within the stage 3 circuits of the neural system.
The pulse and hybrid neurons of stage 3 are concerned with the transmission (propagation, not conduction)
of neural signals over distances too great to be accomplished effectively by analog signaling. This class of
“projection neurons” are used throughout the neural system. They are found in afferent signal paths between
the stage 2 of the sensory modalities and the mid-brain, between the mid-brain and the cortex, within the
cortex, and between major engines of the efferent neural system. When these signal paths contain multiple
neurons in parallel, they are known morphologically as commissure within the CNS and as nerves outside of
the CNS.
This section will address the functional types of neurons found within stage 3 projection neurons,
1. the ganglion neuron that accepts an analog signal waveform and creates a pulse stream encoding the
information associated with that analog waveform.
2. the stellite neuron that accepts a stream of one or more action potentials, decodes the pulse stream and
generates a replica of the original analog signal waveform.
To achieve transmission of the information over distances greater than two millimeters, the ganglion neuron
incorporates two unique features.
1. It incorporates a myelin sheath surrounding its extended length axon that fundamentally changes the
character of the signal projected by the neuron.
2. It incorporates a mechanism for regenerating the amplitude of the action potentials without degrading the
encoded pulses (the Node of Ranvier).
Each of these elements will be introduced here but be addressed in detail in Chapter 9. The Node of
Ranvier will be addressed here for completeness. It is functionally a modified electrolytic synapse.
A discussion of the difference between stage 3 action potentials and other pseudo-action potentials will begin
this section.
2.6.1 The Action Potential vs pseudo action potentials EDIT
236 Neurons & the Nervous System
As the neurosciences grew, it was common for investigators to describe any measured waveform recorded
from a neuron as an “action potential,” sometimes including waveforms that are inherently foreign to the in-
vivo system but generated by the test set. It is important to separate the waveforms of essentially fixed pulse
width, generated by stage 3 neurons, from waveforms that exist for indefinite durations, frequently controlled
by the duration of a stimulating source. The narrow monopulse pulses with a pulse width of less than two
milliseconds, and well known thermal characteristics, will be described as action potentials in this work.
They are predominantly found among the mammals. These pulses appear in very complex pulse trains and
individually are not subject to change in characteristics except as a function of temperature. Action
potentials are very similar across mammalian species.
Other waveforms of variable width, and primarily analog in character, are explicitly defined as not action
potentials, but may be called pseudo-action potentials. The neural system exhibits three distinct signaling
waveforms. It also exhibits two analog waveforms related to the cardiac system that are similar to action
potentials and will be described as pseudo-action potentials.
Analog Signaling Waveforms
Stage 1 sensory neurons create an analog signal in response to stimulation that lasts as long as the
stimulation. It is generally described as a “generator waveform.” Its precise form is dictated by the
Excitation/De-excitation Equation of the first amplifier of the sensory neuron, the adaptation
amplifier.
Stage 2 signal processing neurons typically perform summing and differencing operations on
generator waveforms to create an analog “signal waveform.”
Stage 4, 5 & 6 neurons process analog signal waveforms generally received from stage 3 decoding
neurons.
Phasic Signaling Waveforms
Stage 3 encoding neurons (typically ganglion neurons) create the action potentials of the neural
system. As noted, these pulses have very characteristic pulse widths and occur in complex pulse
trains encoding analog information.
Analog Non-signaling Outputs
Stage 7 neurons are neuro-effectors and hybrids. They are similar to stage 3 stellite neurons in that
they accept action potential pulse streams which they decode to produce an analog output.
However, their output are chemical, and include the hormones.
Analog Combined Signaling & Stimulation Waveforms
Stage 8 neurons are unique to the visceral system. They produce pseudo-action potentials that will
be described in Section 2.7.4. They are described as cardiocyte waveforms/potentials in this work.
The width of these waveforms varies with the rate and shape of the stimulating waveform.
This work will use the term action potential only to describe narrow monopulse waveforms (less than two
milliseconds width in mammals at biological temperature) generated within the stage 3 (signal projection)
portion of the neural system.
Research into biological vision has provided a clear picture of the various applications of circuits employing
action potentials. It is necessary to define this phenomenon more precisely at this time. The concept of an
action potential arose from the observation that the axon of many easily accessed neurons exhibited a
uniquely shaped pulse output. While these pulses frequently occurred in groups, the structure of the
groupings were difficult to interpret.
2.6.1.1 The nominal action potential
The action potential found in Chordata has been extensively investigated. It is found to be the fundamental
information carrying medium of stage 3, the signal propagation stage of neural signaling. In this role, action
potentials are found being generated by morphologically identified ganglion and most pyramid cells. The
reason for the introduction of these cells is to provide a more energy efficient method of signal transmission
over long distances. These cells are introduced wherever it is necessary to transmit information more than
about two millimeters within the organism. The individual action potential contains very little information.
The Neuron 2- 237
However, receipt of a single action potential via an intensity type signaling channel does signal the
occurrence of some significant event that is frequently used in the Alarm Mode of stage 4 CNS operations
(Chapter 15).
Groups of action potentials are employed to represent both monopolar (intensity) information and bipolar
(intensity difference) information. Such groups are used to transmit information between analog signal
processing engines of the peripheral sensory and skeleto-muscular systems, and the central nervous system
(the hallmark of a chordate). The action potentials associated with the ganglion cells in Chordata occur in
two similar but distinct forms. The first is the form generated within the hillock of the ganglion cell. The
second is that generated within the Nodes of Ranvier along the length of the ganglion axon (at about 2 mm
intervals). Figure 2.6.1-1 shows a close approximation of this second form179. Schwarz & Eikhof provided
parametrically excited axoplasm potentials for the rat (shown using smooth lines). In a separate paper, the
Schwarz team showed similar data (figure 2A(a) for the parametrically stimulated in-vitro Node of Ranvier
of a human (shown by jagged line in the figure)180.
Parametric excitation means the biological circuit was excited by abnormal means. The axoplasm was
stimulated by direct current injection. The emitter to base potential was only affected indirectly through
capacitive coupling. No direct stimulation of the dendrite (emitter) was employed and neither the
dendroplasm potential nor the emitter to base potential was measured. The significant delays between their
stimulation and the leading edge of the monopulse reflects the time required to raise the emitter from its
quiescent potential to its threshold value, where the feedback factor exceeded 1.0.
Features to note are the distinctly different slopes of the rising and falling edges of the main waveform. The
leading edge is essentially a straight line at this scale (although it is in fact an exponential waveform). The
significant difference in slope between the ascending and descending portions of a monopulse oscillation
waveform is diagnostic for relaxation oscillators based on a common-base Activa within the neuron. The
difference between the slopes of the rising and falling edges of the pulse also suggest a switching action at
the peak of the waveform (a second diagnostic characteristic of relaxation oscillators based on a common-
base Activa). Note also the significant delay between the peak of the output waveform and the peak near
threshold attributed to the parametric stimulus (dashed vertical lines). Transition to pulse formation
occurred at an axoplasm potential of 18.5 mV above quiescence in these waveforms. Schwarz & Eikhof did
not provide data point on their original graphs and only a few neural specimens were documented.
While their human data in figure 2A(a), measured at 25 degrees Centigrade, shows a high degree of
similarity to the rat action potential measured at 20 degrees C, both curves differ significantly from the curve
for 37C.
The modeling by the Schwarz team at 20C using numerical integration of a set of Hodgkin & Huxley
equations required several adjustments from the accepted values in the 1980's and 1990's. They also
encountered “rundown” using a Ringer’s solution. The rundown was probably due to a lack of glutamic acid
in the solution. Note the extended duration of the recharging period in the figure. Such long recharging
intervals significantly affect the refractory period of the neuron and subsequently limit its maximum firing
rate.
Whenever, the temperature of the experiments and subsequent modeling activities related to mammals are
carried out at non-endothermic temperatures, the resultant figures and tabulations must indicate the specific
temperature to which they apply or be labeled pseudo-action potentials. Pseudo-action potentials cannot be
used to reliably represent the physiological situation in endothermic animals (Section 2.6.1.2.3).
Schwarz et al used 20C as the standard temperature for their numerical solution to the H & H equations; that
temperature clearly leads to pseudo-action potentials. They offered that their equations could be modified
using different values of Q10 from a table and references supplied. However such usage rests on the
assumption that the discharging and recharging portions of the action potential are affected by temperature
equally. This assertion appears doubtful from their waveforms and is false based on the analytical solution
to the action potentials provided by the Electrolytic Theory of the Neuron. As seen from the figure, the
overall waveform involves three sectors, the pre-threshold, discharging and recharging sectors. The time
constant of the discharging (leading edge) portion of the waveform is determined by the saturation resistance
of the Activa collector-base circuit and is minimally temperature dependent. The recharging (trailing edge)
179Schwarz, J. & Eikhof, G. (1987) Na currents and action potentials in rat myelinated nerve fibres at 20 and
37 C. Pflugers Archive--European Journal of Physiology. vol. 409, pp. 569-577
180Schwarz, J. Reid, G. & Bostock, H. (1995) Potentials and membrane currents in the human node of Ranvier
Eur J Physiol vol 430, pp 283-292
238 Neurons & the Nervous System
portion is determined by the impedance of the current supply recharging the collector capacitance and is
quite sensitive to temperature.
The initial linear ramp of the axoplasm potential (for the human NoR) during the prethreshold sector was in
response to the integration of the fixed stimulus current flowing through the patch clamp (0.5 ms duration)
onto the axoplasm capacitance formed by the myelinated axolemma.
As usual, the designation of the currents in the Schwarz papers employed the typical chemical euphemisms
and the continuity assumption regarding the actual currents involved (no switching type monopulse oscillator
was recognized although their equations employed binary switching functions).
Ramachandran used the same 2 mm interval as the
maximum length of an axon segment between two
Nodes of Ranvier in 2002 although he did not
recognize the detailed character of the node in his
conceptual Node of Ranvier181.
Action potentials are necessarily limited in pulse
width in order to satisfy the sampling requirements
of information theory. These pulses are fixed in
amplitude and in pulse width. The information
contained in the analog waveforms is now
represented by the time interval between the
pulses. In the biological system, the action
potential pulses are not binary; they are mono-
stable. Their only stable state is at the quiescent
voltage in the absence of any analog stimulation.
The set of partial differential equations of Hodgkin
& Huxley (unsolved) and their followers are not
compatible with a switching phenomenon within
the duration of the action potential waveform. To
avoid this problem, Hodgkin & Huxley select the
applicable differential equation using the auxiliary
parameters labeled, h, m & n (page 518) and then
speak conceptually of early currents, late currents
etc. These parameters are in fact binary switching
functions controlling the applicability of a given
equation as a function of time. Schwarz et al.
continued to use h, m and n to vary the values of
and at arbitrary times corresponding to the times
at which threshold was reached and the identified
switching points. these are the same switching points employed within the Electrolytic Theory of Neuron
operation.
Schwarz and colleagues continued to employ the binary switching parameters, h, m & n in their numerical
integration in order to achieve continuous waveforms that fit the observed data to an arbitrary degree of
accuracy based on fundamentally conceptual initial equations. As the quality of the recorded data has
improved, it has become more and more difficult to use numerical integration to achieve such matches. The
discussions of Schwarz and colleagues reflect this fact with their frequent use of presumptive, as opposed to
explicit, expressions about the actual currents present. By changing to an electrolytic model, the equations
are all deterministic and easily integratable in closed form when required. No approximation techniques,
such as numerical integration, are required.
Figure 2.6.1-2. provides additional detail relating to the astable, or free-running action potential generator,
and the driven action potential generator. The left frame shows an action potential departing from the
transition value abruptly and proceeding to follow a nearly straight line ramp until approaching saturation (3)
at –20 mV. The feedback gain drops abruptly at this point. As a result, input and output circuits become
isolated. The axoplasm potential begins to repolarize along a nominally exponential curve leading to point
(5) as the power supply recharges the axolemma capacitance. Simultaneously, the emitter to base potential,
Figure 2.6.1-1 Measured action potentials
vs temperature for rat & human motor
neurons. The technique used the patch
clamp technique and the waveforms are
therefore parametric in character.
Smooth curves from the rat. The 37C
response was elicited by a 30 sec
current pulse. The 20C response was
elicited by a 100 sec pulse. Rough
curve, actual recording of a stimulated
action potential in-vitro at 25C from
human. Stimulus was 0.5 ms pulse. See
text. Assembled from Schwarz & Eikhof,
1987 & Schwarz et al., 1995
181Ramachandran, V. (2002) Encyclopedia of the Human Brain. San Diegeo, CA: Academic Press
The Neuron 2- 239
Figure 2.6.1-2 Features of action potentials. Rising axoplasm waveforms
assume Activa is acting as a current source charging the axolemma
capacitance. Dashed line in upper waveforms shows the usually
unmeasurable effect of the electrostenolytic supply opposing the current
source. Left; the target bias of the emitter to base potential is positive. The
circuit will generate a monopulse every time the emitter to base potential goes
positive. Right; the target bias of the emitter to base potential is negative.
The circuit will not generate a monopulse until an external stimulation raises
this potential into the positive region. See text for detailed discussion.
which has been driven negative by the feedback voltage across the poda impedance, begins to increase
exponentially from its power source(s) and impedances. Its target potential is a positive steady-state value.
When this potential becomes sufficiently positive for the Activa to begin conduction and the feedback gain
to become positive (2), the circuit again goes into monopulse oscillation and the axoplasm potential again
departs the transition value abruptly.
The right frame shows the driven-oscillator case. The target voltage of the emitter to base potential, based
on its bias supply, is below the threshold value where the Activa feedback factor reaches a value of 1.0. The
circuit will not oscillate. However, if an external stimulant causes the emitter to base potential to rise above
the threshold value only momentarily, the necessary feedback factor of 1.0 is attained and the circuit will
proceed to generate an action potential as in the above scenario. While the emitter to base potential is
positive but below the threshold level, the Activa will act as a class A amplifier. The axoplasm potential will
track the emitter to base potential in the region between the cutoff potential, Vcut, and the transition potential,
Vtrans, resulting in the small rise in the axoplasm potential before the main ramp begins.
An auxiliary graph is shown of the potential at a distant point on an extended length dendrite to illustrate a
point. It is possible to have a significant delay between stimulation of the dendrite and the beginning of the
axoplasm response due to the low signal transmission velocity along a dendritic tree.
Since the shape and duration of the action potential is determined by the circuit elements, its shape is not
subject to significant change due to changes in the stimulation pulse interval (as it specifically is in the
cardiac system waveforms, Section 2.6.1.2.3).
- - - -
The figure shows the features of the chordate action potential gleaned from the literature and interpreted
using the theory of this work. As indicated, these action potentials occur under two different conditions.
240 Neurons & the Nervous System
They may be generated continuously in the absence of stimulation, or they may be generated individually in
response to stimulation. The two waveforms show a slight difference near the beginning of the output pulse.
Several critical voltage levels are associated with the operation of both oscillator circuits.
In the absence of instrumentation problems, neither the free-running or the driven oscillators associated with
stage 3 signal projection neurons exhibit any over or undershoot under the formal definition of the term. The
observed signal waveforms, actin potentials, do not extend outside the maximum and minimum potentials
established by the power supply circuits.
The Neuron 2- 241
2.6.1.1.1 The refractory period of a relaxation oscillator
The term refractory period is frequently introduced into introductory neuroscience texts with limited
definition. It is obvious from the above figure, the so-called refractory period of a ganglion cell is not a real
or fixed parameter. It is fundamentally, the interval between event 3 and event 2 in that figure. During this
period, the emitter to base potential is more negative than the threshold potential. To force the neuron into
oscillation during this period, a larger stimulus than normal will be required. The required amplitude of this
stimulus during the refractory period is given by the difference between the instantaneous emitter to base
potential and the threshold potential. This amplitude is clearly a variable that can be measured during
parametric stimulation of the neuron.
2.6.1.1.2 The measured nonlinearity of the axon (collector) circuit of the neuron
The following material in this paragraph is based on the more complete analysis of the operation of stage 3A
encoding circuits, the circuits that generate action potentials. This analysis appears in section 7.3 of
“Processes in Biological Hearing” on the Internet by this author (2008). It is also available in many
academic libraries under the title, “Hearing: A 21st Century Paradigm.”
Stampfli182. has provided a very valuable confirmation of the performance of the Activa within each neuron
used to generate action potentials. Figure 2.6.1-3 shows his data. The shapes of the data matches shape of
the curves in Section 2.3.3.2 (frame B) This material is explored in more detail in Section 9.1.1.6.2.
182Stampfli, R. (1969) Dissection of single nerve fibres and measurement of membrane potential changes of
Ranvier Nodes by means of the double air gap method In Passow, H. & Stampfli, R. eds, Laboratory
Techniques in Membrane Biophysics. NY: Springer page 165
242 Neurons & the Nervous System
The striking fact about these two frames of data; They are virtually identical within statistical variation.
They are both stage 3A encoding neurons with the motor response associated with an efferent stage 3 circuit
and the sensory response associated with an afferent stage 3 circuit.
The variation in response related to the concentration of potassium ion within the neuron is largely
irrelevant. Similarly, the concentration of potassium in the Ringer’s solution is also largely irrelevant. The
variation with different resting potential is also largely irrelevant for these static current-voltage
characteristics.
The curves labeled 2.5 mM/L K, are above their dashed lines and do not relate to any negative feedback.
They represent the diode (input) characteristic of the emitter (dendrite) of the Activa within their neuron.
Where these curves merge with the dashed lines, the emitter of the Activa is reverse biased and in cut-off.
Within the cut-off region, the three curves labeled with other values of potassium concentration are all to be
found at the same resting potential.
Reviewing the feedback mechanism creating the negative resistance region of both the Stampfli data and the
theoretical model of Section 7.3.1.2 in of “Processes in Biological Hearing,” it appears that Stampfli was
actually varying the potassium concentration within the podaplasm and its surrounding matrix. It is the
impedance between the base (poditic) terminal of the Activa that determines the degree of feedback and
hence the region of negative resistance to the right of the resting potential, V.
Figure 2.6.1-3 Steady state current-voltage curves of a Node of Ranvier in
Ringer’s solution (2.5 mM/ Liter K) and in high potassium concentrations (40, 80,
117 mM/Liter) for a motor fibre (A) and a sensory fibre (B). The horizontal axis is
20 mV per division. V = resting potential. Note the marginal change in the
vertical scale between the two frames. The dashed lines, representing the zero
internal feedback condition at voltages below V, are nearly parallel when the
vertical axes are equalized. See text. From Stampfli, 1969.
The Neuron 2- 243
On closer reading, it appears Stampfli restricted the abnormal potassium levels to only the exterior of the
poditic portion of his three chamber measuring set, and the interior podaplasm of the same portion of the
neuron. See Section 2.6.1.2.2 for further discussion related to the similar work of Mueller & Rudin.
Noble183 has also provided a generic current–voltage characteristic for “excitable cell membranes” i.e., stage
3A action potential generators (figure 8.1). He does not address how this function is achieved, referring the
reader to the work of Katz of a decade earlier. The figure is in total agreement with the terminology of
electrical engineering discussed in Section 7.3.1.2 for the three-terminal Activa that replaces Katz’s concept
of a two-terminal neuron. Noble has also presented what he described as a current–voltage characteristic for
a simple lipid membrane. It does not exhibit any feedback phenomenon. The curve is that of an excellent
quality diode plotted on linear coordinates. It claims to show a breakdown voltage at about –150 mV in the
reversed-bias third quadrant. It shows a rapidly rising current in the forward-biased first quadrant (until
thermal destruction). His curve terminates at about +70mV.
2.6.1.2 The pseudo-action potentials
The true biological action potential only exhibits the waveform components shown in the previous figure. It
has a very fast exponentially rising edge that is nominally presented as straight in most graphics. It exhibits
switching at the peak of the waveform. Its width is independent of the stimulus repetition rate. And, it is
less than one millisecond wide at 37C. The refractory period following the switching that occurs at the peak
is relatively short– on the order of 1/4 millisecond–and leads to a maximum pulse rate on the order of 500-
600 pulses per second in most mammalian situations.
A pulse believed to be similar to an action potential had been observed in several cephalopods of the Order
Mollusca. Based on this observation, Hodgkin & Huxley investigated the source of the assumed action
potential associated with the giant axon of the squid Loligo. Following their work, Mueller & Rudin
attempted to fabricate synthetic bilayer membranes exhibiting the same properties as those described for the
axolemma of Loligo.
There is considerable difference between the in-vivo chordate action potentials and the in-vitro waveforms
measured and interpreted by Hodgkin & Huxley, Mueller & Rudin and others, generally from non-chordates.
2.6.1.2.1 The pseudo–action potentials of Hodgkin & Huxley
Hodgkin & Huxley obtained a relatively large neuron from a neural engine of a mollusc, Loligo, believed to
control the operation of a large group of muscles involved in swimming (in general, locomotion). They
removed the associated neurons packed closely around the large neuron (and apparently acting as an
alternative to myelination in Chordata). They then removed all neurite tissue from the neuron to pacify its
operation. “Careful cleaning was important since the guard system did not operate satisfactorily if the axon
was left with small nerve fibres attached to it.” They then cut off the region of the nominal axolemma
pedicle, removed the axoplasm and inserted a long cannula into the cylindrical axolemma. The resulting
configuration exhibited little similarity to a functional neuron. Specifically, the electrical properties of the
long cannula were inconsistent with the propagation of electrical signals along the axolemma. They
proceeded to parametrically stimulate the axolemma by applying a depolarizing pulse voltage between the
cannula and the external fluid bath using the voltage clamp technique (not patch clamp technique).
They recorded a wide range of electrical waveforms that do not resemble what are currently considered
action potentials of stage 3 in Chordata, Figure 2.6.1-4 (their Fig. 8, 1952, pg 433). The figure also appears
in Section 6.3.7.3.2. In some cases, the peak voltage amplitude of the stimulus exceeded the peak amplitude
of the putative action potential. In many cases, the waveform hyperpolarized for an interval after the
stimulus and before depolarizing to form the response. Hodgkin repeatedly attempted to fit these curves to a
Poisson Equation. However, he had to adjust the parameters of the Poisson Equation as he varied the
intensity of the stimulation pulse.
183Noble, D. (1975) Physico-chemical properties of ionic channels in excitable membranes In Parsons, D. ed.
Biological Membranes. Oxford: Clarendon Press Chapter 9
244 Neurons & the Nervous System
Interpretation of the waveforms recorded by
Hodgkin & Huxley were limited by the
instrumentation of their day. These limitations
included the use of an excessively bright trace on
their oscilloscope that obscured the change in the
waveform near its peak, the poor compensation for
the stray capacitance introduced by their test probe
and the limited stability of oscilloscopes when
used in the DC mode (when available). Proper
probe compensation is addressed in Stuart, Dodt et
al184., 1993.
The Hodgkin & Huxley waveforms are clearly
pseudo-action potentials at best. They appear to
represent the impulse response of his combined
test article (the passive axolemma of a mutilated
neuron of the squid) and test set to parametric
stimulation in-vitro.
2.6.1.2.2 The pseudo–action potentials
of Mueller & Rudin
Mueller & Rudin, working in the 1960's, used the generic term action potential to describe virtually any
pulse response, whether driven or not and whether related to the nervous system or not. They were working
to emulate a biological membrane through reconstitution from recovered biological material or synthesis
from stock materials. They studied the effect of a wide variety of chemical agents, particularly on their
synthetic membranes. These membranes were generally symmetrical bilayers of single phospholipids
available at the time. The chemical agents centered on Alamithicin and protamine, two relatively small
protein families. They did not specify the precise molecular formulas for these materials, although
alamethicin does contain a carboxyl group. They used the simple Leyden Jar test configuration.
Although they studied their materials from the perspective of exploratory research oriented organic chemists,
it appears they could have simplified their work by looking at the previous work of manufacturing
semiconductor metallurgists (chemists). While they discuss their data from many perspectives, they did not
recognize that many of the membranes they created exhibited the quantum-mechanical tunneling effect well
documented in the manufacture of semiconductor based tunnel (Esaki) diodes ((Section 2.2.3.4). Their
current-voltage data shows the classical form of the tunnel diode with a very low forward band gap, Figure
2.6.1-5, reproduced from Section 8.3.2.1.2 of “Processes in biological Vision.”
Figure 2.6.1-4 Time course of membrane
potential following a short parametric
shock at 23C. Current pulse was
nominally eight microseconds duration.
Labels on left represent shock energy in
milli-micro-coulombs/cm2. From Hodgkin,
Huxley & Katz, 1952.
184Stuart, G. Dodt, H-U. & Sakmann, B. (1993) Patch-clamp recordings from the soma and dendrites of neurons
in brain slices using infrared video microscopy Pflugers Arch vol 423, pp 511-518
The Neuron 2- 245
Figure 2.6.1-5 Current-voltage characteristic of a bilayer of sphingomyelin
prepared from a bath of 2.5% sphingomyelin dissolved in
tocopherol:chloroform:methanol::5:3:2. 0.1 M sodium chloride as the electrolyte
on both sides. The asymmetry is purported to be due to the addition of 10– 7
g/ml of alamethicin to one of the electrolytes. From Mueller & Rudin, 1968.
Figure 2.6.1-6 shows one of their measured characteristics with a conventional load line of electronic circuit
theory added. The curve drawn through the x’s represents their membrane before it was doped with
protamine. The membrane appears to have been an insulator below the breakdown potential of about +70
mV. The curve drawn through the o’s is the result of doping. The effect of doping level is shown in their Fig
1 of their paper in Nature185. The negative peak in the doped membrane response is quite variable in
position when using their preparation technique. However, this sample from that figure is illustrative. They
185Mueller, P. & Rudin, D. (1968) Op. Cit. Nature vol. 217, pg 714
246 Neurons & the Nervous System
Figure 2.6.1-6 The I-V characteristic of the “tunnel (Esaki) diode” membrane of
Mueller & Rudin. Two load lines have been added to the figure. See text.
reported on this or a similar membrane in a contemporaneous article186. They describe their test
configuration in the second paper. They also describe the transient response of their membranes, and most
notably the three stable points in their waveforms. These points are clearly shown in the figure as
intersections with the load line. The figure shows two load lines to illustrate the sensitivity of the results to
this parameter. The 3 x 104 Ohm-cm2 load line is optimized for this membrane. It provides near maximum
dynamic range along both the voltage and current axes while maintaining the three stable points noted by
Mueller & Rudin. Also shown is a higher impedance load line. This load line of 3 x 107 Ohms is still one
order of magnitude lower than the load line of 2 x 108 used by Mueller & Rudin. Their load line is nearly
parallel to the horizontal axis and difficult to see in this figure. While this load line maximizes the voltage
differences in the waveforms, it reduces the stability of those waveforms. The nominal negative resistance,
RM, of their doped membrane was –3,250 Ohms (–32.5 Ohm-cm2)
While Mueller & Rudin have shown that their doped membranes can be driven into oscillation, or even
oscillate on their own (achieved “with some difficulty”), the transient responses of their membranes were
very slow, with rise times of about 50 ms. [As an aside, tunneling occurs at the speed of light within the
material itself. It is the capacitance of the circuit, along with the resistive components present that
186Mueller, P. & Rudin, D. (1968) Op. Cit. J Theor Biol vol. 18, pg 237
The Neuron 2- 247
determines the transient response of the circuit.] By further analysis using the I-V characteristic with a
realistic load line and the known capacitance of the membrane, the transient performance can be described in
detail. The predicted, and separate, exponential rise and fall times are closely related to their test
configuration and show little relevance to the rise times of in-vivo biological action potentials.
While this work finds the data of Mueller & Rudin useful, it does not support their use of a two-terminal
neuron and their explanation of its operation based on a “tunneling mechanism.” A three-terminal neuron
provides a much more realistic operating mechanism.
Mueller & Rudin defined three distinct types of pseudo-action potential when exploring their synthetic
biomolecular membranes. Each is based on a conceptual de-convolution of the observed response into
components. Many of their waveforms involve a significant rectangular pedestal (their resistive action
potential component) underneath a transient component. The transient operation of the circuit described by
the above I–V characteristic and load line show the true nature of the observed responses in-toto. There is
no need to de-convolve the waveforms into arbitrary components to match a putative alternate operation.
Mueller & Rudin employed only potassium chloride on both sides of their membranes (except when
they only used sodium chloride) in their experiments. Their waveforms, though understandable from an
electrical circuit perspective, are bizarre from the perspective of the chemical theory of the neural
system. The waveforms exhibit bistate and tristate stability and responses lasting for the duration of the
pulse excitation. Many pulses lasted longer than one second. These waveforms are clearly not action
potentials as found in the stage 3 neural system.
2.6.1.2.3 The pseudo–action potentials of endotherms in-vitro
The local environmental temperature plays a major role in the formation of action potentials. The
temperature plays a major role in explaining the lethargy of exothermic animals that “sun bath” until mid day
to raise their internal temperature. Endotherms on the other hand have developed internal methods of
maintaining a nominally constant internal temperature.
It is common to perform in-vitro experiments on neural tissue from endothermic animals at other than
normal endothermic temperatures. A majority of the reported action potential measurements and simulations
related to mammals, primates and even humans have been performed at such unrealisitic temperatures. Such
experiments must be considered physiologically irrelevant, or at least highly suspect pseudo-action
potentials.
Solving sets of equations derived from Hodgkin and Huxleys papers on exothermic molluscs using numeric
integration to determine a set of parameter values applicable to endothermic mammals is questionable on its
face. Reporting these sets of values for other than endothermic temperatures is of little physiological value.
As noted earlier, most of the data collected by Schwarz and colleagues et al. would be categorized as
pseudo-action potentials because it was collected at non-endothermic temperatures. This is also true for the
majority of the earlier work cited by those authors.
Smith et al. have provided action potential data for human’s at 37C in Section 9.1.2.3.
2.6.1.2.4 The pseudo–action potentials of the cardiocytes
The cardiac literature frequently uses the term action potential to describe the signals recorded from
myocytes in two different contexts. The nodal signal generator neurons generate a broad but bell-shaped
monopulse waveform. They are distinctly broader (100x) than stage 3 action potentials. The cardiocytes
focused on mechanical contraction operate as analog interneurons with a broad waveform with rapidly rising
and falling edges. While these waveforms are closely associated with the mechanical action of the
cardiocytes, they are best described as stimulation waveforms. They stimulate the release of the calcium
ions that cause contraction. The pulses also exhibit a property not found in stage 3 neurons; they vary in
pulse width as a function of the stimulus interval. . These waveforms will be discussed briefly in Section
2.7.4, and developed in detail in Chapter 20.
2.6.2 The encoding (ganglion) neuron of the PNS, mid-brain & cortex
Ganglion neurons, by whatever name, are found wherever it is necessary to transmit neural signals more than
a few millimeters. They are introduced as a matter of power efficiency at the expense of some time delay.
They typically appear first accepting signals from the stage 2 neurons of a afferent sensory modality. They
appear later accepting signals from stage 4 neurons within the CNS.
248 Neurons & the Nervous System
Rodieck has provided a survey of the morphology of the ganglion cell in the retina and identified five major
varieties including a total of at least 12 types187. Of these varieties, the axons of all “midget” ganglion cell
types are known to project to synapses with parvocellular layers of the lateral geniculate nucleus. Separate
studies indicate that the “parasol” ganglion cells project to synapses with the magnocellular layers. These
paths suggest the functional performance of these two neuron types.
The ganglion cell is a neuron that operates as a relaxation oscillator (Section 2.3.3) to generate action
potentials (Section 2.6.1.1) with pulse intervals that deliver information to the brain. It accomplishes this
with the same morphological, topological and electrical element features as in the Bipolar Cell but it
employs different values of the parameters.
Figure 2.6.2-1 shows the ganglion cell in its typical topology. It is receiving an input directly from one
Bipolar Cell and an input from one Lateral Cell. In practice, the dendritic tree can be highly arborized,
providing many individual inputs. The output is shown connecting directly to a synapse in the lateral
geniculate body of the brain--and possibly to a second location elsewhere in the brain. The axon may be
significantly longer than shown in this figure relative to the dendrite shown. If it exceed two millimeters,
there are two distinctly different situations to be addressed, the introduction of myelination and the
introduction of Nodes of Ranvier..
187Rodieck, R. (1998) The first steps in seeing. Sunderland, MA: Sinauer Associates, pg. 271-291
The Neuron 2- 249
Figure 2.6.2-1 Ganglion cell topology and circuit diagram. (A); the topology of the
ganglion circuit. (B); the electrical schematic of the cell showing a large dendro-
capacitance.
As developed for relaxation oscillators, there are two parameters that are key to the operation of the
Ganglion Cell; the poda impedance and a large capacitance (relative to the ones encountered so far). In the
Ganglion Cell, the poda impedance is so large that it actually distorts the Activa transfer function due to
internal feedback. If this distortion is large enough and the biases are properly arranged, the output
characteristic of the Ganglion Cell will be bimodal (typically a pathological condition within the neural
system). If, in addition, there is a large capacitance shunting either the emitter or the collector terminals of
the Activa, there will be sufficient phase shift related to the feedback to cause the net feedback to be
positive. This positive internal feedback will put the circuit in a position to generate one or more monopulse
oscillations in response to a sufficiently large input signal. If it oscillates continuously, its frequency will be
determined by the time constant of the circuit containing the capacitor and the time constant of the transfer
impedance closest topologically to the capacitor. The figure emphasizes these two features by showing them
explicitly in (b) and implicitly in (a).
250 Neurons & the Nervous System
Figure 2.6.2-2 Pulse to Pulse intervals of ganglion cells as a function of
excitation. The pulse interval of R-channel ganglion cells is indeterminately long
in the absence of excitation. The pulse interval of the P- and Q- channel ganglion
cells exhibits a nominal value of 0.033 seconds (a calculated frequency of 30 Hz.)
in the absence of excitation. It appears that the polarity of the signals applied to
the midget ganglion cells is such that excitation of the short wavelength (S-
channel) and long wavelength (L- channel) photoreceptors tends to drive the
pulse to pulse interval longer. This has a profound impact on the transient after-
effects related to flicker.
Note in (a) that an extended power source sector in the wall of the dendrite will automatically provide a
significant shunt capacitance between the dendroplasm and the interneural plasma. This capacitance is
shown as Cd in (b). A similar result could be obtained in the axon region (not shown). At present, there is no
data in the literature that indicates whether the capacitance needed for action potential generation is in one
location or the other. The resistive component in the poda lead is not as easily shown graphically in (a). The
smaller the sector of the external poda membrane or the longer the poda conduit, the larger the resistive
component of the diode characteristic. Thus Rp is shown explicitly only in (b).
In normal operation, the Ganglion Cell is biased in either of two conditions as shown in [Figure 2.6.1-2]. If
an analog signal in presented to the emitter that causes the emitter to base potential to become more positive,
the free-running oscillator will reduce its pulse-to-pulse interval for the duration of the stimulation in
proportion to the magnitude of the change in stimulation. If the emitter to base potential becomes more
negative, the pulse-to-pulse interval will become longer. Thus, this type of ganglion neuron is able to
produce monopolar output signals that encode bipolar input information. In the case of the driven oscillator,
a positive stimulus will cause a single pulse to be produced. If the stimulus remains positive, additional
pulses will be produced at an interval that is reduced in proportion to the stimulus amplitude. This type of
ganglion neuron can only encode monopolar input information. These modes of operation are illustrated in
Figure 2.6.2-2 as they are encountered in the visual modality of mammals. The two frames show the
transfer functions of the ganglion neurons as a function of their relative input signal potentials.
In the visual modality, the driven oscillators (a.k.a. parasol ganglion neurons) support the monopolar
luminance channels (R-channels) of vision. In the absence of stimulation, they rarely produce any action
potentials. The free-running oscillators (a.k.a midget ganglion neurons) support the bipolar chrominance
channels. These channels include the Q-channel (long wavelength channel minus the mid wavelength
channel). These channels produce a nominal 30 Hertz pulse stream in the absence of stimulation. They are
driven to higher frequency by positive stimulation and to lower frequencies by negative stimulation. The
asymmetry of these characteristics account for many interesting phenomena associated with vision.
In terms of polarization, the action potentials always are positive going with respect to the negative potential
of the axoplasm during the quiescent period of the circuits operating cycle. In this sense they are
depolarizing.
The Neuron 2- 251
In general, the minimum pulse-to-pulse interval for the ganglion neurons appears to be near 0.0066 seconds
(a calculated instantaneous frequency of 150 Hz) and the maximum interval appears to be near 0.33 seconds
(about 3 Hz).
2.6.2.1 Signal input via the poditic conduit
Although not a well-developed situation in the neuroscience literature, there are indications that some
ganglion cells do have arborized poditic conduits that accept signals. These signals would be treated as out-
of-phase with respect to the dendritic inputs. They could therefore subtract from the critical signal amplitude
needed to initiate generation of an action potential. If an exceptionally large signal, it could be considered
inhibitory
2.6.2.2 The introduction of myelin in connection with the axon
As indicated above, a lengthening of the axon of the ganglion neuron relative to the bipolar neuron can
introduce capacitance in shunt with the other impedance elements of the output circuit and lead to oscillation
in the ganglion circuit. However once a critical level of capacitance is reached, additional capacitance is not
desirable. This lumped capacitance requires the Activa to switch more current between the input and output
circuit to achieve the same level of action potential amplitude. To avoid this problem while achieving
maximum axon length, a portion of the axon is wrapped in myelin. This process has the effect of thickening
the dielectric between the axoplasm and the surrounding plasma and thereby lowering the effective
capacitance per unit length of the axon.
As the axolemma necessarily becomes a cylinder as it lengthens, another electrical phenomenon is
introduced. A conducting cylinder surrounded by insulating material or an insulating cylinder surrounded by
conductors introduces an inductance per unit length of the cylinder.
As a result, an extended axolemma contributes two electrical elements that profoundly affect the
performance of a given Activa. The lumped capacitance near the unmyelinated ends of the axon, in
combination with the resistive elements of the collector (axon) circuit directly control the temporal
performance of the axon. The distributed capacitance, in combination with the distributed inductance, both
on a per unit length basis, control the propagation velocity of signals along an extended axon. The
propagation of neural signals is a phenomenon not previously described in neuroscience. The term
propagation is introduced here to differentiate stage 3 neuron signal distribution from the concept of signal
conduction (by chemical diffusion) which is not employed within a long axon. Propagation is a distinctly
different mechanism. It is a key to understanding the operation of the stage 3 neurons (Chapter 9).
2.6.2.3 Waveforms at the poditic terminal before and during pulse generation
Mastronarde has described the waveforms measured at the poditic terminal of a pyramid (encoding) neuron
of the lateral geniculate nucleus using early techniques of the 1960's188. “These extracellular signals are
shown inverted (negative up), as in earlier reports. Each sweep is triggered by a firing of the ganglion cell.
The sweeps from the LGN cell show the two characteristic features of excitatory input described in earlier
dual-recording studies. . . .This deflection, called the S potential, has been interpreted as an extracellular
signal arising from the excitatory postsynaptic potential. Second, spikes from the LGN cell often appear
within a short time after the start of the S potential.”
Bishop and colleagues have provided most of the background and the proposed explanation of the S
potential based on extracellular recordings189. Their data was collected in an early day when sine waves
were used as the baseline timing generator. They were exploring neurons near the surface of the dorsal
nucleus of the LGN in cat. Figure 2.6.2-3(left) shows their basic waveform with its separation into
identifiable but arbitrary segments. Text labels have been added in accordance with the nomenclature of
this work. More explicitly, the S potential is being measured between the contact labeled F and the fluid
surround in Figure 2.6.2-3(right) reproduced from Figure 2.5.2-2 above. The fluid is represented by the
poditic impedance, RP in [Figure 2.6.2-1 ].
188Mastronarde, D. (1987b) Two classes of single-input x-cells in cat lateral geniculate nucleus. II. Retinal
inputs and the generation of receptive-field properties J Neurophysiol vol 57(2), pp 381-413
189 Bishop, P. Burke, W. & Davis, R. (1962) Single unit recording from antidromically activated optic radiation
neurones. J Physiol Lond vol 162, pp 432-450
252 Neurons & the Nervous System
Bishop et al. do not provide a graphic of their experimental configuration. However, their description is
highly consistent with the right frame of this figure. They note their extracellular probe signals are most
identifiable when the probe is near the “soma” rather than the hillock or the myelinated axon. They note the
closer the probe is to the “cell,” the smaller the B component and larger the S–A component. They also note
that the transition from the A representation to the B representation is typically accomplished by changing
the stimulus intensity (as expected within the sub-threshold region of a monopulse oscillator).
The Bishop et al. discussion is totally compatible with a three-terminal pyramid cell (a stage 3A neuron)
within the LGN. It provides excellent confirmation for the Electrolytic Theory of the Neuron. The Bishop
waveforms have never been explained in terms of the chemical theory of the neuron and/or a two-terminal
neuron. It is difficult to ask a question about the source of the S potential or the ratio between the poditic
impedance and the axon load impedance in the context of the chemical theory of the neuron.
The pulse width of the illustrated waveform B is the same as the nominal action potential. Whereas the
typical action potential is on the order of 100 mV positive-going in the axolemma, this waveform is about 5-
8 mV negative-going at the base or poditic terminal of the neuron because the two waveforms share a
common current profile but exhibit different impedances. As the action potential goes positive in potential,
Figure 2.6.2-3 Nomenclature used by Bishop et al. in discussing the extracellular
LGN cell responses. Up is negative and the height of the negative peak above the
quiescent level is typically 5–8 mV. Left; figure from Bishop et al., with text labels
by this author. Stimulation is applied at time = zero. The response is in fact the
current through the poditic terminal of the neuron multiplied by the impedance
of the external fluid environment with the S and A segments reflecting sub
threshold currents primarily in the dendritic to poditic circuit. the B response
represents the poditic current dominated by the current in the axon–poditic
circuit during action potential generation. See text. Right; Typical action
potential generating pyramid cell showing current flowing through the normal
biasing connection at F of the poditic neural circuit in to the surrounding fluid
(dashed line from podite to ground in inset. By introducing a voltage probe near
F, the waveforms on the left are normally acquired. See text. Original art on left
from Bishop et al., 1962. Art on right from Figure 2.5.2-2 of this work
The Neuron 2- 253
the S-potential goes negative a proportional amount suggesting the ratio between their respective
impedances.
254 Neurons & the Nervous System
2.6.3 Electrical characteristics of pulse regenerators–Nodes of Ranvier
The ganglion neurons do not grow following neurogenesis. Thus their requirements related to homeostasis
are low. However, even when myelinated, the attenuation of signals propagated along their axon is limiting
(Chapter 9). Therefore, a feature is needed that can regenerate the action potential pulses without requiring
an additional neuron nuclei and supporting structures. The Node of Ranvier satisfies this need. The axon is
subdivided into axon segments for signaling purposes and the segments are separated electrically by Nodes
of Ranvier, but the segments remain part of the ganglion neuron for homeostasis. Because of the attenuation
incurred, the Nodes of Ranvier are typically spaced at intervals of two millimeter or less (while the
myelinated axon segments are typically less than 10 microns in diameter, a ratio of 200:1).
Measurements related to individual pulses traveling along the ganglion axon have been described as saltatory
(showing periodic increases in amplitude with distance from the hillock of the ganglion neuron).
The Node of Ranvier are specialized in that they accept only action pulses at their input and generate action
pulses at their output. They contain Activa circuits that are configured as driven monopulse oscillators.
Each Node of Ranvier accepts pulses, of arbitrary spacing, and regenerates the pulses after a fixed time
delay. The resulting pulse stream at the axon pedicle exhibits the same pulse-to-pulse spacing as the original
pulse stream but a fixed delay dependent on the number of Nodes of Ranvier encountered. There is no
performance limit as to how many Nodes may occur within a single axon of a ganglion cell. As in man-made
pulse systems, any waveform distortion, other than a differential delay on a pulse-to-pulse basis, is
insignificant.
A feature of the electro-magnetic mode of propagation employed in stage 3 projection neurons is that the
signal propagates along the axoplasm without regard to the direct current potential gradient along the
axolemma or the potential at the two ends of each axolemma. This allows the two ends of each axon
segment to be supported by separate electrostenolytic supplies. A detailed discussion of electro-magnetic
propagation along an axon will be developed in Chapter 9. This section will focus on the unique
cytological/histological configuration of the Node of Ranvier and how they contribute to the regeneration of
the signal pulses by each Node.
2.6.3.1 Introduction of the Node of Ranvier of the axon
Wrapping a significant part of the axolemma in myelin is an effective way of allowing the axolemma to be
increased in length. However, it is not an adequate modification if the action potential is to be projected
over distances beyond a few millimeters. In that case, active signal amplification is necessary. This can be
provided by analog amplifiers while accepting the degradation of the signal waveform implicit in
transmitting a pulse waveform over a relatively simple electronic transmission line, e.g., one without
equalization stages to compensate for the normal phase distortion per unit length. The alternate approach is
to regenerate the waveform. This actually involves replacing the received signal waveform with an alternate
waveform, typically of similar waveshape. This regeneration of the waveform is the purpose of the Node of
Ranvier.
The Node of Ranvier is a driven monopulse oscillator such as those discussed in Section 2.6.3 above. This
oscillator is unique in that it is introduced between sections of interaxon formed by subdividing the axon of a
single cell. The resulting ganglion cell takes on a greater degree of complexity. However, the complexity is
a result of replication and not new techniques. See Section 2.6.4. The difference between a ganglion with
and without Nodes of Ranvier is a subject of interest in morphology. However, if the questions of genesis
and metabolism are set aside, the difference is trivial based on cytology and signaling performance.
2.6.3.2 The topology & cytology of the Node of Ranvier
Figure 2.6.3-1 shows the topology of the Node of Ranvier between two axon segments. Each segment is a
totally enclosed tube of axolemma, except for the homeostatic shunt (which should be shown connecting the
two axoplasms). In the areas wrapped by the myelin sheaths, the ratio of capacitance to inductance supports
propagation. In the areas between the wrapped portions and the junction area, each piece of the axon is
represented by a lumped capacitance. This capacitance and represents a matching section from the
perspective of electrical filter theory. There may also be dedicated electrostenolytic power supplies in these
areas (not shown). The important feature is the Activa formed between the rounded ends of the axon
segments, with the base region of the Activa formed outside of the lemma, and therefore the neuron. It is the
same configuration as the previously discussed synaptic junction. In this case, it is important that the
electrolytic path between the base region, shown hatched, and the extra neural matrix be constricted. When
constricted, the impedance of the path is sufficient to act as an internal feedback impedance like the poditic
The Neuron 2- 255
Figure 2.6.3-1 Node of Ranvier topology. The homeostatic shunt is shown
passing behind the axon. The synapse area outside of the semi-metallic water
base is highly constricted resulting in a resistive poda impedance. The
unmyelinated matching sections of each axon segment represent significant
capacitances.
impedance at the Activa within the neuron. This internal feedback will introduce a unique characteristic into
the input impedance, the output impedance and the transfer impedance of the neuron. When combined with
the lumped capacitance of the matching sections, this feedback impedance supports the operation of this
conexus as a relaxation oscillator acting as a driven oscillator (an action potential regenerator).
Figure 2.6.3-2 provides a higher resolution image of the cytology of the Node of Ranvier.
Frame A shows the gross cytology of the axon segments at a resolution beyond the resolution of light
microscopy in caricature, including the nominal reticulum of each axon segment with a diameter of 0.3
microns. The outer ends of the two axolemma are not detailed. It shows the axolemma (follow the lower
axolemma) necking down to form a nominally 0.3 micron diameter junction area. It simultaneously supports
one or more areas, flutes, of electrostenolytic activity in the larger synaptic junction area (black line
segments representing potential regions of charge concentration).
Frame B expands the scale further and shows in caricature the structure observed by electron microscopy.
The caricature shows two small synaptic disks representing a few of the elements in the full synaptic array
of 0.3 microns diameter. Each of the tubes, flutes, extending from the reticulum press against the axolemma
resulting in a puckered surface for the axolemma within the synaptic array. The spacing between these
puckered areas of the juxtaposed lemma are less than 100 Angstrom (nominal value is 45 Angstrom). One
area of electrostenolytic activity is also shown.
256 Neurons & the Nervous System
Figure 2.6.3-2 Node of Ranvier with dimensions. Frame A; a caricature of the
gross geometry (but the junction area is still below the resolution of light
microscopy). Other potential areas of high charge density shown by black bars.
See text. Frame B; the detailed geometry (showing only two of the array of a few
dozen “flutes” and associated synaptic disks). Negative charges accumulate
initially in the area of the black ellipse.
It is difficult to locate electron microscope images illustrating these features. Typically the investigators
were not seeking detail about the Node of ranvier and the features are extremely small, and the homeostatic
shunt is much easier to image.
The Neuron 2- 257
Figure 2.6.3-3 Node of Ranvier isolated in
living tissue by dissection. Top; the
internal synapse between the two
segments of the axon is clearly seen. It is
also clear that the point of contact is
extremely small and that the base region,
the poditic terminal, has direct conductive
contact with the medium surrounding the
nerve at this “void” in the myelin sheath.
From Ottoson & Svaetichin, 1953.
Bottom; a similar image of a peripheral
neuron pointing to the Node of Ranvier. It
shows the butt joint of the Node as well as
the continuity of the separate
homeostasis channel adjacent to it. From
Krassioukov, 2002.
Figure 2.6.3-3(top), taken from a larger image does show the juxtaposition of the rounded ends of the two
axon segments190. The magnification is not high in this very early electron microscope image. It is quite
clear that these two axon segments do not form a continuous fluid channel between them, although the
structure above the axolemma may represent the homeostatic shunt. The active region of the Node, the area
of the Activa, is less than 100 Angstrom wide and 100 Angstrom in height (probably a diameter) in this
image. The bottom of that same figure shows a more recent image from Krassioukov in Ramachandran
(page 824). By staining with osmic acid, it also shows the continuity of the homeostasis channel along with
the putative butt joint character of the Node of Ranvier.
Similar figures of Nodes of Ranvier can be found
in Waxman191, see next Figure,
Page 518 of Ramachandran shows an alternate
representation of a Node of Ranvier obtained by
rotating the neuron 90 degrees when preparing it
for electron microscopy and selecting a different
slice. As a result, the actual Node is obscured
behind the homeostatic path. Note the structure in
the nodal gap on each side of the homeostatic path
does not easily relate to the suggested continuous
homeostatic path.
190Ottoson, D. & Svaetichin, G. (1953) The electrical activity of the retinal receptor layer Also, (1983)
Physiology of the Nervous System. NY: Oxford Press page 27
191Waxman, S. Ed. (1978) Physiology and Pathobiology of Axons. NY: Raven Press Figs 2-6, 2-18, 2-19 &.
2-20
258 Neurons & the Nervous System
Figure 2.6.3-4 shows a better cross section of a Node of Ranvier appearing in Berthold192, Plate 12. The
two areas labeled myelin sheath attachment,“MySA,” segment would be continuous with the upper and
lower membranes if a true sagittal slice through the Node of Ranvier, NR, was obtained. This is difficult to
achieve. They spend several pages discussing other evidence describing possible functional elements (not
shown until later Plates) in the “nodal gap.” The caption to their Plate 38 notes the distinctive difference in
charge density on the proximal and distall side of the junction, under similar magnification, X6,500.
Waxman193, writing in 1995, provides a different “working model, figure 11-1 and figure 11-18, with the
axon area between the upper and lower astrocytes shown as undefined, by dashed lines. Waxman noted,
“Figure 11-1 shows the critical question that hahad to be addressed. The properties of the nodal axolemma
amenable to relatively direct examination, because this membrane is accessible to the extracellular
compartment and thus can be studied readily via various recording techniques. In contrast, the properties of
the internodal and paranodal axon membrane are more difficult to study, because these parts of the axon
are masked by the overlying myelin sheath. As early as 1955, Tasaki and Freygang showed that the
resistivity of the axon membrane at the node was much lower than that of most other excitable membranes
that had been studied. In addition, voltage-clamp studies ( Horackova et al.,1968; Nonner
andStampfli,1969) and noise analysis (Conti et al, 1976) studies provided evidence for a high Na+ channel
density at the node of Ranvier. Nevertheless, in the absence of more direct results, the characteristics of the
internodal/paranodal axon membrane remained poorly understood.
A priori, it might have been hoped that the properties of the internodal/paranodal axon membrane could be
inferred from observations of conduction block or decreased conduction velocity in demyelinated axons.
This turned out not to be the case.”
The last assertion in each of these paragraphs were underlined here to re-emphasize, the models of both
Berthold (1978) and Waxman (1995) are not viable, The electron micrograph of Ottoson & Svaetichin of
1953,shown in Figure 2.6.3-4(top) and showing the both axolemma turning inward to form and end-cap,
These two end-caps can form a Node of Ranvier, NoR, as proposed above in this work if,
the two lemma are of type 2 lemma in the junction area (semiconductors as described in Section 2.1.4.2.1
),
are juxtaposed at an appropriate distance (nominal value is 45 Angstrom, see above), and
are appropriately electricaly biased to generate Action Potentials.
192Berthold, C. (1978) Morphology of Normal Peripheral Neurons In Waxman, S. Ed. (1978) Physiology and
Pathobiology of Axons. NY: Raven Press page 40
193Waxman, S. (1995) Voltage-gated ion channels in axons: localization, function, and development In
Waxman, S. Ed. (1978) Physiology and Pathobiology of Axons. NY: Raven Press Chap 11
The Neuron 2- 259
Figure 2.6.3-4 “Longitudinal section through the node-paranode region of a large
myelinated feline ventral root axon. The constricted axon segment transforms
proximally and distally into the more dilated parts of the paranodal axon. The
nodal axon segment is bordered bilaterally by the MySA segments. Arrows
indicate ears of terminal cytoplasmic pockets.” X6,000. No effort was made to
achive a sagittal slice, in conformity with the common wisdom of the time. From
Berthold, 1978.
2.6.3.3 The circuit schematic of the Node of Ranvier
The topology indicates the Node of Ranvier utilizes the same circuit schematic as the driven relaxation
oscillator of Section 5.3 and Section 9.2.5. It depends on the poda impedance, created by the limited
electrolytic access of its base with the extra-neural matrix, to introduce internal feedback. It uses the lumped
capacitances associated with the two matching sections to provide the necessary phase shift to achieve a
feedback factor of +1.0.
As indicated in the earlier discussions, Nodes of Ranvier and other driven monopulse regenerators need not
have a significant current through the Activas during the quiescent period. They are typically biased to an
emittor-to- base just below cutoff and the axon is at or near quiescence (–140 to –154 mV) during this
period.
260 Neurons & the Nervous System
With this topology and circuitry in mind, portions of Tasaki’s194 text make very interesting reading because
the effects of pharmacological treatments become clearer. However, his treatment of a series of interaxons
and Nodes of Ranvier as a passive cable of only resistors is far too elementary (Section 6.3.3).
Tasaki notes that the effect of an anesthetic on the myelinated portion of a neuron is virtually nil. It is only
when it is applied to the area of a Node of Ranvier (or other terminal area) that the anesthetic has an impact.
2.6.4 The decoding (stellite/stellate) neuron of the mid-brain and cortex
The term stellate neuron has been used very widely in neural research associated with the
morphology/histology of the CNS. Traffic analysis would suggest many different functional types of
neurons within this general morphological classification. However, the functional operation of these types of
neurons has not been specified.
This work will use the functional label stellite neuron to describe a typically stellate (star-shaped) neuron
whose purpose is to decode the action potential pulse stream it receives from a stage 3 ganglion neuron and
generate an electrotonic replica of the waveform originally encoded by the ganglion neuron (regardless of its
physical location within the organism).
In this respect, the stellite neurons operate in a manner analogous to a “ratio detector” circuit in a frequency
modulation (FM) radio. The ratio detector circuit is slightly different from the “frequency discriminator”
circuit used in higher quality FM radios.
Depending on the quiescent bias between the emitter and the base of the Activa within the stellite neuron, the
average output level may be at the intrinsic axoplasm potential due to electrostenolytic action, or it may be at
a less negative quiescent value caused by continual current flow in the collector circuit of the Activa. If it is
at the intrinsic level, the signal output is necessarily a positive going one, a de-polarization, for increase
signal input levels. If the quiescent level is less negative (closer to zero) than the intrinsic electrostenolytic
level, the output signal can be either more positive (de-polarizing) or more negative (hyperpolarizing)
depending on the rate at which pulse signals are applied to the input of the circuit.
Figure 2.6.4-1 Illustrates the basic circuit of a generic stellite pulse decoding circuit. The circuit is at cutoff
in the absence of any stimulation, the horizontal axis of the inset is at –140 to –154 mV. The nominal
collector potential during recovery of the waveform shown (dashed line) is –70 mV. The circuit accepts
pulses at its dendritic input of nominal pulse amplitude (100mV). This amplitude would suggest either,
local regeneration by the last Node of Ranvier immediately prior to the axon synapsing with the dendritic
input via an analog synapse, or
the synapse following the axon pedicle acting as a phasic pulse regenerating Node of Ranvier in connecting
to the dendrite of the stellite neuron.
The literature does not provide sufficiently precise information to resolve this dichotomy.
The circuit may accept inputs at its poditic terminal acting to inhibit the operation of the circuit under
specific conditions. The values of the collector capacitance and resistive component of the impedance
shown result in an integration frequency limit of nominally 100 Hz. The output shown is the result of an
analog input signal to the stage 3 ganglion neuron consisting of a sinewave sitting on a pedestal. As a result,
the pulse stream passed to the stellite neuron consisted of a set of pulses exhibiting a distinct average pulse
rate but groups of pulses gather together at point of maximum analog amplitude and groups of pulses thinned
out at points of minimum analog amplitude. Specific analog signal recovery examples will be illustrated in
Chapter 9.
194Tasaki, I. (1982) Physiology and electrochemistry of nerve fibers. NY: Academic Press. pp. 37-61
The Neuron 2- 261
2.6.4.1 Cytology of the stellite neuron
The cytology of the basic stellite neuron is similar
to that of the basic ganglion cell compared to the
fundamental neuron typified by the bipolar neuron.
The output impedance associated with the stellite
neuron consists of a larger capacitance than found
in the bipolar neuron. In this case, there is little or
no feedback through the poda impedance and the
circuit is not subject to oscillation. The
capacitance is so high, that the circuit accepts
individual current pulses injected into the
axoplasm by the Activa and does not dissipate the
resulting change in voltage within the time interval
expected for the following action potentials. Thus
the average voltage of the axoplasm becomes a
facsimile of the average current caused by the
injection of a unit charge in response to each
action potential arriving at the stellite neuron
divided by the pulse interval between those action
potentials.
2.7 Other hybrid neurons, the hormonal, visceral & mobility interface
Several special classes of neurons have been discovered that exhibit unusual properties that suggest they be
described as hybrid neurons. They are all built around the core structure of the cell, becoming more
commonly labeled a stem cell. They are not associated with signaling between two neurons but between
neurons and other classes of tissue. One of these classes will be labeled stage 7 neurons. These neurons are
similar to the conventional stage 3 pulse neurons addressed in Section 2.6. However their axon termini are
modified. The stage 7 neuro-effector neurons pass “information” to neural and non-neuron tissue by
releasing a variety of chemical agents (in the case of neurons, these chemical agents are received
parametrically, via auxiliary receptors). The actions of these stage 7 neurons are best described using a
multidimensional matrix since these actions can be quite complex. Figure 2.7.1-1 presents a preliminary
table organizing these actions.
Figure 2.6.4-1 Fundamental stage 3 pulse
decoding neuron. The time constant of
the collector (axon) circuit is set to allow
the recovery of a sinewave (typically 100
Hz maximum) on a pedestal.
Figure 2.7.1-1 Preliminary table of neuro-effector actions. This table will be
populated in Chapter 16 of this work. See Section 16.3.1.
262 Neurons & the Nervous System
When affecting non-neuron tissue, the agents can act between the releasing neuro-effector and a single
orthodromic cell, or they can act on a broader range of cells essentially simultaneously. When the agent
affects only a single striate muscle cell, the action is considered paracrine (acting at a short range). This is
the situation that has long been associated with the label synapse.
When the agent affects more than one orthodromic cell, the action is considered endocrine. This is the
essence and origin of the endocrine hormonal system.
Some authors have chosen to describe hormones that only affect tissue within the blood-brain-barrier of the
CNS. Such action is occasionally labeled pericrine, acting at a longer range than paracrine but shorter than
endocrine.
Finally, some agents released by neuro-effectors are released outside the organism as a whole, either into the
external environment or into the digestive tract. These agents are described as exocrine agents. They may
be exocrine hormones or exocrine enzymes associated with digestion.
When one of these chemical agents affect neurons, it is not as a signaling agent but as a modulating agent
(affecting the efficacy of the neuron in handling the signaling by electrons between neurons).
The subject of neuro-effectors is so broad, it will be discussed in detail in Chapter 16. The following
material will summarize material found there.
The paracrine, endocrine and exocrine actions appear to employ significantly different chemical agents. The
paracrine agents are molecules with a molecular weight of less than 146. The endocrine agents occupy two
distinct groups, those based on cholesterol and those based on lengthy peptides. Some of these agents
involve molecular weight considerably higher than 146. The exocrine agents include pheromones that are
typically volatile alcohols of low molecular weight..
2.7.1 The paracrine stage 7 neuro-effector neurons
The interface between a stage 7 neuro-effector neuron and striate muscle tissue has frequently been
described as a synapse and that label has played a major role in exploratory research defining the synapse.
However, this interface will be examined more closely in this section in order to arrive at a more precise
terminology.
Two chemicals are recognized as the major paracrine agents, acetylcholine and nitric oxide. Neither of these
is considered a hormone in most texts. They are generally associated with only very local neuron-to-cell
action. They are neither peptides or derivatives of cholesterol like most hormones. Acetylcholine (ACh)
was one of the first chemicals identified as causing striate muscular contraction under neural control. More
recently, nitric oxide has been identified as causing relaxation of the perennial contracted state in smooth
muscle.
under neural control.
The action of the paracrine neuro-effector can be described as releasing a chemical agent that has been
stored in a different form on a stereochemical receptor site on the external surface of the axolemma. The
release is controlled by the potential of the axoplasm with respect to the surrounding neural matrix.
The chemical reaction involved in release of nitric oxide is reasonably well understood. L-arginine, is the
amino acid that binds to the neuro-effector neuron. When in the presence of oxygen (O2) and at a specific
axoplasm potential, it can react to form nitric oxide (NO), or NO (to more clearly indicate its free radical
status). Oxygen is readily available via hemoglobin. Both the nitric oxide and the residue, iso-leucine are
released from the stereochemical receptor site. Iso-leucine is either cleared from the body or reprocessed
back into L-arginine. Nitric oxide has a very short lifetime within the organism and is only affective over
very short (paracrine) distances. Nitric oxide is occasionally described as produced by neuronal nitric oxide
synthesis (nNOS) to differentiate it from that produced by enzymatic means (eNOS).
The chemical reaction involved in release of acetylcholine by the neuro-effectors is poorly understood. It is
important to note that acetylcholine is classified as a choline and not a catacholine, which is a distinctly
different chemical group. ACh is a much more complex molecule than nitric oxide. Its normal generation
within the organism is usually described as a reaction between choline and Acetyl Co-A. However, there
may be alternate paths not widely documented, such as the direct combination of choline and acetate at a
substrate surface. Choline is a nitrogenous alcohol, but there is no indication it is capable of releasing a
simple agent like NO. No proposal could be found as to how the formation of ACh could be controlled by
The Neuron 2- 263
the neuro-effector neuron. Neither was any proposal found as to how ACh, once formed could be released
by a neuro-effector, except conceptually by a putative vesicle. The presence of choline as one moiety of the
outer phosphatidyl choline bilayer of the neurolemma provides many possibilities. The chemical
hemicholinium-3 is known to inhibit the formation of acetylcholine, probably by occupying the choline
binding site of the enzyme choline acetyltransferase (CAT) or of the receptor site of the outer bilayer. The
structure of both acetylcholine and hemicholinium-3 suggest coordinate chemistry, rather than or in addition
to reaction chemistry, may be involved in the formation of acetylcholine.
The pharmacology of ACh and its antagonists, blockers, inhibitors and chemicals that mimic its actions is
highly developed. There appear to be two major “receptors” associated with ACH, the nicotinic and
muscarinic ACh receptors. These receptors are named without regard to their function. They were named
for their joint sensitivity to ACh and these other chemicals. The action of acetylcholine within the
neuron/muscle junction is unknown. However, the effectiveness of acetylcholine outside the junction is
terminated by hydrolysis, a chemical reaction that forms two products (choline and acetate) which are
essentially inactive. Diffusion of ACh from the synaptic region plays a minor role because AChE is so
active. A broad overview of Acetylcholine is available on the Internet195..
The subject of signaling between neurons and other types of tissue involves more than a synapse. Chapter
16 develops all of the methods by which the neural system interfaces with the rest of the organism. It shows
that besides direct cell to cell connections, one group of terminal neurons (stage 7) are the initial elements of
the hormonal system..
2.7.1.1 The paracrine stage 7 neuron interface with striate muscle
The interface between a stage 7 neuron and a striate muscle myocyte has frequently been associated with or
described as a synapse. In this work, it is defined as the chemical synapse between a neuron and a non-
neuron in a confined space. Such a synapse is generally associated with the end-plate of a myocyte.
Ganong has presented a detailed cross-section of an end-plate196. The complex intertwining of the multiple
pedicles of the neuro-effector axon and the convoluted surface structure of the end-plate of the myocyte
insures any chemicals released at the pedicles remains in the immediate area for a prescribed period. Figure
2.7.1-2 presents a simplified version. The axon termini are shown only in cross section, although they
extend in and out of the plane.
195- - - http://courses.washington.edu/chat543/cvans/sfp/acetylch.html
196Ganong, W. (1975) Review of Medical Physiology, 7t h Ed. Los Altos, CA: Lange Medical Publishers pg
56
264 Neurons & the Nervous System
It is proposed the neuro-effector agent, primarily if not exclusively acetylcholine, is created on the outer
surface of the pedicle, at an area of type 2 lemma optimized for the stereochemical capture of the necessary
progenitor chemical. Upon capture, this chemical is stored on the surface until the axoplasm potential,
relative to the exterior matrix is changed to cause the generation, and release, of acetylcholine and ammonia.
The ammonia diffuses into the surrounding matrix.
The acetylcholine stimulates the myocyte until it is eventually hydrolyzed into choline and acetic acid
(acetate). The time constant of the acetylcholine presence is sufficient to insure the muscle establishes a
condition of tonicity even though the release of stimulant by the neuro-effector is pulse driven. Choline and
acetic acid are removed by diffusion into the surrounding matrix
How the acetylcholine stimulates the myocyte to cause contraction of the sarcomere is outside the scope of
this work.
2.7.2 The endocrine stage 7 neuro-effector neurons–The hormonal system
The endocrine neuro-effectors are the beginning of the hormonal system as normally conceived. The
volumetric requirements for hormones leads to the formation of knots of neuro-effector neurons into what
are known as the primary glands, the hypothalamus, one of its minor components the epiphysis, one of its
major components the hypophysis (pituitary gland), etc. The hypophysis is very interesting because part of
its neural tissue is formed within the blood-brain-barrier (BBB) of the CNS but its neuro-effector termini are
outside of the BBB. This gives the pituitary gland immediate access to the cardiovascular system which runs
Figure 2.7.1-2 Schematic of the neuro-effector/myocyte interface for striate
muscle. Note the limited fluid conductance between the point of release of the
neuro-effector agent and the surrounding matrix. Myelination of the stage 7
neuro-effector (motor nerve) not shown. Simplified from Ganong, 1975.
The Neuron 2- 265
through the gland. The other portions of the hypothalamus generally have their neuro-effector termini within
the BBB of the CNS. The agents they release are typically described as pericrine, and operate primarily
within the CNS.
The large hypophysis releases at least six primary hormones that are used to affect the output of a number of
more remotely located thyroid, parathyroid, and adrenal glands along with the gonads and portions of the
pancreas. The complexity of many of these agents is much higher than that of nitric oxide or acetylcholine.
Many are multi-ring aromatics. Those of the adrenal cortex are derived from cholesterol. Others are
peptides with typical molecular weights of 30,000. This complexity suggests a different mechanism of
production than for the paracrines, at least for the peptides. These relationships are discussed in detail in
Section 16.3.
The literature suggests these agents are formed within the neuro-effector neurons and released by excretion,
probably like the excretion of the peptide opsin by the visual sensory neurons.
The release of chemicals by the axon of a stage 7 neuron can hardly be associated with a synapse. The
mechanisms and dimensions involved are significantly different.
2.7.2.1 The amino acids as progenitors of many hormones
Many of the most important hormones are derived from simple amino acids, frequently by decarboxylation
and the addition of one or more hydroxyl groups. The resulting chemicals are no longer peptides. They are
used as they stand without being incorporated into longer peptides. They are frequently found as pericrine
hormones within the CNS, some of these potentially released by the hypothalamus to influence the
hypophysis.
Chapter 16 will explore and provide a framework for the hormones released by the neuro-effectors in greater
detail.
2.7.3 The exocrine stage 7 neuro-effector neurons
The exocrine neuro-effectors operate essentially as do the endocrine neuro-effectors. Their operation will be
discussed mor fully in Chapter 16.
2.7.4 The hybrid cardiocyte of the cardiac system
The hybrid cardiocytes of the cardiac system incorporate the capabilities of a neuron and a myocyte in a
single biological cell. These cardiocytes will be placed in a class by themselves, stage 8 hybrid neurons
within the neural system. Chapter 20will discuss the characteristics of the cardiocytes in detail within the
context of the cardiac system as a distinct mini-neural system (not just as a mini- brain). Considerable
controversy remains within the cardiocyte academic arena, partly because the functional properties of the
cardiocytes have not been clearly documented. Chapter 20 shows clearly that the neural portions of the
cardiocytes receive electrolytic signals and pass those signals along by electrolytic means. The signals are
analog in character as demonstrated by the interval-duration relationship so well known within clinical
medicine. Being analog neurons, they share many properties with the stage 2, 4, 5 & 6 neurons. In
achieving this interval-duration relationship, the major cardiocytes associated with contraction of the cardiac
muscle appear to act as an over-driven analog amplifiers. As a result the interval-duration relationship
provides an extra degree of cardiac muscle performance under conditions of stress (such as very high pulse
rates) without the danger of encountering a tetanus. Unlike the stage 2, 4, 5 & 6 neurons, the stage 8 neurons
appear to require a separate positive potential power supply. This power supply insures a positive poditic
potential that in turn, insures the quiescent axon potential of the neuron can be very close to zero relative to
the surrounding matrix. This appears to be a critical value in controlling the release of calcium ions from the
sarcoplasmic reticulum and the subsequent stimulation of the sarcomeres.
The both the electrolytic and histological forms of the schematic of a cardiocyte are shown in Figure 2.7.4-1
The details of these circuits will be discussed in Section 20.3.5. As noted in Frame A, the electrolytic
potential of the axoplasm is used to stimulate the orthodromic cardiocyte and also stimulate the release of
calcium ions from the sarcoplasmic reticulum. this release is conceptually similar to that performed by other
stage 7 neurons but no definitive mechanism has been found in the literature. Frame B shows the poditic
power supply as well as the axonal power supply.
266 Neurons & the Nervous System
Figure 2.7.4-1 Proposed electrolytic circuit of a cardiocyte (myocyte). A; the
neural circuit controlling the sarcomere as the chemical energy to mechanical
energy (tension) transducer. The role of the sarcoplasmic reticulum remains
open to question. B; the histological representation of the same circuit showing
an end-on view of the cardiocyte. The lower left power supply converts lysine to
iso-leucine and creates a nominal +52 mV. See text.
The Neuron 2- 267
2.7.4.1 The functional properties of the cardiocyte
The cardiocytes are hybrid cells, exhibiting significant electrical parameters within the family based on their
roles as both control system sources and inter neuron. The interneurons in particular exhibit an operating
characteristic not found in other neurons. They operate in the analog (not phasic) mode but are over-driven,
by signals of greater amplitude than their input dynamic range. The interneurons simultaneously exhibit
significant characteristic as electrical-to-mechanical transducers. These properties lead to describing them as
stage 8 neurons. These unique properties of the cardiocytes will be addressed in Chapter 20.
2.7.4.1.1 The electrical characteristics of the cardiocytes
Figure 2.7.4-2 shows the electrical operating characteristic of the cardiocyte as a neuron. The first feature to
note is the cardiocyte operates differently when stimulated by a single pulse or widely spaced pulses. This is
a pathological case for a cardiocyte. Under this condition, the base terminal of the Activa is near the positive
podaplasm supply potential of +52 mV. The quiescent potential of the axoplasm is near –85 mV. If
stimulated by a pulse of saturating amplitude , the axoplasm potential will traverse from –85 mV to a +35
mV for a short interval before dropping to about 0.0 mV during the remainder of the stimulation (due to
charging of the podalemma acting as a capacitor).
At higher stimulation pulse rates, the podaplasm potential remains close to +20 mV throughout the series of
pulses and the output signal goes from the quiescent value of –85 mV to near zero mV during each pulse
cycle (using the dynamic curves).. These different pulse shapes are shown in the lower frame. The peaked
response is seen to be a pathological condition. The normal, and in-vivo, cardiocyte operation is the
smoother (solid line) waveform. These two waveforms bound the variety of waveforms reported in the
literature for cardiocytes (Section 20.3).
268 Neurons & the Nervous System
The pulse duration is determined by a combination of the length of the stimulation over-driving the
cardiocyte, and the relaxation time constant of the axonal circuit of the Activa–as recognized in the Interval-
Duration Phenomenon.. Over-driving alone tends to broaden the width of the output waveform.
2.7.4.1.2 Is the cardiocyte a driven monopulse oscillator?
[This subsection is repeated in Section 16.5.4.]
Figure 2.7.4-2 Electrical operating characteristic of a cardiocyte. Top; operating
characteristic of the cardiocyte showing both the static and dynamic position of
the collector current to voltage characteristics. The base potential of the Activa
falls below the positive potential of the poditic power supply under dynamic
conditions. Bottom; the two bounding waveforms of the cardiocyte temporal
response. The peaked (dashed) response is due to a pathological condition, an
abnormally low pulse rate, or single pulse stimulation of a cardiocyte in-vitro
(corresponding to the static condition above). The more rounded (solid)
response is the nominal, in-vivo, condition or that encountered in-vitro with
normal stimulation pulse rates for the species (corresponding to the dynamic
condition above).
The Neuron 2- 269
The medical profession describe an “Escape Pulse” when the pulse is recorded on a electrocardiogram. This
escape pulse is of unknown origin and it typically occurs when the normal pulse-to-pulse interval exceeds
150% of the nominal.
These escape pulses are considered life saving and medical texts indicate no effort should be taken to
hinder these escape pulses.
I encountered a series of missed heart beats at the age of 85. The missed beats occurred every three beats at
the shortest interval and at every 20-25 beats in each spasm lasting at least one minute. While wearing a
Holter Device for 24 hours, after complaining of “missed hear beats” during the night. The report was that
my lowest heart rate occurred early in the morning and was 43 ppm. The average resting rate was 60 ppm.
From a physiological perspective, this pattern raises the question of whether the cardiocytes are driven
monopulse oscillators. It is possible the cardiocytes are set to oscillate at a nominal rate of 43-45 ppm, and
are normally driven to operate at a nominally faster rate of 60 ppm while resting. The rate of the driving
oscillator would be able to rise higher based on exertion level in accordance with commands from prior
circuits in the minibrain or the CNS.
2.7.5 Special case of the giant (swimming) neuron (not only axon) of squid
The giant neuron of the dwarf squid, Loligo forbesi, that Hodgkin & Huxley explored in the 1940's was not
what they thought it was (Section 1.2.2.1). It was not a neuron that spontaneously produced action
potentials (Section 2.6.1.2.1). After they stripped the locomotion neuron of all neuritic material (Section
1.2.2.1.4), they had to take special steps to apply a parametric stimulation to the soma or axon of the neuron
to get it to “oscillate” (See below). The giant axon of the squid is a special class of neurons called
locomotion neurons found in many molluscs, fish and insects that provides the synchronous stimulation to
the muscles of multiple legged insects and molluscs such as octopus. In other molluscs and fish, the
stimulation is applied to multiple muscles in fish resulting in a swimming motion. The locomotion neurons
are typically unmyelinated, although tightly wrapped in the neurites of target neurons.
Briefly excerpting from Hodgkin et al197.,
Page 431–Shows their circuit diagram for exciting the axon after the cleaning described on page 432. A
very complex bridge configuration (figure 6) was employed, which they described as a feedback circuit.
Their figure 7 shows rectangular voltage pulses were first passed through a 700 F capacitor, then applied
across the unmyelinated axolemma of the locomotion neuron after all adherent tissue had been removed.
They calculated the axolemma had a capacitance “of about 0.3 F.” No resistance was provided for the
axolemma.
Page 432–“Careful cleaning was important since the guard system did not operate satisfactorily if the axon
was left with small nerve fibers attached to it. A further advantage in using cleaned axons was that the time
required for equilibration in a test solution was greatly reduced by removing adherent tissue.”
Page 433–Figure 8 shows “the time course of membrane potential following a short shock at 23 C”
waveforms in response to the stimulation described on page 431. The results of both positive and negative
excitation are shown. The Resultant waveform shapes are not related to an action potential (Section 9.2.6).
They do not exhibit a threshold typical of the axoplasm potential, they do not show the typical shape of the
rising waveform, they do not show a discontinuity at the peak of the response, and they do not exhibit an
exponential shape to the falling waveform.
The test sample, following “cleaning” (the removal of all dendrites, and possibly podites) was no longer a
viable neuron.
The waveforms are what would be expected from a passive Resistor-Capacitance-Diode circuit excited in the
described manner and the diode was associated with the axolemma.
The giant neuron of the squid, Loligo, is classified as a locomotion neuron (Section 1.2.2.1). As such it does
not produce action potentials. It exhibits a series of pickoff points along its axon. These pickoff points are
pedicles that send signals with different delays to the target neurons, individual stage 7 effector neurons
driving the swim muscles. It produces a unique pulse signal of variable velocity along the length of the axon
appropriate to the swim speed desired. The velocity of the signals along the axon appear to be varied by
197Hodgkin, A. Huxley, A. & Katz, B. (1952) Op. Cit.
270 Neurons & the Nervous System
adjusting the properties of the multiple neurons enclosing the giant axon like a sheath. The result is a change
in the shunt capacitance between the giant axon and the neural matrix. The velocity of signal diffusion is
controlled by this capacitance. See a contrary view by Metuzals et al. in Section 2.7.5.4.
The stage 6 locomotion (swim) neuron is found within the mollusc phyla, and possibly the reptiles and fish;
however it has not been reported among mammalian species. It is reasonable to expect some of the marine
mammals may have developed a substitute for this type of neuron.
2.7.5.1 Problems with the H & H model–Frankenhauser & Huxley, 1964
The problems with the Hodgkin & Huxley model, H & H, of the neuron surfaced early following its
publication in 1952. By the 1960's the problems with the H & H model, forming the foundation of the
chemical theory of the neuron, were well known. The literature supported the need for a new functional
model of the complete neuron.
In 1964, Frankenhauser & Huxley (one of the original authors of H & H) summarized many of the problems
with the H & H model of the axon (as well as its extension to the neuron)198. Those authors explore fifteen
distinct aspects of the previously proposed differential equations (A primary equation with approximately 16
auxiliary equations). As an example:
“(15) It has not been possible to carry out a complete analysis on one single fibre; different parts of the data
refer to different fibres.”
Frankenhauser & Huxley go on to say,
“The equations and the quantitative data obtained in the voltage clamp analysis must to a large extent be
considered as approximations. A fair amount of scatter appears especially between values from different
fibres. The equation system is so involved that it is impossible in most cases to get even a fair idea of the
effect of a change of a single value without going through a complete computation.”
These aspects plus others in the more recent literature demonstrate why the H & H model is untenable
following the advances of the last seventy years.
A mathematician would suggest that any set of differential equations with more than 10 variables (at least six
of which “are arbitrary and of uncertain origin”–pg 304 of Frankenhaueser & Huxley) can be made to match
any arbitrary waveform that can be drawn on paper. It is also noteworthy in hindsight that the delay as a
function of temperature between the stimulus and the beginning of the response does not appear explicitly in
the equations. This delay is intrinsic to four of the “variables of uncertain origin,” the unmeasured, and
hence undocumented, variations in the permeability of the membrane to different ionic species, m, h, n & p.
These variables are defined by differential equations that have no intrinsic relationship to the permeability of
the membrane or the temperature. They are defined only with respect to time and a series of arbitrary
constants. However, these “constants” have been shown to also be variables with respect to the peak
response amplitude by Frankenhaueser & Huxley. It can be shown they are also variables with respect to
temperature. The equations defining m, h, n & p, reproduced in Frankenhaueser & Huxley, also suffer from
inconsistency in the units associated with the variables.
Frankenhauser & Huxley proceeded to “solve” the H & H equations for a toad, Xenopus laevis, by numerical
means using a digital computer available before1964. The solution is not in closed form as defined by a
mathematician.
Their solution in figure 1, reproduced in Figure 2.7.5-1, is only a crude representation of an action potential
198Frankenhaeuser, B. & Huxley, A. (1964) The action potential in the myelinated nerve fibre of Xenopus laevis
as computed on the basis of voltage clamp data J. Physiol. vol. 171, pp 302-315
The Neuron 2- 271
Figure 2.7.5-1 The “action potential”
sol ved by numerical means by
Frankenhauser & Huxley is an inadequate
representation of the performance of the
axoplasm potential. See text. Annotated
from Frankenhauser & Huxley, 1964.
It is now documented that the there are two major
discontinuities in the axoplasm of a switching type
monopulse neuron oscillator generating action
potentials; the first when the stimulation raises the
axoplasm to the threshold of oscillation, the
second upon saturation of the Activa at the peak of
the action potential where it changes operating
mode. It is also documented that both the falling
waveform of a relaxation oscillator is an
exponential (Section 9.2).
As Cole199 noted on page 476,
“As to curve-fitting, the procedure and the results
of Hodgkin & Huxley (1952b) are entirely
unorthodox and are looked at with both
amazement and admiration by trained
mathematicians.”
An alternate expression might be “courteous
consternation” or simple “courteous disbelief.”
The orthodox goal of a mathematician is to derive
a set of mathematically consistent equations that
provide incite into the underlying mechanism
being studied. It is difficult to comprehend the
goals of Hodgkin & Huxley when all they have
prepared is a very complex mathematical
procedure for creating a template approximating a poorly characterized response intimately related to their
test configuration. As noted above in statement (15) of Frankenhaueser & Huxley, the resulting template
does not describe any specific fibre but only an undocumented ensemble of fibers.
The reader is cautioned that exception is not taken to any of the data presented by Hodgkin & Huxley, or
Cole. It is the interpretation and the calculated waveforms (as a function of time) that fail to satisfy the
operational requirements of a valid theory/model that are questioned. Two important notes should be made
about this situation.
1. Frankenhaueser & Huxley based their work on a myelinated axon from Chordata not an
unmyelinated axon from Mollusca. Specifically, they were studying the frog, Xenopus, not the
squid Loligo.
2. The leading and trailing edges (and the absolute delay) of the action potential are affected
differently by temperature. The computer emulation program, Neuron, purports to replicate the
equations of Hodgkin & Huxley. An investigator should be sure this program properly reflects
these differences in actual neurons as shown in Section 10.8.3 and documented by Hodgkin in 1951
and by Schwarz & Eikhof in 1987.
Further consideration of the sodium ion-based Dual Alkali-ion Diffusion Theory of the axon or neuron will
be postponed until after an alternate theory is presented. The alternative provides a theoretical framework
with which to evaluate the propositions developed by Hodgkin & Huxley (that were based entirely on curve-
fitting to empirical data (Sections 10.8.2 to 10.8.4).
The summarizing comments of Cole (1966) concerning “The Melding of Membrane Models” are pertinent
to this summary and should be reviewed200.
2.7.5.2 Hodgkin & Huxley never solved their differential equations
Even after Katz joined their team, they never solved their partial differential equations to obtain a single
closed form solution (including the necessary boundary conditions) in order to validate their solution.
199Cole, K. (1968) Membranes, Ions and Impulses. Berkeley, CA: University of California Press
200Cole, K. (1966) The melding of membrane models Ann NY Acad Sci pp 405-408
272 Neurons & the Nervous System
It is difficult to rationalize why H&H did not solve their differential equations before
attempting to fit them to their data. Performing extensive tabulations using unsolved
differential equations without confirming the boundary conditions associated with the solved
equations are correct would not be acceptable today. The solved equations would invariably
contain both transient and steady state terms. These would provide considerable insight as to
the actual operation of their test configuration (or uncover shortcomings in their assumed
initial conditions).
2.7.5.3 Hodgkin & Huxley never identified the “charge carrier” in their Model
After recording their data on the giant axon of the squid, they sought to interpret the data
within the chemical theory of the day (ignoring any potential electrical explanation). They
noted the higher concentration of sodium ions in the matrix surrounding a neuron and the
relatively high concentration of potassium ions in the axoplasm of neurons. They therefore
adopted these species as their assumed carriers, and the euphemistic labels were accepted
under the simple two-terminal concept of a chemical neuron. Their concept was that
sodium ions flowed through the lemma into the axoplasm as the axoplasm potential rose, and
potassium ions flowed out through the lemma as the axoplasm potential fell. They then were
faced with the problem of how to maintain the nominal concentrations of the ions under
intense operation of the neurons; they conceived of an “ion-pump” to solve the problem of
removing excess sodium ions from the axoplasm and restoring the potassium ions within the
axoplasm. So arose the chemical theory of the two-terminal neuron.
With the three-terminal electrolytic theory of the neuron (Section 2.2 and Section 2.3). The
actual “charge carriers” are known to be the negatively charged electrons. The electrons flow
out of the axoplasm through the semiconductor known as the Activa within every neuron as
the axoplasm potential rises; and flows into the axoplasm through areas of the type 2 lemma
as the axoplasm potential falls through the electrostenolytic process (Section 3.2). The
complete processes is illustrated in using Figure 2.7.5-2. The inset shows the complete circuit
shown in the main figure; the main figure shows the cytology of the neuron in a cross section
view of the axon.
The Neuron 2- 273
Figure 2.7.5-2 Fully implemented electrophysiological/histological Neuron,
showing charge entering and leaving a cylindrical axon. All current flow is via
electrons. The capacitance of the axon, CA, is indicated at lower right. The
capacitance of the dendrite, CD, is shown on left.
The axoplasm is charged initially to –154 mV, with the Activa in cutoff (Vds < Vps), by the
electostenolytic power supply (Vas). This is the nominal voltage at the output synapse
(orthodromic synapse). If the voltage across RD (Vds) is increased to marginally greater than
cutoff (Vds = Vps), the Activa operates as a class A amplifier; electrons are removed from the
axoplasm in proportion to how much Vds exceeds Vps, the axoplasm begins to become more
positive and this is reflected in the voltage across RA and reflected in the voltage at the
output synapse. The electrostenolytic power supply attempts to restore –154 mV at C1.
If the impedance represented by RA & CA is chosen properly and the amplification of the
Activa is sufficiently high, a threshold voltage (Vds – Vps = VTH) which if exceeded will cause
the neuron to go into monopulse oscillation (Section 9.1.1.6), and an action potential will be
generated in the axoplasm. This action potential can be measured in the axoplasm, by the
patch-clamp procedure, or at the output synapse.
274 Neurons & the Nervous System
Summarizing the difference between the charge carriers in the two-terminal chemical theory
of the neuron, and the three-terminal electrolytic theory of the neuron,
AP positive Two-terminal Three-terminal
potential Chemical theory Electrolytic Theory
rising potential Na+6H2O enter axoplasm electrons leave axoplasm via Activa
falling potential K+6H2Oexits axoplasm electron enters axoplasm via
electrosten.
Restoring equilibrium Conceptual ion-pump req. no mechanism required
There is no question concerning electrons transiting a Type 2 (assymetrical) lemma or flowing
through the semiconducting Activa. There remains a significant question concerning how the
euphemistically named ion current would, if taken literally, actually transit the lemma of a
neuron.
After 70 years of research, there is still no identified ion-pump as required by the
chemical theory of the neuron.
2.7.5.4 cytology of the unsheathed axon of the giant neuron--Metuzals, 1983
Metuzals et al201. examined the unsheated axolemma & ectoplasm of the squid giant axon in considerable
detail. The ectoplasm being identified as adjacent to the inner surface of the actolemma. Figure 2.7.5-3
reproduces their page 58.
Metuzals et al. did not identify the material surrounding the giant axon as neural material (Section 6.3.7.3)
as have previous investigators (Section 2.7.5). They identify the immediate surroud as a sheath of Schwann
cells. This is a major difference and raises the question, are both groups of investigators looking at the same
region of the axon. Neither group has specifically identified the precise location along the giant axon of
their investigation. Section 6.3.7.3 also identifies multiple giant axons in the dwarf squid, Loligo forbesi,
In frames 5 & 6 of the figure, the surface is compatible with the presence of 10 micron diameter, or smaller,
axons. The twist among the grooves in the axolemma has not been reported earlier. This is not likely to be
intrinsic to the molecular structure of an axolemma or to that of the surface of a Schwann cell.
201Metuzals, J. Clapin, D. & Tasaki, I. (1983) The Axolemma--Ectoplasm Complex of Squid Giant Axon In
Chang, D. et al. eds. Strucure and Function in Excitable Cells. NY: Plenum pg 53
The Neuron 2- 275
Figure 2.7.5-3 Unsheated Giant Axon of Squid. “Figure 4. Scanning electron
micrograph of desheathed giant nerve fiber of the squid: exposed surface of the
axon (A), Schwann sheath (S), and everted layer of Schwann sheath (C). Bar: 0.1
mm. Figure 5. Scanning electron micrograph of axonal surface at survey
magnification: a ridge and groove pattern on the surface of the desheathed axon
can be seen . The ridges are oriented in a right-handed helix with a tilt angle
( of about 10°. Bar: 50 microns. Figure 6. Scanning electron micrograph of
surface of the desheathed axon at high magnification: grouping of ridges
(opposed arrows) oriented approximately parallel to the long axis of the axon,
protuberances (P), and finer ridge and groove pattern (asterisk). Bar: 10
microns.” From Metuzal et al., 1983.
276 Neurons & the Nervous System
2.7.6 The special case of the eccentric cell of Limulus
The visual system of Limulus exhibits many transitional features along the evolutionary trail. In particular,
the system appears to be a transitionary form between Arthropoda and Mollusca. While its eyes employ
ommatidia and cartridges contained therein very similar to Arthropoda, they differ in having one or more of
the cells that have been replaced or modified to generate action potentials. As discussed elsewhere, either
bipolar or lateral cells can be caused to oscillate by adding capacitance to their collector (axon) circuit. This
capacitance can be introduced by increasing the surface area of the axon, either by increasing the volume or
the overall length of the axon beyond a critical value. This appears to be the case for the so-called eccentric
cell. This type of cell is addressed in the Author’s book on vision202. There appear to be two forms of
eccentric cells. The first type contains a driven monopulse oscillator that produces action potentials on
demand, as characteristically found in ganglion cells transmitting monopolar signals derived from luminance
information. The second type contains a free-running oscillator that produces action potentials with a
frequency proportional to the level of the bipolar stimulus, as characteristically found in ganglion cells
transmitting bipolar signals derived from polarization or chrominance information. No references to this cell
type was found outside of the Limulus literature.
2.7.7 The mossy and climbing fibers of the cerebellum & hippocampus
The fanciful names, mossy fibers and climbing fibers have long been used in the anatomy and histology of
many engines of the neural system. However, the available data related to the cerebellum and the
hippocampus appears to be more clearly presented. The neuroanatomy program at the University of
Wisconsin has attempted to identify these fibers and describe their role.
Mossy and climbing fibers are presumed to be myelinated axons of stage 3 neurons as they arrive at different
engines within the neural system. At some point, these axons reach a stage 3B decoding circuit that provides
an analog output to a synapse. See Chapter 9 on signal transmission.
A goal of the following discussion is to describe more functional names for these stage 3 signal propagation
neurons if possible.
202Fulton, J. (2005) Processes in Biological Vision. www.neuronresearch.net/vision Chapter 14, Section 14.6
The Neuron 2- 277
2.7.7.1 The neural anatomy relating to the cerebellum
The figures in Subsection 2.7.7.1 are reproduced from the University of Wisconsin–Madison
website203.
The summary provided with the figures indicates,
“1. all cerebellar inputs (entering a folium) are excitatory
2. mossy fibers (from) dorsal spinocerebellar tract, DSCT, cuneocerebellar tract, CCT,
PONTOCEREBELLARS, PCT and vestibulocerebellar tract, VCT– terminate (excite)
on granule cells. All arrive via the inferior cerebellar peduncle except thePCT which
dominates the middle cerebellar peduncle
3. climbing fibers (from) OCT-terminate (excite) directly Purkinje cells (by-passes granule),
cause complex spikes in Purkinje cell “
3a. the superior cerebellar peduncle is dominated by efferent fibers from the cerebellum
The summary also asserts the following, which are not supported in this work without further discussion.
This is because of the revision of all neurons from two-terminal to three-terminal devices with differential
inputs. Thus, it is whether the presynaptic axon synapses with the inverting (inhibiting) or non-inverting
(excitatory) input that determines whether the output of the post synaptic neuron is excited or inhibited.
“4. granule cell is only excitatory cell in the cerebellar cortex-terminates (excites) on Golgi,
basket and Purkinje cells--results in simple spikes in Purkinje cells(50-100/sec)
5. Purkinje, Golgi and basket cells are all inhibitory
6. Basket (introduce) feedforward inhibition on Purkinje cells
7.Golgi (introduce) feedback inhibition on mossy fiber-granule cell relay
8. mossy and climbing fiber collaterals to the deep cerebellar nuclei are excitatory”
Thus these items can be replaced with the following that are more compatible with the differential input of a
three-terminal neuron,
4. The output of granule cells are excitatory, terminate on Purkinje, Golgi, and basket cells; in the
absence of any excitation, the Purkinje cells generate individual AP’s at 50-100 pps
(Eccles).
5. The output signal of Purkinje, Golgi and basket cells are all positive-going AP’s & excitatory.
6. The output of basket cells are applied to the inhibitory input of Purkinje cells.
7. Golgi signals are applied to the inhibitory terminal of a mossy fiber-granule cell relay.
8. Mossy and climbing fiber collaterals to the deep cerebellar nuclei are excitatory.
Figure 2.7.7-1 illustrates the area under discussion in the cerebellum. An encircled plus sign near a synapse
indicates an excitatory signal at that location. Conversely, an encircled minus sign near a synapse indicates
an inhibitory signal.
203Ne u ro an a to m y D ep t . at U n i v er si ty o f W i s c on s i n– M a di so n ( 2 00 6 )
http://www.neuroanatomy.wisc.edu/cere/text/P4/folia.htm
278 Neurons & the Nervous System
Figure 2.7.7-1 The anatomy of the cerebellum of human for discussion. Eacg
expanded view beginning at upper left will be explored separately below. From
Univ. Wisconsin–Madison, ca. 2006.
The Neuron 2- 279
Figure 2.7.7-2 illustrates an important relationship not often made in the literature ADD. The Purkinje cells
and their synapses are arranged in planes of finite thickness. The authors note, “You can see that the
dendrites of the Purkinje cells (the most popular cells in the cerebellar cortex) are oriented TRANSVERSE
or perpendicular to the LONG axis of the folium. Spread your fingers out and look at your palm. You are
now looking at how a Purkinje cell dendritic tree looks when the folium is sectioned TRANSVERSE to its
LONG axis.
Now, rotate your hand 90o and see how the dendritic tree of that same Purkinje cell looks when the folium is
sectioned PARALLEL to its LONG axis. Sadly, you do not see the full extent of the Purkinje cell dendritic
tree from this view!! This is shown below.”
Additional details relating to this figure will be introduced in the following subsections.
Figure 2.7.7-2 Perspective view of a folium of the cerebellum showing Purkinje
cells ADD. Note the naming of the Molecular layer has nothing to do with
molecular chemistry. No scale is provided for this figure, allowing a distance
between the Purkinje cells to be determined. See text. From Univ.
Wisconsin–Madison, ca. 2006.
280 Neurons & the Nervous System
2.7.7.1.1 Anatomy of the climbing fibers entering the cerebellum
When discussing climbing fibers, the lecturer at Wisconsin–Madison asserted,
“These fibers go to all parts of the cerebellum, that is, they are not restricted to a particular zone. The
drawing above shows that a climbing fiber sends a collateral to the deep cerebellar nuclei, which is
excitatory, and then "climbs"up and like ivy, entwines and synapses all over the dendrites of the Purkinje
cell. Each Purkinje cell receives input from only 1 climbing fiber axon, but each climbing fiber axon can
split to innervate several Purkinje cells. These climbing fiber-Purkinje cell synapses are excitatory.
Since climbing fibers have synapses all over the dendritic tree of a Purkinje cell, their total excitatory action
is extremely strong. In fact, the synaptic connection between the climbing fiber and the Purkinje cell is one
of the most powerful in the nervous system. A single action potential in a climbing fiber elicits a burst of
action potentials in the Purkinje cells that it contacts. This burst of action potentials exhibited by a Purkinje
cell is called a complex spike. Climbing fibers are "lazy" (but strong), thus Purkinje cells exhibit complex
spikes at a rate of about 1 per second. The illustration above depicts an intracellular recording from a
Purkinje cell that has just been turned on by stimulating the climbing fiber a single time. This single climbing
fiber stimulus has a powerful effect in that it results in 4 action potentials (i.e., complex spike) of varying
amplitudes in the Purkinje cell.”
Figure 2.7.7-3 illustrates the anatomy of the climbing fiber (myelinated axon) of a stage 3 neuron originating
in the Inferior Olivary complex and progressing directly to a Purkinje cell of the Purkinje Layer of a folium
of the cerebellum.
Figure 2.7.7-3 The climbing fibers entering the cerebellum. The complex spike
(action potential) sequence may not be shown properly. Based on Marr, the
stimulating electrode may establish a window for pulses from the dendritic input
to reach the axon of the Purkinje neuron. See text. From Univ.
Wisconsin–Madison, ca. 2006.
The Neuron 2- 281
The climbing fibers entering the cerebellum introduce a new scientific consideration having to do with the
indexing of the presumed database supported by the cerebellum as described by Ito (Section 17.7.2.8).
There is also a question of why the pulses in pulse train shown in the figure are not all of equal height. If the
data is acquired in-vitro, it is likely the electrostenolytic process providing energy to the neuron under test in
the tissue sample is becoming depleted. Alternately, the pulse rate of the stimulus may be too high and is
driving the neuron farther and farther into its refractive state.
Finally, what is the purpose of the Purkinje cell circuits receiving signals from climbing fibers? The
interpretation of the climbing fibers provided above may need to be expanded. Based on Marr (Section
2.10.3.3) and the material in Section 2.10.3, the signals from the climbing fibers and the inferior olive
complex are used to switch the Purkinje neuron circuit into the learning mode from the normal operating
mode. In this mode the climbing fibers provide a wide pulse that acts as a window. This window, when
present, allows one or more pulses from the parallel fibers to establish new memories within a microzone of
the cerebellum by changing the “state” of the cruciform synapses (Section 17.7.2.3).
2.7.7.1.2 Anatomy of the mossy fibers entering the cerebellum
Figure 2.7.7-4 illustrates a Mossy fiber (myelinated axon) of a neuron emanating from one of several
engines of the CNS and entering the granular layer of the cerebellum. The source of the figure notes,
“ Like climbing fibers, the information carried by mossy fibers is heading for the Purkinje cells. However,
unlike climbing fibers, mossy fibers DO NOT go directly to the Purkinje cell.”
Figure 2.7.7-4 The mossy fibers entering the cerebellum ADD. The connection
of analog neurites of each Purkinje cell to pedicles of a single axon of individual
granule cells suggest a synchronization, or reset, function in a memory circuit.
See text. From Univ. Wisconsin–Madison, ca. 2006.
282 Neurons & the Nervous System
Each mossy fiber branches profusely in the white matter. Each of these branches has multiple (up to 50)
swellings (that resembled moss to the old time neuroanatomists) that contain round vesicles and synaptic
thickenings. Each swelling, called a "rosette", is a synapse of the mossy fiber onto the dendrite of a granule
cell. In the detail above you can see two rosettes contacting two different dendrites of the same granule cell.
These are excitatory synapses. A rosette can also occur where the dendrites of several (up to 15) granule
cells are contacted. Each mossy fiber can have up to 50 rosettes.” It is apparent that there is considerable
time divergence of the mossy fiber signal by the time it traverses the parallel fiber and synapses with the
individual Purkinje cells. (Univ Wisconsin) The complexity of the rosettes lead to their frequently being
identified as glomeruli.
Figure C38 from the Wisconsin-Lecture series, shows additional detail. It shows a Golgi cell with neurites
sensing each of the parallel fibers and with an axon synapsing with a mossy fiber rosette. The figure
continues to lack context. Is there just one Golgi cell for a group of granule cells? Does the Golgi cell only
synapse with the first rosette of the mossy fiber? Etc.
2.7.7.1.3 Details of the synaptic structure of the Purkinje cells
The individual neurite traces in the above figures are difficult to interpret due to the complexity of the
rendition. Figure 2.7.7-5 provides an inset not shown in [Figure 2.7.7-1]
The concept displayed is of a climbing fiber with a highly arborized terminal section of its axon. The
arborization of the terminal axon section closely match the arborization of the individual neurites of the
Purkinje cell and synapses occur frequently upon the entangled axon segments and neurites.
Figure 2.7.7-5 Details of the climbing fiber/Purkinje cell interface ADD. See text.
From Univ. of Wisconsin–Madison, ca. 2006).
The Neuron 2- 283
The term dendrite in the inset is taken to represent either a dendrite or podite in the Purkinje cell based on
the Electrolytic Theory of the Neuron of this work (Section 2.1.1). Such a dendrite represents a non-
inverting, or excitatory differential input to the Activa. A podite represents an inverting, or inhibitory
differential input to the Activa. The signal crossing the synapse may be either analog or pulse in this
configuration.
The terms glutamatergic and GABA-ergic are not supported in this work. Glutamate and GABA are major
constituents in the electrostenolytic powering of the neurons (Section 3.2.2). While their relative abundance
near a neuron can influence the operation of the neuron, they have nothing directly to do with the signaling
through the neuron.
The result is thousands, or more, of synapses between the axon segments and the neurites. These neurites
may be either dendrites (constituting a excitatory synapse) or podites (constituting an inhibitory synapse) A
question arises as to the character of the signal impressed on the Purkinje cell. Is the signal so impressed
analog, with the terminal pedicle of the axon acting as the stage 3B decoding element of the stage 3 climbing
fiber (myelinated axon) or does the point where arborization begin constitute a Node of Ranvier acting as the
stage 3B decoding element.
Alternately, are the pulse signals of the terminal segment of the myelinated axon impressed directly on the
neurite at the synapse.
Either of the above choices suggests a very complex summation process associated with each branch of the
neurite tree of the Purkinje cell and ultimately an equally complex summation of all of the neurite branches
at the input terminals of the Activa within the Purkinje cell.
The synaptic structure of [Figure 2.7.7-4] associated with the mossy fibers and granule cells is much
simpler. While the mossy fibers may connect with a large number of granule cells, through unique boutons
on their axons, the signals passed to the individual Purkinje cells through the parallel fibers are much
simpler. It should be noted that the granule cells are represented by an undetailed arborization. The
suggestion from the figure is that the granule cells form a switching signal matrix that is decoding signals
addressing specific memory locations (Section 17.6.3). These locations appear to represent specific neurite
locations along the branchlets within the Purkinje cells.
2.7.7.1.4 Early Simulation of Purkinje cells–Rapp, 1994
Rapp et al204. provided the most comprehensive attempt to model the Purkinje neuron to date. It contains a
great deal of useful morphology. Unfortunately, many of the electrical parameters described rely on the
faulty model of the Purkinje neuron and their lack of understanding of the semiconductor properties of the
synapse between the parallel fibers and the dendrite of the Purkinje neurons (Section 17.7.2).
The thesis and the difficulty of their paper is given in their Introduction,
“The present study is a first step in the construction of plausible models of cerebellar Purkinje cells (PCs)
which are the principal neurones of the cerebellar cortex. These neurones have many fascinating aspects;
they are among thelargest neurones in the mammalian central nervous system (CNS) and have a unique
dendritic arborization. Significantly, the mapping of synaptic inputs is highly specific on their dendrites. The
parallel fibres make excitatory contacts selectively with spines that densely adorn the thin tertiary branchlets.
In terms of numbers of synapses this input is the largest for any known neurone in the CNS; a single PC
contacts more than 100000 parallel fibres. Each PC receives another excitatory input from a single climbing
fibre. This
fibre has several hundred contacts with the thick primary dendrites of the PC, thereby forming a potent
excitatory synapse. Inhibitory inputs arrive from basket and stellate cells. The former tend to contact the
soma and proximal dendrites whereas the latter synapse with the more distal regions of the dendritic tree
(Llinas & Walton, 1990).”
They also present a brief history of the science in their area of investigation and list six findings in their
Abstract. Unfortunately many of the principles noted in the Abstract are obsolete (such as the Rall cable, see
Section 9.1.1.3.1.
However, many of the electrical and morphological parameters are useful when reinterpreted.
204Rapp, M. Segev, I. & Yarom, Y. (1994) Physiology, morphology and detailed passive models of
guinea-pig cerebellar Purkinje cells J Physiol vol 474.1, pp. 101-118
284 Neurons & the Nervous System
Under the heading, Theory, they note their ultimate goal,
“The final goal is to construct a passive electrical model of the cell such that the voltage transient produced
by the model for a given current input would closely match the experimental transients generated by the
same input. In the process of constructing such a model, one tries to constrain the values and distribution of
Ri, Rm and Cm, the specific cytoplasmic and membrane resistivities, and the specific membrane capacitance,
respectively. Briefly, the process starts by implementing the efficient analytical (cable) approach developed
by Rall (1959) to calculate a value for the specific membrane resistivity (Rm) that, for the observed
morphology, fits the experimentally measured RN.”
Their model is based on the chemical model of the neuron, but their physiological models are constrained by
the two-terminal model of the neuron contained therein. The three-terminal of the neuron under “The
Electrolytic Theory of the Neuron,” and the three internal electrical compartments within each neuron solves
many of their problems. The attenuations relating to the axons they modeled are extremely high and
associated with their assumed Rall cable.
Another major problem area, also highlighted under their Theory section involved the use of the archaic
Chemical theory based on Hodgkin & Huxley, HH,
“Somatic (fast) action potentials were simulated by a SPICE circuit using the original Hodgkin & Huxley
(HH) equations and parameters at 20 °C (Bunow et al. 1985). Matching the parameters of the fast sodium
spike that was recorded experimentally (90 mV amplitude, 0-5 ms half-width) to the theoretical spike,
required a decrease in the Na+ inactivation time constant (h) and the K+ activation time constant (n) by a
factor of two.”
A factor of two is an unacceptable value in a Theory section. It is due to the early SPICE program emulating
the archaic chemical theory of the neuron, long espoused by Hodgkin until his death.
See Section 17.6.1.3 for more details concerning the function of the Purkinje neuron within the cerebellum.
2.7.7.1.5 The unusual axonal structure of the Purkinje cells
Section 9.7.1.3 discusses the unusual axonal structure and the associated synaptic arrangements of the
Purkinje neurons of the cerebellum.
2.7.7.2 The neural anatomy relating to the hippocamus EMPTY
2.7.7.2.1 Anatomy of the climbing fibers entering the hippocampus EMPTY
2.7.7.2.2 Anatomy of the mossy fibers entering the hippocampus
Henze et al. has developed the multifarious roles of mossy fibers in the hippocampus205. In section 5, they
note,
“WHAT IS THE FUNCTIONAL ROLE OF THE MOSSY FIBERS?
From the studies described above, it is clear that the hippocampal MF synapse has many properties that
make it unique among cortical synapses. Thus, the question is raised, do these unique properties indicate a
unique functional role for the MF synapse? The large synaptic terminals, proximal dendritic location,
large frequency facilitation, and large mean (or median) EPSP/C size all suggest that MF synapses
are designed to have a higher net probability of release than most other cortical synapses. That is,
whenever a GC fires, a limited group of hilar cells, CA3 pyramidal cells and CA3 interneurons that receive
input from that GC all experience some amount of depolarization. However, the role of this
depolarization in modulating the output of the target cells remains a matter of debate.”
205Henze, D. Urban, N. & Barrionuevo, G. (2000) the Multifarious Hippocampal Mossy Fiber Pathway: a
Review Neuroscience vol 98(3), pp 407–427
The Neuron 2- 285
The section goes on to discuss a multitude of possible options. Their section 6, Conclusions, is also worthy
of closer study.
Rollenhagen & Lubke have addressed the boutons associated with these specific mossy fibers from the
histological perspective206. The paper does provide considerable numerical and spatial data but no
schematics. They noted, “Only recently the structural geometry of a synapse embedded in a higher cortical
microcircuit, the hippocampal mossy fiber bouton (MFB)-CA3 pyramidal cell synapse, has described in
great detail (Rollenhagen et al., 2007a). In particular, those structural subelements relevant for synaptic
transmission and plasticity at the MFB-CA3 pyramidal cell synapse have been investigated using
computer-assisted 3D-reconstructions of serial electron micro-scopic images and subsequent quantitative
analysis based on serial ultrathin sections through individual MFBs.” Some of their electron microscope
images show electrical charge buildup at the locations of synapses but they do not discuss these charged
areas.
2.7.7.2.3 Mossy fiber sprouting & recurrent excitation in the hippocampus
The material in this section may suggest how memories are formed, stored and altered and will be explored
more fully in Section 17.6.3.
Dudek & Shao have provided a commentary on mossy fiber sprouting in the context of epilepsy207 in
reviewing a paper by Scharfman et al208 on the same subject. How this phenomenon, clearly in the
exploratory research phase and found in epilepsy, might contribute to memory creation is not known at this
time.
Scharfman et al. conclude their paper with, “Therefore one would predict that the net effect of mossy fiber
sprouting will only become clear when we understand the nature and the number of recurrent synapses, not
just among granule cells, but also synaptic reorganization among other dentate neurons. Furthermore, it will
be necessary to understand the impact of other changes in the epileptic brain, including alterations in axonal
structure and neurotransmitters/neuromodulators.”
Buckmaster has provided a massive volume, with extensive bibliography, describing mossy fiber sprouting
in the dentate gyrus209. He notes a variety of situations where the degree of sprouting increases with age
among children. However, he makes it clear that “Mechanisms underlying mossy fiber sprouting remain
unclear, but available evidence suggests likely triggers.” He then lists a variety of potential mechanisms
and/or reasons for such sprouting. Some are compatible with the growth of memory. Under the heading,
“How Does Mossy Fiber Sprouting Develop?” Buckmaster provides a wealth of information concerning the
density of such fibers and associated elements. An interesting comment is, “Overall, there is considerable
anatomical evidence that mossy fiber sprouting creates a positive-feedback circuit among granule cells.”
This phenomenon could be a key to forming “latches” such as are used to create latching relays, a form of
memory in electronic circuits.
2.7.7.2.4 Details of the synaptic structure of the Purkinje cells EDIT
2.8 Other important features of neurons and neural paths EMPTY
Several important features of neural architecture have not been addressed in previous sections. The same is
true of certain morphological features of individual neurons. These features are addressed here for
206Rollenhagen, A. & Lubke, J. (2010) The mossy fi ber bouton: the “common” or the “unique” synapse? Front
Synaptic Neurosci pp 1-9 doi: 10.3389/fnsyn.2010.00002
207Dudek, F. & Shao, L-R. (2004) Mossy Fiber Sprouting and Recurrent Excitation: Direct Electrophysiologic
Evidence and Potential Implications Epilepsy Curr vol 4(5), pp 184-187
208Sharfman, H. Sollas, A. Berger, R. & Goodman, J. (2003) Electrophysiological Evidence of Monosynaptic
Excitatory Transmission between Granule Cells after Seizure-induced Mossy Fiber Sprouting J Neurophysiol
vol 90, pp 2536-2547
209 Buckmaster, P. (2012) Mossy Fiber Sprouting in the Dentate Gyrus in Jasper's Basic Mechanisms of the
Epilepsies [Internet]. 4th edition
286 Neurons & the Nervous System
completeness. In some cases, references to other sections developing these ideas in greater detail are
provided.
2.8.1 Merging and bifurcating signal paths
The above discussion provides a variety of tools that can be used to discuss the merging and bifurcation of
signal paths. Where the merging or bifurcation only employs a synapse, no regeneration is involved. The
action of the circuit relies upon the following circuit elements. Alternately, if a hybrid neuron is used as the
core of the merging or bifurcation process, several situations are possible. Complete description of all of the
options available in both the analog and pulse domain is not called for here.
The literature suggests that all of the presynaptic axoplasms associated with the merging of signals can be
represented by a voltage source. This appears to be true in both the analog and pulse domains.
2.8.1.1 Merging and bifurcation in the analog signal domain
The merging of the signals from two or more axoplasms via synapses into a single neuroplasm is primarily a
matter of the impedance of the individual synapses relative to the input impedance of the Activa in the post
synapse circuit. In the analog domain, the result is straight forward and amounts to a summation or a
differencing of signals as indicated above. In the case of bifurcation, the situation is similar. If the output of
the presynaptic axoplasm is of low impedance, it can act as a voltage source and support any reasonable
number of synapses without introducing crosstalk due to circuit loading.
2.8.1.2 Merging and bifurcation in the pulse signal domain
In the pulse domain, the merging of the signals from two or more axoplasms via synapses into a single
neuroplasm can be as simple as the analog case. However, there are more options. The options vary with a
variety of circuit element impedances and ratios of impedances. They also depend on the refractory state of
the subsequent action potential generator or regenerator. In the simplest case, the two pulse streams would
merely be merged. The merged pulse streams would then be regenerated by the next Node of Ranvier. This
would result in a single pulse stream. However, if the following regeneration circuit exhibits a significant
refractory period, the pulse train might be significantly distorted. It is not clear what significance this option
would have from an information theory perspective. In a second option, the two pulse streams could be
decoded in a post synaptic hybrid neuron circuit, either summed or differenced and a new pulse stream
generated. This pulse stream would appear orderly and could represent the difference between two signaling
channels. This appears to be the situation, with possibly additional signal manipulation, that happens in the
LGN and the Pretectum of the mid-brain before the signals are sent on to the cortex. A third option would
be where the two pulse streams are applied to two input terminals of a projection neuron without decoding.
In this case, the output would be strongly influenced by the refractory period of the projection neuron. The
output pulse stream would be subject to significant distortion, including what might be called inhibition. The
integrity of the information content of such a pulse stream would be questionable.
2.8.2 Relationship of nuclei to conduits and sheaths
As indicated earlier, while the neuron is considered the fundamental morphological unit of the neural system,
it is not the fundamental functional element of the neural system. The fundamental functional structure is a
series of interdigitated conduits and active electrolytic semiconducting devices. The nuclei and supporting
metabolic elements of a cell are able to support a variable number of conduits and active devices based on
topographic considerations. The presence of multiple Nodes of Ranvier is the quintessential example of this
situation. Thus, the number of neurons is not directly related to the number of functional units in the neural
system.
The method of providing myelin wrapping to a (generally axonal) conduit also differs from a one-to-one
relationship. The terminology is also somewhat convoluted in this area. In the peripheral nervous system,
the myelin is provided by Schwann cells. In the CNS, it is provided by oligodendroglia cells. The
difference between these two cell types may be significant. It appears an individual Schwann cell only forms
myelin around one axon segment; whereas, an individual oligodendroglia may provides multiple myelin
The Neuron 2- 287
segments that enclose multiple axon segment of distinctly different neurons. Figure 5.2 in Matthews210 and
the comments of Afifi & Bergman211 are consistent with this description of the Schwann cells.
2.8.3 Biasing and the non-uniformity of axoplasm potential
The previous discussion has not concentrated on the precise voltage of the plasma within a given conduit
when discussing the biasing of the Activa for two reasons. First, the precision required in specifying these
potentials is not supported by the literature. A change of only a few millivolts can be significant when the
average potential difference is less than 100 millivolts. Second, there is a difference in potential between the
two ends of most conduits. Although the plasma does not exhibit a significant dissipative resistance, it does
exhibit a significant time delay in the propagation of a potential from one end to the other. Thus, the two
ends of a plasma are typically at different average potentials. This allows the bias voltage applied to an
Activa at one end of a conduit to be different from the bias voltage applied to an Activa at the other end.
To specify the actual quiescent bias levels of each node of a multi-stage direct coupled electrolytic circuit
requires considerable precision and very careful measurement.
2.8.4 Confirmation of the physical circuit and analytical models
Two papers by Schwarz and colleagues provide excellent support for the physical and analytical models of
this work. Unfortunately they use the euphemism, Na current, to represent the discharge current through the
collector-poditic circuit of the Activa. They also identified voltage dependent potassium currents as
euphemisms for the recharging current passing through the collector impedance of the axon.
They also attempted to fit a simple exponential decay equation to the decay portion of their action potentials
and generator potentials. Their difficulty is explained by the more appropriate models and equations of this
work.
The 1987 paper of Schwarz, Reid & Bostok & Eikhof212 provides a remarkable set of figures confirming the
models of the neuron developed in this chapter apply to a variety of neurons in the rat. Figure 1 shows
action potentials including their pre-threshold portion in excellent agreement with the predicted values as a
function of temperature. Figure 2 shows the non-oscillatory current responses (equivalent to generator
potentials) in response to long voltage pulses. The waveforms exhibit distinctly different leading and trailing
edge time constants except for the Hodgkin Condition where the overall waveform corresponds to the
Poisson Equation of the 2nd kind. All of the waveforms are as predicted by the excitation/de-excitation
equation (Eq. 2.5.3-1 of Section 2.5.3.5). Figure 3 shows the static current versus voltage characteristic for
one of their neurons for both the zero poditic impedance condition and the finite poditic impedance
condition. It is equivalent to [Figure 2.3.3-2 of this work.
The 1995 paper of Schwarz, Reid & Bostok213 provides a remarkable set of figures confirming the models of
the neuron developed in this chapter apply to the human Node of Ranvier. Their figure 2( C) provides a
static current versus voltage characteristic for the analog neuron with and without feedback in the poditic
circuit path. The figure is virtually identical to that of [Figure 2.3.3-2 in Section 2.3.3 developed based on
first principles and well accepted semiconductor physics practice.
Their figure 2(B) illustrates the response of a real neuron to parametric stimulation in the absence of
significant impedance in the poditic circuit path. The waveforms of (a) are precisely as developed using the
closed form analytic equations of Section 2.5.3.5 for a temperature of 20C.
Their figure 2(A) shows their measured action potential (including the pre-threshold portion) resulting from
the monopulse oscillation of their neuron. The figure is in excellent agreement with the same characteristic
developed from first principles in Section 2.6.1.1.
210Matthews, G. (1991) Cellular physiology of nerve and muscle. Boston, MA: Blackwell Scientific
Publications. pg. 61
211Afifi, A. & Bergman, R. (1998) Functional neuroanatomy. NY: McGraw-Hill pg. 19
212Schwarz, J. & Eikhof, G. (1987) Na currents and action potentials in rat myelinated nerve fibres at 20 and
37 C. Pflugers Archive--European Journal of Physiology. vol. 409, pp. 569-577
213Schwarz, J. Reid, G. & Bostock, H. (1995) Potentials and membrane currents in the human node of Ranvier
Eur J Physiol vol 430, pp 283-292
288 Neurons & the Nervous System
All of the Schwars and colleagues data, and most of the other data cited above was obtained by electrolytic
stimulation via patch clamp experiments. This fact demonstrates that the neural system can operate
entirely independent of any chemical reactions other than those associated with generating the electrical
power to drive the neuron(s). Although they use the Na current euphemism, they did not in fact observe any
currents identifiable as based on Na ions.
2.8.4.1 Confirmation of the switching characteristic of the oscillating neuron
The use of the binary switching functions, h, m & n in the unsolved partial differential equations developed
by Hodgkin & Huxley, and used by most subsequent modelers, introduce switching points that are not
otherwise identified in their numerical integrations. These switching points are the same as those defined by
explicit events in the Electrolytic model of the neuron.
2.8.5 Specialized regions of outer lemma of a neuron
Multiple special areas of the outer lemma of neurons are recognized. These support the receptor function of
sensory receptors, the electrostenolytic function providing electrical power to all neurons (and potentiation
of all biological cells in general), and the formation of both the upstream and downstream portions of
synapses and Nodes of Ranvier. From the perspective of neuroanatomy, these regions have frequently been
described as rafts on the lipid surface of the outer bilayer of lemma214. At the conference, the cited article
arrived at a consensus definition of a raft as,
“Membrane rafts are small (10–200 nm), heterogeneous, highly dynamic, sterol- and sphingolipid-enriched
domains that compartmentalize cellular processes.” The report went on, “This definition was arrived at by
listing all possible terms that could be used to describe lipid rafts, discussing and prioritizing them, and then
working them into a definition for these domains. The terms that did not make it into the definition are at
least as revealing of the state of the field as are the terms that did make the final cut. The definition is
intended to apply specifically to micro-domains in cells, not in model membranes, which are thought to be
governed by a different, but overlapping, set of rules.” The classes of lipids named in the definition can now
be extended to include a variety of phospholipids esterifiec with a variety of amino acids in support of the
reception function of sensory neurons and electrostenolytics.
The paper provides an excellent view of the problems a committee of scientists face when trying to arrive at
a consensus.
Neishabouri & Faisal discussed salutatory conduction with respect to their concept of lipid rafts215. Their
conceptual framework is limited in they do not differentiate between analog type generator potentials and
pulse type action potentials, grouping them as action potentials. They even quote Hodgkin and Huxley,
1952, who made a similar mistake, as a principle source of information. They note, “Saltatory
conduction(Huxley and Stämpfli,1949; Fitzhugh,1962) in myelinated axons refers to the rapid propagation
of the electrical waveform from each node to the next (the AP seems to jump between nodes).” Clearly, they
do not understand how the action potential is propagated from one node to the next. See Sections 9.1.1 &
9.1.2. The Introduction to their paper includes an inordinately high number of equivocating adjectives and
verbs.
They define a variety of cellular surface features such as “C-fibers are very thin unmyelinated peripheral
axons responsible for transmitting nociceptive pain sensations. A variety of Na+ channels are found on the
membrane of C-fibers, including TTX-sensitive Nav1.6 and Nav1.7 channels.” Their focus appears to be on
the proposed sodium channels of Hodgkin & Huxley, even though such channels have not been identified to
date, even with the advent of atomic force microscopy (AFM) in recent years.
Their effort focused on computational modeling, “We investigated the effects of the lipid-raft clustering of
Na+ channels on the function of neural fibers, using both deterministic and stochastic simulations. In
stochastic simulations, the changes of conformations of ion channels were individually modeled.” Their
modeling resulted in an unusual finding. They predict action potentials of different temporal and physical
214Pike, L. (2006) Rafts defined: a report on the Keystone symposium on lipid rafts and cell function J Lipid
Res volume 47, pp 1597-1598
215Neishabouri, A. & Faisal, A. (2014) Saltatory conduction in unmyelinated axons: clustering of Na+ channels
on lipid rafts enables micro-saltatory conduction in C-fibers Front Neuroanat 10 pages, |
http://dx.doi.org/10.3389/fnana.2014.00109
The Neuron 2- 289
characteristics depending on their location, ostensibly as a metabolic energy saving feature. They do note
some difficulties with their protocol, “Due to their very small diameter, it is extremely difficult to obtain
intracellular data from C-fibers, and therefore we can only estimate the propagation velocity in these fibers
using extra cellular recordings (Tigerholmetal.,2014). These estimations can not be reliably linked to
axonal diameter. C-fiber axons are known for their very low conduction velocities. The conduction velocity
is estimated to be 69cms-1 for a 0.25μm diameter axon.”
Many of their simulated and recorded action potentials are actually generator potentials based on the
distinctive features found in the E/D responses and equations of this work, particularly the variable temporal
period of the waveforms with excitation. Recognizing their action potential are frequently actually generator
potentials (see the “recorded AP” in their figure 2), their assertion, “Because there is no myelin sheath
around C-fiber axons, the membrane capacitance and leak conductance are too high for Na+ clusters to be
placed at distances on the order of the axon’s length constant( 200μm). In our simulations, the maximum
distance Lmax between lipid rafts which allowed action potential [actually a generator potential] propagation
was ~20μm.” appears totally appropriate. They close with the equally rational statement, “This is in stark
contrast with myelinated axons, where the myelin sheath lowers the capacitance and leak conductance of the
membrane. As a result, nodes of Ranvier can be placed much further apart.”
The contribution of the Neishabouri & Faisal paper to the understanding of the almost totally deterministic
features of the neural system is minimal.
2.8.6 Neural pathway genesis and growth cones
The mechanism by which neurons establish a path between the antidromic origin and orthodromic
termination point remains in a highly speculative state. A special issue of Current Opinion in Neurobiology
(2005) summarizes this situation. A paper by Kalil & Dent in that issue sets the current research focus on
the subject matter216. Their abstract begins;
Growth cones, the highly motile tips of growing axons, guide axons to their targets by responding to
molecular cues. Growth cone behaviors such as advancing, retracting, turning and branching are driven by
the dynamics and reorganization of the actin and microtubule cytoskeleton through signaling pathways
linked to guidance cue receptors.
Their paper says little about how the actual neuron pathway is represented to the individual neuron. They
provide several cartoons containing few if any specifics. They describe growth path cues by plus symbols in
the environment external to the axon of a neuron. The paper is rife with expressions incorporating the words
“could,” “might” and “may.”
As of 2005, they note, “Understanding how guidance cues regulate microtubules through their association
with tip proteins awaits further studies in living growth cones.”
Their Conclusion section begins, “In neuronal growth cones the actin and microtubule cytoskeleton is the
ultimate target of signaling pathways from extracellular guidance cues. As we have discussed, our
understanding of how guidance cues modulate the dynamics of actin filaments and microtubules in addition
to regulating the interactions between these two filament
systems is far from complete. Furthermore, as exemplified by the puzzling differences between neurons and
non-neuronal cells, the mechanisms by which changes in cytoskeletal organization and dynamics lead to cell
motility are still controversial.”
Jang et al., writing in 2010 provided a somewhat broader context but still did not describe the method of
pathway identification that a neuron is intended to follow during neurogenesis217. “Here we explore the
topographical cues that are present in the extracellular matrix (ECM) in vivo and how ECM nanotopography
influences neurite outgrowth.” They go on,
“The mechanisms by which nanotopographic ECM cues influence differentiation appear to involve changes
in cytoskeletal organization and structure, potentially in response to the geometry and size of the underlying
216Kalil, K. & Dent, E. (2005) Touch and go: guidance cues signal to the growth cone cytoskeleton Cur Opin
Neurobiol vol 15, pp 521-526
217Jang, K-J. Kim, M. Feltrin, D. et al. (2010) Two Distinct Filopodia Populations at the Growth Cone Allow
to Sense Nanotopographical Extracellular Matrix Cues to Guide Neurite Outgrowth PLoS ONE vol 5(12):
e15966. doi:10.1371/journal.pone.0015966
290 Neurons & the Nervous System
features of the ECM. This might influence the clustering of integrins in focal adhesions and the formation of
actin stress fibers, and thus the adhesion and spreading of cells. Secondary effects, such as alterations in the
effective stiffness perceived by the cell or differences in protein adsorption due to the structural features of
the substrate are also possible [14]. However, the cellular mechanisms of cell fate control by ECM
nanotopography remain largely unexplored.”
Jang et al. employed engine-ruled 3D substrates to encourage neuronal growth along the fine groves of the
resulting substrates. Such substrates hardly model the natural in-vivo environment for neurogenesis.
By 2013, Sur et al. have made some progress218. Their Abstract begins, “The mechanical properties of the
extracellular matrix (ECM) are known to influence neuronal differentiation and maturation, though the
mechanism by which neuronal cells respond to these biophysical cues is not completely understood. Here we
design ECM mimics using self-assembled peptide nanofibers, in which fiber rigidity is tailored by
supramolecular interactions, in order to investigate the relationship between matrix stiffness and
morphological development of hippocampal neurons.”
They do begin to investigate substrates of organic origins.
Wanner & Prince provide more recent information219. Their abstract begins;
“Appropriate localization of neurons within the brain is a crucial component of the establishment of neural
circuitry. In the zebrafish hindbrain, the facial branchiomotor neurons (FBMNs) undergo a chain-like
tangential migration from their birthplace in rhombomere (r) 4 to their final destination in r6/r7. Here, we
report that ablation of either the cell body or the trailing axon of the leading FBMN, or ‘pioneer’ neuron,
blocks the migration of follower FBMNs into r5. This demonstrates that the pioneer neuron and its axon are
crucial to the early migration of FBMNs. Later migration from r5 to r6 is not dependent on pioneer neurons
but on the medial longitudinal fasciculus (MLF), a bundle of axons lying ventral to the FBMNs.”
Their Introduction begins;
“Migration of neurons from their birthplace to their final destination is central to the formation and proper
wiring of nervous system circuitry. Understanding how neurons successfully navigate to their proper targets
is important because defects in neuronal migration can result in human neurological diseases.”
However, their paper begs the question what led the pioneer neuron into its proper position?
They conclude with;
“However, migration of pioneer neurons requires neither Cdh2 (N-cadherin) nor interactions with the MLF,
suggesting that pioneer neurons migrate using a separate mechanism to all other FBMNs.”
Plazas, Nicol & Spitzer introduced a potential electronic mechanism into neurogenesis220.
“The role of electrical activity in axon guidance has been extensively studied in vitro. To better
understand its role in the intact nervous system, we imaged intracellular Ca2+ in zebrafish primary motor
neurons (PMN) during axon pathfinding in vivo.” They went on, “Our results provide an in vivo
demonstration of the intersection of spontaneous electrical activity with the PlexinA3 guidance molecule
receptor in regulation of axon pathfinding.” They conclude, “The mechanisms underlying such
regulation remain unclear, but the response of neurons to chemotropic molecules in vitro is modulated by
electrical activity.”
2.8.6.1 ADD Potential neurogenesis mechanisms EMPTY
218Sur, S. Newcomb, C. Webber, M. & Stupp, S. (2013) Tuning supramolecular mechanics to guide neuron
development Biomaterials vol 34(20), pp 4749–4757
219Wanner, S. & Prince, V. (2013) Axon tracts guide zebrafish facial branchiomotor neuron migration through
the hindbrain Development vol 140, pp 906-915; doi: 10.1242/dev.087148
220Plazas, P. Nicol, X. & Spitzer, N. ( Activity-dependent competition regulates motor neuron axon pathfinding
via PlexinA3 PNAS vol. 110(4), pp 1524–1529, doi: 10.1073/pnas.1213048110
The Neuron 2- 291
2.9 Mathematical and computer modeling of neurons
The present state of mathematical and computer (numerical) modeling of neurons is unsatisfactory. All
modeling found in the literature prior to 21012 has attempted to model the very early conceptual
descriptions of a neuron by Hodgkin & Huxley based on examination in-vitro of a parametrically
stimulated and highly mutilated neuron from a species of Mollusca. Such modeling has not recognized
the special class of the so-called giant axon of the locomotion neuron explored by Hodgkin & Huxley.
2.9.1 Modeling difficulties up to the current day
Carnevale & Hines have provided an excellent discussion on “Why model?” They note, “In order to
achieve the ultimate goal of understanding how nervous systems work, it will be necessary to know many
different kinds of information” related to the anatomy, pharmacology, biochemistry and many related
sciences. They develop the complexities involved in describing the mechanisms involved and the
features of signaling and one paragraph and then go on to assert,
“Hypotheses about these signals and mechanism, and how nervous system function emerges from their
operation, cannot be evaluated by intuition alone, but require empirically based modeling.”
They use a simpler version of Figure 2.9.1-1 to address “Just what is involved in creating a . . . model of
a physical system?” There are several approaches including physical circuit modeling, analytical
modeling and numerical modeling. Based on a two-terminal neuron evolving from Hodgkin and Huxley
(H&H), there has not been adequate knowledge of the neuron to allow realistic physical circuit modeling.
Similarly relying on the equations developed by H&H during their exploratory investigations of 60 years
ago has not led to adequate analytical or computational models. Recent analytical and computational
models have frequently not examined whether the equations of H&H even address the generic neuron or
are only an attempt to describe a specific type of neuron. Thus the notation in the figure. It is necessary
that the modeler strain to understand what is actually known about his subject and only then attempt to
simplify his conceptual model (hopefully by stating a clear null hypothesis he intends to explore). Once a
clear null hypothesis is established, it is important to be faithful to the Scientific Method when evaluating
the physical, analytical, computational or other model of the system.
During the 1950's, the label “action potential” was not clearly defined (Section 6.3.2). It was frequently
applied to any pulse-like response to almost any stimulation. This included the stimulation of a stage 1
signal generating neuron in response to a short pulse as well as a stage 3 Node of Ranvier regenerating a
pulse designed to be identical in shape to the action potential exciting it. The former is not identified as
an analog waveform describing the excitation/de-excitation mechanism intrinsic to the sensory neurons
Figure 2.9.1-1 Framework for modeling the neuron ADD. The Conceptual and
Physical circuit models are developed in Section 2.7.5. The analytical model
is developed throughout this Chapter. Any Computational model should avoid
the use of transcendental mathematics which are not used in the actual
Physical System. Annotated from Carnevale & Hines, 2006.
292 Neurons & the Nervous System
only. The latter is now identified with the encoding and regenerating pulse neurons of stage 3. These
waveforms arise from substantially different mechanisms in substantially differently configured neurons.
The waveforms reported by Hodgkin & Huxley clearly reflect the above problem with definitions. The
neuron they studies was of a special class generally described as a locomotion waveform generator. It is
neither a stage 1 signal generating neuron nor a stage 3 signal projection neuron (with a requisite
myelinated axon). It is in fact a modified stage 6 command generation neuron implemented as a tapped
analog delay line. As such, it does not generate action potentials. The responses H&H recorded were
actually parametrically stimulated analog waveforms after the removal of all neuritic tissue to the best of
their ability.
2.9.1.1 Major problems with the McCulloch & Pitts mathematical neuron
As recently as 2007, Baars & Gage have published an introductory textbook on neuroscience that
includes no material on the operation of the fundamental neuron and presents a conventional model of the
neuron in Appendix A that was used in forming simple networks (that failed so badly during the artificial
intelligence (AI) fervor of the 1990's. They focused on the McCulloch & Pitts model of 1943 and
noted McCulloch was a physician and Pitts was a self-taught logician. This model illustrates the basic
flaw that has hampered neural research ever since that time. It treats the neuron as a two-port digital
input/digital output summing device as shown in Figure 2.9.1-2(A). In their model, Xn were all digital
signals of either 0 or 1. Wn were scalar weighting factors between 0 and 1.0 or 0 and –1.0. There was a
thresholding function, , within their neuron that created a signal of +1 whenever A exceeded a threshold
level. Otherwise the output remained at 0.
The situation in 1943 involves many difficulties when viewed from a modern perspective;
• Neither McCullock or Pitts had any training in electronics or electrophysiology.
• The age of the digital computer had not yet dawned (Turing was only conceiving it in England under
highly secret circumstances.
• Feedback theory as it applies to oscillators was in its infancy (The Radiation Laboratory of MIT down
the street from their laboratory was developing the theory at that time under highly secret conditions.
• Hodgkin & Huxley had not published their electrophysiology data on the neuron (They were working in
London at the same time under wartime conditions.
• The invention of the transistor at Bell Laboratories was five years in the future.
The critical role of myelination in the operation of stage 3 neurons was totally unknown.
• McCulloch & Pitts were unaware that over 90% of the neurons did not generate action potentials
(Section 2.5).
• McCullock & Pitts were unaware the neural system was asynchronous and used return to zero (RZ)
pulse coding rather than binary coding.
As a result, the McCulloch & Pitts model is that of a binary logic unit but not that of a fundamental
(analog) neuron or its extended RZ pulse forming variant. As a model of a neuron, the McCulloch &
Pitts model is totally falsifiable in the (translated) language of Popper. The mathematical example on
pages 456-457 of Baars & Gage has no relevance to a real neuron. In fact, their artist’s impression of a
neuron on page 455 requires expansion to show a bilateral dendritic tree if they are to address the
general case. The material on pages 457-459 related to “Learning in a Neuron” is total conjecture on the
part of the author’s. The example they give may apply to a logic unit with many arbitrarily adjustable
parameters but it is irrelevant to neuron operation.
Recall, Baars & Gage limited their textbook to the exploration of pulse neurons (page 60), thereby
overlooking more than 90% of the actual neurons of the neural system.
Baars & Gage dropped the entire Appendix A written by Aleksander, including all references to the
McCulloch & Pitts model of 1943, from their 2010 edition. They also dropped the simplified neuron
presented by Aleksander without citation. It is expected this was done to allow more modern views
relating to the neuron to be presented in the main text. On page 65 of the 2010 edition, Baars & Gage
present a neuron (page 65) from Byrne & Roberts of 2004 that is more elaborate but continues to follow
their stated objective (page 64) “to focus only on an integrate and fire neuron.”
2.9.1.2 An alternate realistic model of the mathematical neuron
Baars, writing in Baars & Gage, has made a major statement that is best introduced by an allegory;
The Neuron 2- 293
The academic neuorscience community has just placed its toe in the waters of real neuroscience when
Baars noted (page 62, 2007), “It is now known that electrical synapses, which use no neurotransmitter al
all, are much more common than was previously believed. Even the dendrites of a single nerve cell may
be able to compute useful information. . . Other surprises keep coming.”
As a matter of fact, virtually all synapses (greater than 95%) are electrolytic (the precise form of
electronic) synapses. Furthermore they are three-terminal electrolytic devices (like the Activa within the
neuron) that are sometimes wired to emulate an active diode (a two-terminal device). And, the role of the
“neurotransmitters” glutamic acid and GABA is to power the neuron or synapse. They act as neuro-
facilatator and neuro-inhibitor respectively.
Although Baars reverts nearly instantly to the common wisdom, his including the above statement shows
the winds are changing.
This paragraph will be repeated and expanded upon in Section 2.4 on the synapse.
This work is based entirely on the electrolytic neuron paradigm. It is proposed that the neural system is
fundamentally an electrolytic system and that inter-neuron signaling is by electrical means. Only in the
case of paracrine, endocrine and exocrine signaling are chemical signaling important. These activities
are found at the termini of the neural system. Furthermore, the neuron within the neural system contains a
biological equivalent of a transistor (an Activa) and is fundamentally an analog device.
Figure 2.9.1-2(B) shows two variants of a more realistic model of the fundamental neuron. It is a three-
terminal device with a bi-stratified input structure consisting of the well known dendritic tree (typically
the apical tree) and the less well known poditic tree (typically the circumferential tree), and a well known
axon output structure ( a single long structure bifurcating a few times near its terminus). Depending on
the requirements on the neuron, either the dendritic tree or the poditic tree may be minimized
morphologically, but its presence is easily recognized by plotting the electrolytic potentials of the fluid
surrounding the neuron. Similarly, the axon need not extend outside of the soma of the real neuron but its
presence is easily demonstrated by recording the electrical potentials of the fluid surrounding the neuron.
Whereas in (A) the values for Wn are scalar
values, in the real neural circuit, as well as the
model in (B), the values for Zn are complex
numbers describing transfer function of a filter
circuit between the synapse and the summation
terminal of the neuron. In (A) the threshold,
theta, is set by an unknown mechanism
(Aleksander, writing in Baars & Gage, suggest
it is set by some sort of iterative learning
process of unknown mechanism to this day). In
(B, right) the threshold, theta, is set by the
fixed bias applied to the dendrite to podite
potential (Vdp) described in detail in following
sections of this work. Zfb is the feedback
impedance from the axon to the dendritic
terminal of the internal Activa (the biological
transistor described in detail below). This
impedance has a complex value involving
significant phase shift.
The circuit on the left in (B) represents the
nominal neuron (greater than 90% of the
population) generating an analog output as the
result of multiple analog inputs (where all Yn
are positive-going signals). The output is a
biphasic analog signal resulting from the
algebraic summation shown multiplied by an
amplification factor (typically varying from less
than one to about 200:1 depending on the
application). The analog output has the same
phase as the signal applied to the dendritic
input.
Figure 2.9.1-2 The falsifiable model of
McCulloch & Pitts (A) vs a realistic model
(B) of two neuron configurations. Theta
has a different meaning in the two frames
and an external feedback path is not
actually used in physical neurons. See
text. Modified from Baars & Gage, 2007.
294 Neurons & the Nervous System
The same fundamental model on the left in (B) can be converted to a stage 3 neuron by the application of
a feedback mechanism as shown on the right. By setting the value of Zfb and the bias voltage, Vdp, at the
time of morphogenesis, the RZ pulse generating performance of the stage 3 neuron is determined. For
pedagogical purposes, Zfb is shown in an external feedback path to the dendritic input which does not
actually exist. This representation has caused difficulties in the laboratory because naive investigators
have sought endlessly to locate the feedback path. The feedback is achieved by an internal path not
subject to isolation in the laboratory. Its performance is easily demonstrated by means of the transfer
function of the complete circuit (Section 2.6.2).
The initial treatment of the morphogenesis of the neuron will necessarily be relatively conceptual. The
morphogenesis of the complete neuron is beyond the scope of this work. However, there appears to be
little argument as to how neurons are formed. This chapter relies upon the characteristics of the
biological lemma developed in Chapter 1. See Section 3.1.5 of “Processes in Hearing: A 21st Century
Paradigm” by this author for additional discussion.
The simple neural models in (B) can be definitized to any degree required using the models of transistor
action applied to man-made transistors introduced in Section 2.2.3. With the acceptance of a three-
terminal neuron as discussed in this chapter, there is no reason for mathematical modelers to use curve
fitting techniques applied to the conceptual curves presented by Hodgkin and Huxley and elaborated
upon by many later modelers.
2.9.2 Major problems with subsequent mathematical neurons
Efforts to model the biological neuron effectively have taken drastically different paths over the years.
Some have attempted to expand on the totally mathematical approach of McCulloch & Pitts introduced
above. Others have proceeded to frame their models on the empirically based work of Hodgkin &
Huxley from the same time period. These models have generally adopted the (unsolved) differential
equations of H&H, expanded them in various ways to make them more tractable and then continued to
solve the expanded equations by numerical integration.
These models have invariably accepted the two-terminal model of the neuron presented by H&H in their
extensive reports and conjectures of 1952221. The two-terminal chemical model is untenable in
competition with the three-terminal electrolytic model
2.9.2.1 Analytical models spanning the last 60 years
Within the mathematical community, little attention has been paid to the evolution of separate and more
detailed definitions of the generator potential and action potential subsequent to the work of H&H. The
short comings of the H&H equations have been long recognized in the analytical modeling community.
However, by continuing to consider the two-terminal model of the neuron circuit, little real progress has
been made. A significant problem is the dimensional order of the subsequent models. They vary from
fewer dimensions than H&H to a considerably larger number of dimensions, all generally following an
exploratory approach. Byrne & Roberts (page 192) summarized the various analytical approaches in
more detail than here.
One of the earliest was the FitzHugh-Nagumo model of the 1960's. This model made no claim to
quantitative relevance and adopted a generic cubic equation as an initial function from which the results
of H&H could be fitted. The variable in this cubic was defined as the membrane potential of a two-
terminal neuron.
During the 1970's and 1980's, the Morris-Lecar qualitative model appeared. It differed little from the
fundamental H&H equations but made a series of different assumptions. These assumptions suggested
different mathematical manipulations and led to the possibility of a Hopf bifurcation as a mechanism of
action potential generation. This model remains a subject of study, however, it does not address many of
the fundamental properties of the real neuron such as their temperature sensitivity, the sensitivity of the
shape of the action potential to the amplitude of the stimulus or the delay associated with the stimulus
amplitude and temperature.
The Hindmarsh–Rose model of the 1980's was similar to the FitzHugh-Nagumo model and was
ostensibly derived from first principles (although these were not stated to this author’s satisfaction).
221Hodgkin, A. Huxley, A. & Katz, B. (1952) Measurement of current-voltage relations in the membrane of the
giant axon of Loligo. J. Physiol. vol 116, pp. 424-448
The Neuron 2- 295
They began with a cubic equation of somewhat more general form involving two (unsolved) differential
equations and about ten arbitrary constants. This number of arbitrary constants should allow a cubic
equation to fit almost any arbitrary waveform. This model has more recently been expanded into a
“three-dimensional model.”
None of these analytical models are in fact representative of the general equations and waveforms of
H&H. They at best attempt to fit the degenerate form of the H&H equations defined here as the Hodgkin
Condition, i.e., the Poisson Equation of the 2nd kind, without any terms relating directly to the
temperature of the specimen, or addressing the ability of the apical and basilar neurites to perform
differentially with respect to each other, including suppressing the generation of all action potentials.
Any model of the neuron that does not recognize the effect of temperature on the operation of the
neuron, such as illustrated in [Figure 2.6.1-1 above from Schwarz & Eikhof, should be discarded as
an unrealistic model of the physical system.
2.9.3 The NEURON– a computational model with mixed roots
A computer program with a GUI (graphical user interface) and its own tailored programming language
(hoc, pronounced hoak) has evolved from the Moore Laboratory at Duke beginning around 1975 and
continued by Hines and colleagues at Yale222. It has achieved a prominent place in pedagogy, been used
considerably in pre-doctoral research and been documented in considerable detail in a text in 2006223.
While very clearly described from a mathematical modeling perspective, it does not address the complete
biological neuron. The associated modeling of the synapse based on a cartoon (page 273) is extremely
simple.
- - - -
NEURON continues to rely upon the very early interpretation of the neuron from the 1940's up to 1952
by Hodgkin, Huxley and several colleagues. It is built around a core (kernal) based on what is described
as the alpha function (a Poisson Equation of the 2nd kind) that Hodgkin, Huxley & Katz (H&H)
attempted to use to explain their exploratory investigations on the large axon of the squid, Loligo).
Hodgkin’s efforts to apply this equation were of very limited success because of its limited flexibility of
this equation.
NEURON does not specifically describe the physiology of the neuron they are proposing to model but
follow the common approach of attempting to solve the unsolved set of simple differential equations of
H&H using numerical methods.
The guide provided by Carnevale & Hines, the major curators of NEURON, includes virtually nothing on
the physiology of the neuron and is focused on the mechanics of using their GUI interface. The guide is
supported by two more detailed papers224,225. The papers are focused on the topology of the computer
program itself. While citing a variety of sources, the papers basically follow the RC cable models of Rall
applied to both the neuritic and axonal structures and the alpha function attributed to H&H (that contains
no delay or temperature parameters and does not recognize the presence of inductance associated with the
axon). Its solution of the General Wave Equation is limited to the diffusion equation of Kelvin. No
discussion is provided concerning the more recent delineation of the poorly defined action potential of
H&H into two distinct waveforms, the generator potential associated with the great majority of neurons
(~95%) and the true action potential of signal projection found among the stage 3 neurons associated
with about 5% of the total neuron population.
NEURON is only a basic program suitable for entry level pedagogy. The discussions of this chapter
suggest Neuron be re-written to incorporate multiple kernals in order to represent the major classes of
neurons more completely, particularly with respect to temperature and signal delay.
222Moore, J. & Stuart, A. (2004) Neurons in Action: Computer Simulations with NeuroLab. Sunderland, MA:
Sinauer Assoc.
223Carnevale, N. & Hines, M. (2006) The NEURON Book. NY: Cambridge Univ Press
224Hines, M. & Carnevale, N. (1997) The NEURON Simulation Environment Neural Comp Volume 9, Number
6 pp 1179-1209
225Hines, M. & Carnevale, N. (2001) NEURON: A Tool for Neuroscientists Neuroscientist vol 7(2), pp
123–135
296 Neurons & the Nervous System
De Schutter prepared a review of software packages available for modeling neurons in 1992226. He
included NEURON, AXONTREE, GENESIS and NEMOSYS which were still actively supported
packages dedicated to modeling only neurons at that time (but did not generally support a graphic
interface). After a brief overview of the available packages that all ran on the super-computers of that
era, he noted, “They are all based on compartmental modeling, a popular method of representing the
neuron. Compartmental modeling is derived from cable theory and uses discretization to simplify the
differential equations involved.” In fact their idea of compartmentalization consisted of treating each
branch of the dendritic tree as an electrically isolatable compartment without the presence of any internal
membranes within the dendritic tree or the soma. The use of this compartmentalization concept, the use
of a Hermann Cable model (even with extensions by Rall) and discretization are all incompatible with a
real biological neuron. He also included two general purpose electrical circuit modeling, SABER and
SPICE. He noted in a copy of the paper posted on semanticscholar.org that his table in the original paper
was dated and an updated table would be replaced soon. It is not clear this ever occurred.
2.9.3.1 Modification of the symbology in the program, NEURON
NEURON treats all of the neurites and axon as simple cylinders. It does not recognize the coaxial cable
structure of the long axons of stage 3 neurons. It does not recognize the saltatory character of the signals
along the axon of a stage 3 neuron due to the regeneration of the signal by Nodes of Ranvier. As shown
in this work, the complete solution of both the generator potential and action potential are now known
and available in closed form.
By selecting the alpha function for use in its kernal, NEURON employs a simplified equation of the
generator potential rather than the action potential. The generator potential (Eq. 2.5.3-1) is described by
an equation more complex than the alpha function (Eq. 2.5.3-2) as shown in Section 2.5.3.5. The alpha
function does not describe an action potential as used among the stage 3 signal projection neurons (see
Section 2.6).
The following comments are only for discussion leading to a more advanced version of NEURON. Such
an advanced version does not appear to be imminent; the home web page227 has not been updated since
August 19, 2009 and the comments from 2012 (although the web page copyright has been updated to
2013). A variety of guides and tutorials have been assembled228. These do not appear to make major
advances in the program over the Carnevale & Hines guide. They are primarily concerned with minor
modifications to the underlying code to make GUI operation simpler. These documents suggest
significant changes to the kernal used in the program stored on clients computers should not be made
without adequate reason.
NEURON employs a kernal designed to only generate a pulse waveform describable as a pseudo-action
potential, ala H&H, in response to one or more pulse shaped inputs of the same basic form (the specified
alpha function). The initial stimulation is described as a parametric current injected into the soma (fig.
4.1 of the 1997 paper). Although the GUI screen describes a potential variety of input shapes under
“SelectPointProcess,” these are not described in detail in the Carnevale & Hines guide and do not appear
to include simple sinusoidal waveforms and step inputs of either polarity.
When addressing their nominal neuron, not including the more complex signal generation neurons, which
are clearly beyond the scope of NEURON, it is appropriate to re-label the basic functional diagram of
that program as supported in the guide to that program on page 11. Figure 2.9.2-1 shows the
alternatives. Frame A shows the original variant that may be interpreted as the basilar input having a
preferred relationship to the axon compared to the apical input. It does not indicate the polarity of the
apical and basilar input terminals with respect to the axon output (which is always positive going). Frame
B has been modified to indicate more clearly the independence of the basilar and apical inputs and their
respective polarities relative to the output at the axon. Alternate labels have also been provided to more
clearly identify the nature of these input terminals. This variant would be more appropriate if NEURON
could in fact accept analog input waveforms and generate an analog output as do 95% of all neurons.
However, as configured, NEURON cannot address the operation of analog neurons. In addition, it does
not address the propagation of axon pulse signals along the necessarily myelinated axon or their
regeneration at Nodes of Ranvier. Frame C suggests a schematic that allows the impedance of the poditic
input channel to be set and indicates clearly that the axon is or can be myelinated. The presence of the
226De Schutter, E. (1992) A consumer guide to neuronal modeling software TINS vol 15, pp 462-464
227http://www.neuron.yale.edu/neuron/
228http://www.neuron.yale.edu/neuron/docs
The Neuron 2- 297
poda impedance indicates the neuron is configured to generate either pseudo- or real action potentials
(depending on the equations actually available for the kernal). The poda impedance also sets the
threshold potentials of the neuron (both dendritic input and axon output threshold potentials). The
absence of this impedance would suggest the circuit can only emulate analog circuits (again, if the
appropriate equations were implemented in the kernal). By controlling the degree of myelination, the
program could indicate the importance of myelination in stage 3 neurons generating real action
potentials.
The proposed modifications are compatible
with more modern interpretations of the neuron
as shown in [Figure 2.1.1-1, modified from
Byrne & Roberts, and in figure 1(left) on page
375 of Ramachandran229.
Even these suggested changes would require a
major architectural change in the kernal of
NEURON along with major changes to a
variety of its drop-down menus. It might be
more efficient to create a totally new program
using the GUI architecture to maintain a degree
of similarity for the benefit of current students
and researchers using NEURON. The new
program would employ separate full kernals
for the generator potential and the action
potential that would be functions of
temperature and provide a delay between the
time of stimulation and the output waveform.
The program would also accommodate the
more sophisticated propagation of the signal
instead of the present axonal transmission by
ionic conduction. This would involve
replacing the d-lambda parameter of the
present program with a more realistic limit on
the axon length before regeneration.
Chapter 10 of the guide discusses the
implementation of “graded (chemical)
synapses, gap (electronic) junctions and
ephaptic interactions between neurons.”
However, they do not address the physiology
of these synapses in any detail but focus on
modeling a synapse as an RC circuit of largely
undefined elements. (figure 10.1), all based on
a two-terminal synapse. When discussing the
synapse, they focus only on their assumption
that the current into and out of the junction
must be equal (technically they are not–based
on the physical system and the three-terminal
model). The presynaptic terminal is the pedicle
of the stimulating axon. Reconfiguring their
two-terminal synapse to a three-terminal
synapse would improve their representation with minimal difficulty.
2.9.3.2 Recommendation regarding the software program, NEURON
The 2006 version of NEURON only addresses the neuritic tree of the neuron (providing both an apical
(axial) dendritic input and a basilar (circumferential) poditic input leading to the generation of an action
potential. It does not address the direct relationship between the two with regard to stimulating and
suppressing the generation of action potentials (the fact they are differential inputs to a common internal
mechanism associated with a biological transistor, Activa, circuit). It relies upon the general description
Figure 2.9.2-1 Suggested revision of the
baseline neuron in NEURON. NEURON
uses the unconventional notation of
signal flow from right to left. A; the
schematic used in NEURON. B; the
schematic modified to isolate the basilar
neurite from the axon more clearly and
identify its polarity. The configuration is
implicitly analog and does not generate
action potentials. C; the schematic
modified to explicitly support a stage 3
neuron generating action potentials. See
text.
229Ramachandran, V. ed. (2002) Encyclopedia of the Human Brain. San Diegeo, CA: Academic Press vol 3,
page 375
298 Neurons & the Nervous System
of the elements of the apical and basilar neurites as developed by Rall; that is, it treats them as fluid filled
cylinders formed by the neurolemma. and exhibiting only resistance and capacitance. Their modeling
does not support the presence of diodes in the electrical analogs of their neuron (page 45). While they
incorporate an ideal amplifier in their list of test equipment, they do not incorporate the ideal amplifier
with differential inputs into their neural model. The label ideal amplifier is more appropriately an ideal
operational amplifier in engineering notation. Their assumption was that all charge transfer between
given points is by ionic conduction.
The 2006 version of NEURON relies upon what it describes as the “alpha function” (page 4) which is in
fact the Poisson Equation of the 2nd kind (sometimes called the Kelvin Equation or the Heat Diffusion
Equation. It contains no delay term or temperature term as developed and confirmed in this work. It is
actually a degenerate version (Eq. 2.5.3-2) of the generator potential described empirically by H&H and
developed physiologically in this work (Eq. 2.5.3-1). The full equation includes a significant
temperature parameter that is different for the leading and trailing edges of the generator potential due to
the different mechanisms involved in generating these segments of the waveform.
The 2006 version of NEURON does not address the axon of the biological neuron in any significant way
(cartoon on page 93). It assumes all neurons generate pulse outputs instead of the more realistic value of
less than 5%. While they provide a cartoon of what future versions of NEURON might address, it does
not address the myelination of the axon, the division of the axon into segments separated by Nodes of
Ranvier (NoR), the character of the Node of Ranvier and it does not address the electromagnetic
propagation of energy along the axon and axon segments according to the General Wave Equations
(GWE) of Maxwell. The program does not recognize the character of the axon as a coaxial cable. There
is no mention of the critically important inductance of such a coaxial cable. There is no distinction
between the phase velocity of the energy traveling along the axon segments nor the delay intrinsic with
the regeneration of the action potential at the NoR, or the average velocity resulting from the combination
of the axon segment and the NoR. They use the term node in the sense of the node of a mesh and suggest
axons can be up to at least 1000 microns long without employing any regenerative mechanism along its
length. They do not appear to assign any specific function to the soma of the neuron (page8), treating it
as the root of one or more branched dendritic tree.
The waveforms shown on page 120 of the 2006 text are both analytic and numeric solutions of the
generator potential limited to the Hodgkin Condition. They do not reflect the actual and detailed shape
of the action potential waveform. They are entirely arbitrary with regard to the time constant used.
While a useful pedagogical tool for beginners, NEURON does not provide a realistic mathematical
model of the neuron nor waveforms describing a real neuron as a function of temperature or stimulation
intensity, whether of the analog or pulse generating class. Neither does it compute the actual delay
associated with the neuron for either the pulse neuron (prior to reaching the threshold level) or analog
neuron. Graduate students should be exposed to more sophisticated models of the neuron than available
in the current incarnation of NEURON.
The admonition of the previous section still applies. Any model of the neuron that does not recognize
the effect of temperature on the operation of the neuron should be discarded as an unrealistic model
of the physical system.
2.10 Analyses of the neuron literature
2.10.1 Neurons of the peripheral nervous system
2.10.1.1 Generic stage 1 sensory neuron
As developed in detail in “Processes in Biological Vision, PBV,” and in “Processes in Biological
Hearing, PBH,” there is a generic form of stage 1 sensory receptor neurons used in external environment
sensing, and probably in many instances of internal environment sensing as well.
Figure 2.10.1-1 illustrates the stage 1 sensory receptor of the auditory modality (Section 5.3.2 in PBH.
The Neuron 2- 299
The electrostenolytic power supply in the previous figure can be expanded further if needed for further
analysis. Figure 2.10.1-2 illustrates the stage 1 sensory receptor of the auditory modality expanding on
the power supply. It plays a crucial role in the adaptation process in vision (Section 1.6.6 in PBV).
Figure 2.10.1-1 Generic stage 1 sensory neuron receptor (auditory modality.
The first Activa is provided electrical power through the electrostenolytic
process shown within the dotted box. The potential of –154 mV is supplied
through the network of R2, C1 and C2. More detail is provided in the next figure
in this section.
300 Neurons & the Nervous System
2.10.2 Neurons of the central nervous system
It will be important to differentiate between the Purkinje neurons (giant pyramid cells) of the cerebrum
(neocortex) and the Purkinje neurons of the cerebellum (the fastigial in some communities). They serve
totally different roles; the giant pyramid cells are generally stage 3A encoding neurons generating action
potentials, while the Purkinje neurons of the cerebellum are primarily memory storage elements in very
large physical memory storing symbolically encoded memories in a (indexed) database environment.
2.10.2.1 Multipoint probing of neurons
Williams & Stuart have recently provided data on a variety of neurons from within the CNS, apparently
in–vitro, using three simultaneous probes. While the papers present a large amount of data that can be
interpreted under, and do support, the Electrolytic Theory of the Neuron, their discussions must be
recognized as based on the now obsolete chemical theory of the neuron. A significant failure of the
Williams & Stuart papers is their failure to present any detailed graphic description of the neurons they
are investigating. They fail to differentiate between stage 2 and stage 4 neurons (typically unmyelinated
axons) and stage 3 neurons which have axons that are typically myelinated.
Bahl et al. in a subsection below, provided significant data on a pyramid cell that was awkwardly defined.
2.10.2.1.1 Multipoint probing of pyramid neurons by Williams & Stuart
The cytology of, equivalent electrolytic environment of, and measured static voltages within the pyramid
neurons is presented in Section 2.5.2. The descriptively named pyramid neuron can be found in
myelinated (stage 3) and unmyelinated (stages 2, 4 & 5) forms. It normally consists of an apical neurite
(dendrite), circumferential neurites (podites) and an axon emanating from the “center” of the base of the
pyramid. Both of the neurite structures may be highly arborized. Signals applied to the dendritic
arborization will appear at the axon in the same polarity. Signals applied to the poditic arborization will
appear at the axon inverted. The origin of the axon may vary from the nominal position depending on
packaging requirements within the neural tissue. Figure 2.5.2-1, Figures 2.5.2-2 and its inset and
Figure 2.10.1-2 Physiological map of the stage 1 visual sensory receptor
related to adaptation. Only the adaptation amplifier of the photoreceptor cell
is shown. The load in the collector circuit has been shown explicitly. VC is the
collector potential, CA is the axon capacitance, and R1 corresponds to the
impedance of the electrostenolytic process. R2 & C2, R3 & C3, etc. correspond
to equivalent impedances related to the diffusion of chemicals to the
electrostenolytic site.
The Neuron 2- 301
Figure 2.5.2-3 are particularly pertinent to the following discussion. Figure 9.1.1-1 provides a wider
context for long stage 3 neurons including multiple Nodes of Ranvier.
Williams & Stuart reported on the properties of the pyramid neurons found in the cerebrum of the rat in
two papers, in 2000230 and in 2002231. No graphics of the detailed cytology of the pyramid neuron or of
its operational configuration was provided. In the 2000 paper, they spoke of passive neuronal models.
These models were apparently based on the chemical theory of the neuron supported by the Rall cable
model (from the 1950's) which is generally inadequate, and the Thompson (Lord Kelvin) model of
diffusion of charge (from 1840's) in analogy of heat in a solid. The models appear to depend on ionic
currents through a highly ionized fluid to the exclusion of the much higher velocity of electron currents.
The Rall cable model is based on an electrical equivalent employing only series resistors and shunt
capacitors. The Thompson model requires the stimulant to remain active until the signal traversing the
conductor reaches its terminus. Neither of these conditions applies to a typical pyramid neuron. For
myelinated axons, it is necessary to address a more sophisticated model based on Maxwell’s Wave
Equations. For non-myelinated axons and dendrites, it is necessary to consider “hole transport” rather
than ionic transport. The investigators did not attend to the axon of their pyramid neuron and did not
state whether it was myelinated or not. Hole transport must also be considered as a more appropriate
transport mechanism than that based on Thompson’s heat transfer model. Their discussion in 2000, based
on the chemical theory of the neuron contains a number of occurrences of words like “however,”
“should” and “or”. The dichotomy between the expected and observed excitatory post synaptic
potentials, EPSP’s, in the right column of page 3180 surfaces a problem with their model or protocol.
In the 2000 paper, the term sEPSP refers to simulated EPSP’s. In the 2002 paper, the same acronym
refers to spontaneous EPSP’s. Care is required in interpreting these papers.
All of their data in the 2000 paper appears to be subthreshold in character with the exception of one
waveform presented in figure 3C following doping of the neuron by a bradycardiac agent, ZD7288. This
prompted their remark that such doping “could lead to action potential firing.” The critical waveform in
the central frame of figure 3C extends beyond the limits of the frame.
ZD7288 is a very complex two-ring(one homocarbon and one hetrocarbon with tow nitrogens)
pyrimidinium chloride232, C15H21ClN4 known as a blocker of the hyperpolarization of cardiocyte cells
(Section 20.3). The cardiocyte cell combines neural and muscular functions within a single biological
cell. Its role in less complex neurons is poorly understood.
Although not stated in their paper, the experiments in 2000 were apparently performed in vitro like their
other experiments. Their initial statement in their Introduction is difficult to support. “The integration of
synaptic potentials to form an output signal, the action potential, is the most fundamental operations
neurons perform.” Since less than 5% of all neurons generate monopulse outputs (action potentials in the
strict sense) the likelihood that the output signals (generator potentials) of the other 95% of neurons are
most likely more important from the global perspective. The 2000 paper speaks of attenuations greater
than 100:1 along the dendrites of a pyramid neuron with a soma located in layer 5 of the cerebral cortex.
“The distance between the highly arborized tuft of the dendrite and the soma could exceed one
millimeter.”
The 2000 paper cites a 1998 paper by Stuart & Spruston233 that relies upon the inadequate software
named NEURON and discussed in Section 2.9.3.2. The program is based on the oversimplified cable
model of Rall. Section 6.3.5 of this work presents a more sophisticated and appropriate cable model
utilizing “hole transport” as found in other semiconductor-based biophysical applications.
The 2002 paper of Williams & Stuart contain considerable data obtained by using three electrical probes
simultaneously. They do not indicate whether their pyramid neuron had a myelinated axon or not.
However, their figure 1A appears to show the axon of their neuron becoming a commissure in which case
230Williams, S. & Stuart, G. (2000) Site Independence of EPSP Time Course Is Mediated by Dendritic Ih in
Neocortical Pyramidal Neurons J Neurophysiol vol 83, pp 3177–3182
231Williams, S. & Stuart, G. (2002) Dependence of EPSP Efficacy on Synapse Location in Neocortical
Pyramidal Neurons Science Vol 295, pp 1907–1910
232https://www.rndsystems.com/products/zd-7288_1000
233Stuart, G. & Spruston, N. (1998) Determinants of Voltage Attenuation in Neocortical Pyramidal Neuron
Dendrites J Neurosci vol 18(10), pp 3501–3510
302 Neurons & the Nervous System
Figure 2.10.2-1 A potential map of a
pyramidal type neuron showing the higher
negative potential in the podite arm than
in the bulk of the neuron representing the
dendritic arm. Note the potential gradient
along the arms due to current flowing
within them. Modified from Guyton (1976).
the axon would certainly be myelinated. They speak of very high attenuations (>100:1 over the length of
their dendrites based on previous investigations. They note, “Unexpectedly, we found that the dynamic
properties of unitary EPSP’s, uEPSP’s, depended on synapse location (their figure 3D).” And “The
greater than 40-fold dendro-somatic voltage attenuation of distal EPSP’s suggests that distal dendritic
EPSP’s will have little direct impact on neuronal output.” In the 2002 paper, they seek an explanation
why their measurements do not reflect this level of attenuation, Section 9.7.1.1.
The above paper cited another one prepared by a different lead from their group234. The paper includes
an extensive bibliography but no graphic model of a specific neuron. The assert there are many
functional variants of neurons and a wide variety of dendritic structures and arrangements based on the
literature in their bibliography. The paper is nearly devoid of direct statements or assertions. The paper
reflects a great affinity for the auxiliary verb, “can.” It occurs many times without any detailed support
other than a citation to one or more papers. It offers little but as a bibliographic resource. One suggestion
was that the dendrites of many (not further described) neurons incorporated compartments defined only
by electrical or chemical gradients. They did not describe the physical compart mentation within whole
neurons well documented using electron microscopy (Section 2.2.2.3) and electrical potential mapping
(Section 3.2.1 in PBV). Careful electron microscopy identifies internal lemma.
Guyton has provided an electrical potential mapping of a neuron of the pyramidal type235. A modified
version of that figure is shown in Figure 2.10.2-1. Note the more negative potential in the upper
(poditic) arm of the neuron than found in the bulk of the neuron. The poditic arm is normally 15-25 mV
more negative than the dendrites in order for the dendritic terminal of the Activa to be forward biased
relative to the base terminal. Note also the voltage gradients in the various arms. This is exactly what
would be expected by the current passing through the resistive arms and creating a voltage drop. The
voltage gradient is determined by both the current entering the neuron and the diameter of the arm at a
given location that controls its local impedance. Although Guyton considered the various junctions
shown to be either excitatory, the ones on the two left arms, or inhibitory, generally the ones on the top
arm, these labels have been omitted. In this work, it is the Activa circuit within the neuron and its input
circuits represented by the neurites that determines whether the output is the same or opposite polarity as
the input signal. The circuit and the overall neuron constitute an analog device as illustrated by the
smooth potential gradients within the neuron. The upper poditic arm is the inverting input terminal. The
dendrites on the left are non-inverting input
terminals. The axon potential was not
provided in the original figure. It was probably
near -120 mV (necessarily between -75 and -
150 mV) because of the large voltage
difference between the dendrites and the podite
and because of the considerable current flow
present.
2.10.2.1.2 A Multi-segment math
model of Pyramid neurons–Bahl,
2012
234Hausser, M. Spruston, N. & Stuart, G. (2000) Diversity and Dynamics of Dendritic Signaling Science vol
290, pp 739-744
235Guyton, A. (1976) Textbook of medical physiology. 5th edition Philadelphia, PA: W. B. Saunders pg. 622
The Neuron 2- 303
Bahl et al236. mathematically modeled a pyramid neuron that appears awkwardly defined;
They noted in their Abstract they were departing from the traditional one-compartment model in favor of
a multi-compartment neuron (as advocated throughout this work, but with fewer (functional)
compartment),
“The construction of compartmental models of neurons involves tuning a set of parameters to make the
model neuron behave as realistically as possible. While the parameter space of single-compartment
models or other simple models can be exhaustively searched, the introduction of dendritic geometry
causes the number of parameters to balloon. As parameter tuning (adjusting to obtain a consistent set of
parameters) is a daunting and time-consuming task when performed manually, reliable methods for
automatically optimizing compartmental models are desperately needed, as only optimized models can
capture the behavior of real neurons. Here we present a three-step strategy to automatically build
reduced models of layer 5 pyramidal neurons that closely reproduce experimental data. First, we reduce
the pattern of dendritic branches of a detailed model to a set of equivalent primary dendrites. Second, the
ion channel densities are estimated using a multi-objective optimization strategy to fit the voltage trace
recorded under two conditions – with and without the apical dendrite occluded by pinching. Finally, we
tune dendritic calcium channel parameters to model the initiation of dendritic calcium spikes and the
coupling between soma and dendrite. More generally, this new method can be applied to construct
families of models of different neuron types, with applications ranging from the study of information
processing in single neurons to realistic simulations of large-scale network dynamics.”
The goal of their program (clearly devoted to the chemical theory of the neuron, but extended to a multi-
compartment neuron) is ambitious! They also noted in their Introduction,
“Many parameters of these models have not been directly measured experimentally; therefore, these
parameters must be tuned (adjusted) to match the experimentally observed input–output relation of the
neuron. Solving the resulting nonlinear optimization problem is difficult and requires extensive
computing resources, especially for models comprising a detailed neuronal morphology and a large
number of compartments (Traub et al., 2005; Achard and De Schutter, 2006; Markram, 2006;
Druckmann et al., 2007; Hay et al., 2011). Here we develop reduced models of neocortical layer 5
pyramidal cells with a small number of compartments to representthe dendritic geometry. Compared to
fully detailed compartmental models, reduced models confer significant speed advantages both for the
optimization of the single neuron model and for simulation of networks of such neurons. The reduced
model’s geometry, even though simplified, should still incorporate the fact that synaptic inputs arriving at
different layers in the dendritic tree are integrated differently.”
In their section 2.1, they describe their model neuron,
“Our aim is to create a reduced pyramidal cell model that is simple and fast but detailed enough to show
complex somato-dendritic interactions. The model is based on standard techniques from compartmental
and ion channel modeling (Hodgkin and Huxley, 1952; Rall, 1962), implemented in NEURON 7.1
(Carnevale and Hines, 2005) and controlled via the NEURON-Python interface (Hines et al.,
236Bahl, A. Stemmler, M. Herz, A. & Roth, A. (2012) Automated optimization of a reduced layer 5 pyramidal
cell model based on experimental data J Neurosci Meth vol 210, pp 22– 34
304 Neurons & the Nervous System
2009).
To obtain a simplified geometry of the dendrites, we model the functional neuronal sections (soma, basal
dendrites, apical dendrite and the apical dendritic tuft–its arborization) each by a single cylinder whose
length and diameter will be later determined by the optimization algorithm we describe. The axonal
geometry is based on a detailed reconstruction (Zhu, 2000) and consists of a conical axon hillock (l = 20
m) which has a diameter of 3.5 microns at the soma connection and tapers to 2.0 microns. The conical
axon initial segment (iseg; l = 25 microns) is connected to the hillock and its diameter tapers from 2.0
microns to 1.5 microns. The actual axon (l = 500 microns) is connected to the initial segment and has a
uniform diameter of 1.5 microns. We did not model nodes of Ranvier or myelination. As the reduced
model should be fast, the number of compartments ought to be as small as possible. We chose the
following compartment numbers for the functional sections: soma = 1; basal dendrite = 1; apical dendrite
= 5; apical dendritic tuft = 2; axon hillock = 5; initial segment = 5; axon = 1. Hence, the model has a
total of 20 compartments.”
They proceed to model their rare earth ion channels, but do not provide a graphic model of their neuron.
In their section 2.2, they note the scarcity of reliable ion channel data,
“Reliable data on the biophysical properties of ion channels in pyramidal neurons are rare and
measurements mostly stem from different neurons from different animals or even species. Moreover,
due to experimental limitations many parameters just cannot be measured. In particular, information
about ion channel densities and kinetics in distal dendritic branches are not available. It is, therefore, not
sufficient to put together all existing information on pyramidal neurons and build a working model; a
long list of uncertainties remains.”
In essence, they rely upon Hodgkin and Huxley, on Rall (without any myelination), the software package
Neuron (7.1) & the missing data on ion channels in 2012 to support their 20 compartment mathematical
model of a neuron; all of these fundamental concepts and tools have been shown to be flawed in later
sections of this work. To overcome these fatal errors in their model, they introduced a series of “fudge
factors.” One of these is described as,
“In the next step we estimated the ion channel parameters affecting somatic spiking. This was done using
experimental data on the somatic spiking dynamics under two different conditions, first in the intact
neuron, and second while the apical dendrite has been occluded using a method called Pinching (Bekkers
and Häusser, 2007).”
Pinching was introduced in their second of five reported cycles of their optimization program. In figures
3a & 4a, they have intentionally not drawn in the tops of their predicted action potentials because of their
poor match to data measured and reported by other investigators (Section 9.2.6). They specifically note
in the caption to figure 3,
“No calcium channels were present in this step of the optimization.”
This statement is clearly in conflict with the equations of Hodgkin and Huxley for Action Potential
creation!
Their section 3.4 focuses on the attempt to vary their model to require participation of calcium channels
in their computer program to generate action potentials.
Figure 7b displays exhorbitantly long delays associated “in the back-propagating AP and the underlying
ionic conductances in the reduced model.”
Their Discussion section does not converge on a useful mathematical model, and does not include any
active component in their model.
2.10.2.1.3 Multipoint probing of Purkinje neurons in cerebellum
The Neuron 2- 305
Williams & Stuart reported on the properties in-vitro of the Purkinje neurons found in the cerebellum of
the rat in 2002237. Their technique employed thin slices of whole brain to provide a more realistic
operating environment. Their paper requires considerable re-interpretation that should logically follow
detailed discussions of stage 3 signal propagation in Chapter 9. Lang introduced more advanced
multipoint probing that also is discussed in Chapter 9. See Section 9.7.1.1 and Section 9.7.1.2. See
Section 2.10.3 for more details relating to the Purkinje, and other neurons, of the cerebellum.
237Williams. S. Christensen, S. Stuart, G. & Hausser, M. (2002) Membrane potential bistability is controlled
by the hyperpolarization-activated current IH in rat cerebellar Purkinje neurons in vitro J Physiol vol 539.2,
pp 469–483
306 Neurons & the Nervous System
2.10.2.1.4 Dendrite signal projection velocities
Although scaling from the graphics in a 1997 paper by Stuart et al238. is of limited precision, it does
provide a benchmark. The paper also measured “backpropagation” from several types of neurons and
cited an earlier paper by Spruston et al239. Back propagation is an oddity of the method of stimulation
(stimulation by current introduced into the soma –beyond the hillock). The normal stimulation is at the
dendrite (apical dendrite), or the podite (basal dendrite). See Section 2.2.4.
Figure 2.10.2-2 from Spruston et al. shows valuable information about signal backpropagation in the
hippocampal neuron of CA1 of the rat. This figure includes more information than the author’s realized.
Frame A has been modified to add scales and the dashed line indicating the emitter to base potential of
the Activa within the soma at the time of the dendrite stimulation signal arriving at the emitter. The
means of stimulation was presented in an earlier paper240 where the authors were investigating slices of
neocortical tissue containing pyramid neurons of layer V from the rat. Their figure 4 and discussion
indicates they made no effort to make a patch-clamp contact with the hillock of their neuron, only the
larger central area of the soma. However, the voltages recorded in their experiments does suggest their
“soma probes” were contacting the axoplasm of the neuron.
238Stuart, G. Spruston, N. Sakmann, B. & Hausser, M. (1997) Action potential initiation and backpropagation
in neurons of the mammalian CNS TINS vol 20(3), pp 125– 131
239Spruston, N. Schiller, Y. Stuart, G. & Sakmann, B. (1995) Activity-dependent action potential invasion and
calcium influx into hippocampal CA1 dendrites Science vol 268, pp 297–300
240Stuart, G. Dodt, H-U. Sakmann, N. (1993) Patch-clamp recordings from the soma and dendrites of neurons
in brain slices using infrared video microscopy Pfluger Arch vol 423, pp511–518
The Neuron 2- 307
The Spruston et al. paper of 1995 provides considerable useful information to the laboratory technician
concerning the patch-clamp technique. It concludes in this regard,
“The success rate for formation of high gigaohm seals (i. e. above 5 Giga-ohm with this method can be
greater than 80% when recordings are made from large structures such as the soma of cells, but is lower
for recordings from smaller structures. It is possible, however, to use this technique to record regularly
from neuronal structures in brain slices as small as 2 microns in diameter.”
The Spruston et al. paper of 1995 was one of the earliest in the biophysical literature to speak of using
“shunt and capacitive compensation” when implementing their probes (footnote 13 citing Stuart, Dodt et
al., 1993). The compensation was described more fully in the captions for figures 5 & 7 of the 1993
paper.
The1993 paper described the chemical content of the fluid filling their probes. They also described the
fluid in which their brain slices were maintained. They were predominantly “oxygenated physiological
saline solution” However, no glutamic acid was added to affect a prolonged time the experiments.
They speak of the open-tip pipette resistance as on the order of 12 Meg-Ohm and the operational
dendritic membrane patch as the access resistance after rupturing the neuron membrane. “Access
Figure 2.10.2-2 Montage of signal projection within and action potential
generation in a CA1 pyramidal neuron of the hippocampus of Wistar rats.. A:
Waveforms at soma and at dendrite 250 microns away. Dashed line, forward
propagating dendritic voltage waveform when arriving at the soma. 1.04 ms
is delay between action potential generation and its arrival at the dendritic
probe location calculated from Spruston’s backpropagation velocity of 0.24
m/s. See text. From Spruston et al. 1995.
308 Neurons & the Nervous System
resistances during these whole-cell dendritic recordings ranged from 25 Meg-Ohm to 79 Meg-Ohm(mean
± SEM: 51± 12 Meg-Ohm).” “To obtain patch pipette recordings from small neuronal structures or
processes requires patch pipettes with smaller tip openings than used during somatic recordings and leads
consequently to higher access resistances during whole-cell recording. Recordings from apical dendrites
of neocortical pyramidal neurons were made using patch pipettes made from thick-walled borosilicate
glass with open-tip resistances of 10-13 Meg-Ohms.”
As is common under the chemical theory of the neuron, these authors speak of summation of signals
applied to the dendrites of a specific neuron without addressing integration in the same context.
However, the straight sloping lines, associated with the initial signal (dashed line) recorded at the 250
micron location of the dendrite and the subthreshold waveform recorded at the soma are clear indications
of the integration of a square pulse signal applied to an area of the dendritic tree prior to both of the
recording locations. Their figure 8B clearly shows their square wave applied to the dendrite and the
linear integration of this charge on the capacitance of the dendritic structure (?, including the capacitance
of the emitter terminal of the Activa) at a location of 113 microns from the center of the soma. The
recording shows the dendritic voltage waveform at that location both prior to, during and following
action potential generation. It did not extend in time long enough to show the creation of a second action
potential. The diameter of their soma appear to be about 20 microns.
Figures 7B and 8A clearly show the hyperpolarizing of the dendroplasm due to square wave stimulation
with a time constant on the order of 10 ms. The waveforms in figure 8A do not represent an operational
condition. In the absence of stimulation, the dendroplasm resting potential (sometimes described as the
resting membrane potential, RMP, is near zero millivolts as shown in the figure from Spruston et al. of
1995. The resting axoplasm potential is near –154 millivolts under this cutoff condition. When the
dendrite to podite potential reaches about 18 millivolts, the Activa goes into single pulse (monopulse)
generation with the axoplasm rapidly reaching about –20 to –30 mV. The result is a positive going pulse
with an amplitude of about +110 mV from its threshold level (about +130 millivolts from its resting
condition). For a dendrite-to-podite voltage below the 18 mV level, the Activa operates in the
subthreshold, or linear amplifier, regime as indicated by the linear change in axoplasm voltage mirroring
the linear change in the dendroplasm potential (dashed line).
Frame 8A exhibits a slight inconsistency in the absence of any data points. The soma recording shows a
start of the rise in potential occurring before the stimulation applied to the dendrite arrives at the
emitter of the Activa (based on the 0.24 m/s) velocity of the stimulation as reported in Spruston et al.,
1995. This is a very high velocity for diffusion by ionic carriers. The literature typically describes ionic
transport velocities between 7 x 10–3 m/s and 0.02 m/s (Section 6.3 in this work and Section 8.1.3.2 of
PBV). A value of 0.24 m/s is more compatible with of “hole transport” as found in normal
semiconductor physics. The soma response should begin at 4 ms, simultaneously with the start of the
dashed line representing the dendritic stimulus arriving at the emitter of the Activa. The dendrite
response curve appears to represent the sum of the forward projected and backward projected dendritic
waveforms as recorded at 250 microns from the center of the soma.
In figure 8C, the authors experimented with adding potassium glutamate to their system under controlled
conditions,
“Activation of single-channel currents by the application of glutamate (1 micro-Mole) to a dendritic out-
side-out patch excised 112 microns from the soma of a neocortical pyramidal cell. The patch pipette was
filled with a potassium-gluconate-based intracellular solution and was coated with Sylgard. The dendritic
membrane patch was held at -60 mV. The three traces were taken before (Control), during (Glutamate)
and after application of glutamate (Wash).”
Little comment was made about their glutamate experiments and no obvious effect was encountered.
Their experiments with Lucifer Yellow were more productive,
“In this case this entire layer V pyramidal cell was filled with Lucifer Yellow after rupture of a dendritic
cell-attached patch recording 230 microns from the soma of this cell. All 19 attempts to fill neurons
following rupture of dendritic membrane patches at distances of up to 440 microns from the soma
resulted in filling of the entire neuron with Lucifer Yellow. (At distances greater than 200 microns it was
often difficult to follow a particular dendrite all the way to the soma. The location of the soma could be
identified, however, by filling the dendrite with Lucifer Yellow and locating the soma when the cell was
viewed with fluorescent optics.”
It is interesting to consider whether the Lucifer Yellow penetrated the internal lemma of the neuron
separating the dendroplasm from the podaplasm and axoplasm.
The Neuron 2- 309
Figures 2 & 3 of the Stuart et al. paper of 1995 can not be properly interpreted using the chemical theory
of the neuron. They can only be interpreted fully based on the electrolytic theory of the neuron.
2.10.2.2 Simultaneous Multipoint probing of neurons
Gidon et al241. have reported on their simultaneous dendritic and soma (hillock) patch clamp recordings
when the dendrite or soma was stimulated by injecting current. Figure 2.10.2-3 reproduces parts of their
figure 1. Although they described the resultant waveforms in terms of the chemical theory, they produce
more detailed data when interpreted by The Electrolytic Theory of the Neuron.
Thr neurons of the layers adjacent to the Pia, do not normally produce action potentials in-vivo; they
normally process analog signals as class A amplifiers). However, if the normal bias (ED - EP) is raised
above about 23 mV, they can be made to oscillate in the monopulse mode as shown in Gidon et al.
Looking first at the Di thru Diii traces (the normal operating condition), the square wave applied to the
dendroplasm (apical dendrite) shows an exponential rise in the voltage on the dendroplasm. This is most
clearly shown in Dii where the threshold value has been shown explicitly. Exceeding the threshold (ED -
EP >Threshold) causes the monopulse operating region to be entered from the Class A (linear operating
region), resulting in an action potential to be generated (black waveform). The details related to these
operations are developed in Section 9.2. After a refractory period, Di shows the dendroplasm again
rising above threshold and generating a second action potential. Diii is only discussed in the
supplementary material. Looking at Bi thru Biii (abnormal, or parametric, operation), the stimulus is
applied to the axoplasm (after the hillock). This causes a voltage ramp to form due to the high
capacitance of the axolemma which causes the axon to rise in voltage and the podite terminal (peripheral
dendrite) to fall in voltage until the threshold voltage is reached (ED - EP >Threshold). At this point the
neuron transitions from the Class A operating regime to the monopulse operating regime, and another
action potential is generated as shown in Bii, The Vdend now lags the action potential because it is
capacitively coupled to the axoplasm. There is less variation in the height of the dendroplasm, Biii,
because the capacitive coupling and the constant voltage amplitude of the action potentials.
241 Gidon, A. Zolnik, T. Fidzinski, P. et al. (2020) Dendritic action potentials and computation in
human layer 2/3 cortical neurons Science vol 367, pp 83-87
310 Neurons & the Nervous System
Figure 2.10.2-3 Simultaneous patch clamp with soma stimulus, human cerebral
cortex ex vivo. A; showing the location of their probes, Bi thru Biii; showing
soma stimulated waveform, Di thru Diii; showing dendro stimulated wavforms.
bAP; base-stimulated Action Potential. dCaAP; putative dendro stimulated
Calcium Action Potential “whose waveform and effects on neuronal output
have not been previously described.” From gidon et al., 2020.
They introduce the symbolic logic XOR with the Truth Table as shown in Figure 2.10.2-4 without any
indication of how a single neuron performs this logic, figure 3F and 3G.
The Neuron 2- 311
Figure 2.10.2-4 The symbol a Truth Table
for XOR symbolic logic.
Figure 2.10.2-5 A typical XOR circuit
implemented in binary logic, two-stable-
state logic. All inputs are positive-going
in this figure.
“The logic or Boolean expression for an XOR
gate is A B = Q which means that:”
If A and B are different from each other, then
Q is true.
This is a common function in Boolean Algebra,
but usually requires multiple transistors,
operating in two-stable-state logic to
accomplish. The equivalent Boolean Algebra
is
Q AB AB
The XOR gate is a logic gate where the output
goes HIGH (or “1”) if one – and only one – of
its inputs are HIGH. XOR stands for
Exclusive-OR.
It is refreshing to find a group applying
Boolean Algebra to bioscience but they must
appreciate the requirements. The neural system
does not operate as a two-stable-state system.
The peak amplitude of an action potential does
not achieve, or maintain, a stable state (a binary
“1").
Atypical circuit implementing XOR is shown in Figure 2.10.2-5 . All inputs are positive-going in this
figure. The first two amplifiers on the left , are inverting amplifiers.
312 Neurons & the Nervous System
Figure 2.10.2-6 Putative circuit with
abbreviated Truth Tables. Note X in the
upper truth table is not stable in the high
condition. Notice also, there is no
indicated output terminal for the circuit in
frame G. From Gidon et al., 2020.
The circuit they suggest is shown in Figure 2.10.2-6. Note there is no output terminal indicated and the
circuit in the upper frame F does not represent an X that is stable at the high condition as required to
satify the XOR logic. The text of the right column on page 86 is not convincing.
2.10.3 Purkinje & other neurons of
stage 5C, the cerebellum
The role of the Purkinje neuron within the
cerebellum is one of the most complex of any
neuron in the CNS. Its functional role is
discussed in Section 17.6.1.5 throughout
Chapters 17 and 18 of this work. The lack
ofwaveform from the myriad input structures
make it very difficult to explore the unique
situation of the Purkinje neuron in detail. This
leaves many options still open with regard to
how these neurons are employed within the
cerebellum.
The cerebellum and its neurons, including the
very important Purkinje neurons, have largely
escaped detail examination during the years
since 1960's because of the lack of
understanding of the role of the cerebellum.
This work has begun the detailed study of the
cerebellum as the primary source of memory
storage and manipulation following memory
creation vis the hippocampal formation and
several similar contributing structures.
During the 1950's two separate teams delved deeply into the cerebellum and particularly the Purkinje
neurons from a histological perspective. They also employed the very primitive electrophysiological
instrumentation available to cash starved biophysicists in that time period. These included oscilloscopes
lacking linear time bases, uncompensated oscilloscope probes (Section 2.6.1.2.1 and Section 2.10.2.1.3)
and paper-medium recorder.
Granit led one team242 of Purkinje neuron investigators and Eccle led the second team243. This section
will address the details and reinterpretation of the Granit team material. It related to the
electrophysiology of the neuron specifically. The Eccles team was more focused on the histology of the
Purkinje neuron in its environment (Section 10.2.4.4 and Section 10.2.5) and the cytology of the neuron
itself (Section 17.6.1 ).
The Granit team made much wider use of d.c. recordings of waveforms than did the Eccles team. Thus,
they are much more valuable to the analyst.
The analyst and reader should consider two situations carefully in the following discussions;
1. the Granit team speak of a hillock within the soma of the Purkinje neuron but do not localize it by
means of a figure or additional words, the Eccles team go so far as to suggest the stage 3A analog to
pulse converter (if any) might be located after the narrowing of the axon extending from the soma and
before the axon becomes myelinated (see Section 17.6.1.3).
242Granit, R. & Phillips, C. (1956) Excitatory and inhibitory processes acting upon individual Purkinje cells of
the cerebellum in cats J Physiol vol 133, pp 520-547
243Eccles, J. Ito, M. & Szentágothai, J. (1967) The cerebellum as a neuronal machine NY: Springer-Verlag
The Neuron 2- 313
2. the designation “antidromic stimulation” carefully when speaking of the axoplasm. When the Activa
within the neuron is in cutoff, the ohmic impedance between the axoplasm and both the podaplasm and
dendroplasm is very high (nearly infinite). However, the capacitance between the podaplasm and the
dendroplasm, and the axoplasm may be significant depending on the impedance level between the
podaplasm and the dendroplasm and the neutral (ground) point of the external matrix. When the Activa
is not in cutoff, different conditions apply.
Marr244 presented a marvelous paper on the role of the Purkinje neuron and its surrounding circuitry
within the cerebellum. It was based largely on the Eccles et al. paper of 1967. It did not cite the Granit
et al. paper. The largely philosophical paper was attempting to bound the parameter related to the
Purkinje neuron much in the style of Tsotsos in 1990 for the signal processing portion of the visual
modality (Section 15.2.2.1 in “Processes in Biological Vision.” Marr promised two more papers before
his untimely demise.
The Marr paper focused on only one Purkinje neuron capable of storing several hundred bits of
information. It did not consider the potential of a large array of Purkinje neurons forming storage area
supporting a large general random access database that became well known a few decades later with the
personal computer revolution. The Marr paper will be summarized in Section 2.10.3.3.
2.10.3.1 Background related to the cerebellum
The following material also appears in Section 17.5.1.
The study of the cerebellum has gone on for much of the last two centuries. However, it has occurred in
spurts, and most of the work of the late 20th Century still depends on the work of Cajol in the late 19th and
very early 20th Centuries. As a result, much of the figures displayed in the literature depend on his early
figures, at least for inspiration. The “annals of the New York Academy of Science” vol. 978(1) of 2002
summarized the state pf the art applicable to the cerebellum at the end of the 20th Century. In 2021, the
journal “Neuroscience” (vol 462), under the banner of the “International Brain Research Organization,”
presented a Special Edition, in honor of the late Masao Ito. Unfortunately, none of the included papers
related to the primary function of the cerebellum, the storage of long term memory in a large scale
database. The comprehensive papers of Buckner et al. in the early 21st Century (and relying on a variety
of in-vivo imaging techniques) are incompatible with many of the 20th Century papers.
Unfortunately, the technology used in producing vol 978(1) does not allow searching the PDF form of the
papers when the volume was provided in electronic form in 2006.
A second major problem is the difficulty of the physical laboratory investigations. The result is research
on only a few animals in a given investigation and the resulting small statistical size and a lack of
statistically precise measurements. This situation will become obvious in Section 17.6 were an attempt
is made to focus on a proposed baseline for the 21st Century. A third problem is the sporadic study of
the cerebellum. Different groups have focused on the cerebellum at intervals of a few decades. There
has been inadequate communications between these groups. To still be quoting the camera lucida
sketches of Cajol in the late 20th Century should be an embarrassment to the histological community. A
fourth problem is the recognition that the lower primates and other animals, such as mice, are not
adequate models of the human cerebellum. In the case of a shaven mouse, its total size is smaller than the
human cerebellum.
Haines & Dietrichs245 have provided a comprehensive review of the human cerebellum in an obscure
volume, focused on an entirely different medical field, in 2012 (Section 17.5.1.2.6).
Wright et al246. has provided a broad history of research on the cerebellum, including many of the figures
in the next few subsections. Other figures taken from Gray’s Anatomy are grossly archaic. The authors
244Marr, D. (1969) A Theory of Cerebellar Cortex J Physiol vol 202, pp 437-470
245Haines,D. & Dietrichs, E. (2012) The Cerebellum–Structure and Connections In Subramony, S. & Durr, A.
eds. Ataxic Disorders [vol 103 of Handbook of Clinical Neurology] NY: Elsevier Chapter 1
246Wright, M. Skaggs, W. Neilsen, F. et al. (2016) The Cerebellum WikiJournal Medicine vol 3(1)
doi: 10.15347/wjm/2016.001
314 Neurons & the Nervous System
appear to be not active in this area of research. He relies on multiple citations to extract his text. A
major one is Llinas et al247.
The cerebellum is also discussed from a component perspective in Section 10.2.4.
2.10.3.2 Interpreting a Purkinje cell of Granit & Phillips (1956) with a serape
The serape approach described in Section 9.2.4 can be effectively used to analyze the performance of a
known circuit, or design a desired circuit (whether man-made or of biological origin). The marriage of
the serape approach and the external fields surrounding the Purkinje neuron described by Eccles et al.
provides a major advance in understanding the circuitry and performance of the Purkinje neuron of the
cerebellum.
Granit was a giant of exploratory biophysical research during the middle of the 20th Century. His paper
of 1956 with Phillips was widely acclaimed at the time. The paper focused on the observables related to
the operation of a Purkinje neuron (frequently called a cell in their time period). Their technique, while
state-of-the-art in 1956, was primitive compared what was required.
They used a dual beam oscilloscope without a calibrated time base (probably of Dumont manufacture)
with a signwave at 1000 Hertz on the second beam. It did offer good DC and AC waveform recording
capability.
The paper contained no explicit model of the Purkinje neuron to help them explain the workings of that
neuron. Their implicit assumption was that the neuron was a two-terminal cell with an excitable external
lemma. The external lemma operated in conformance with the common wisdom resulting from the work
of Hodgkin & Huxley (1952). Thus, they were not able to properly account for the actions of the “basket
cells” contacting the soma of the Purkinje neuron exclusively.
Granit & Phillips used a technique similar to that of Eccles et al. (Section 10.2.4 & Section 17.5.1.1).
They did not achieve explicit access to a specific neuron but penetrated the outside of the folium of the
cerebellum and relied primarily on the depth of penetration to determine where their probe tip(s) were,
based on separate histological studies. They were thereby forced to estimate whether their probe was in
intracellular or intercellular space. When their probes reported a reversal in signal polarity, they had to
report this result without being able to explain the reversal based on a two-terminal neuron configuration.
Their figure 2 showed the likelihood of encounters with multiple neurons as the depth of probe
penetration increased.
Granit & Phillips were working before the advent of the patch-clamp technique for interrogating a plasma
within a neuron. As they reported, when they ruptured a lemma, the performance of the neuron degraded
rapidly.
Granit & Phillips hinted at the likelihood that the Purkinje neuron operated fundamentally in the analog
environment but could be induced to generate monopulses of arbitrary polarity under poorly understood
conditions. Like, Eccles and his associates248, Granit & Phillips attempted to perform their experiments
in many cases, in-vivo. In their case, they used exacerbate but living cats. While taking significant steps
to immobilize the cerebellum, they reported difficulties in movement due to vascular-caused motions
associated with the continuing heart beat.
- - - -
Granit & Phillips described the gross histology of the individual folium of the cerebellum (their figure 1)
in close agreement with that of Eccles et al. but with less attention to detail (compare to Section 10.2.4).
They did not concern themselves with the circuitry external to, or, internal to the Purkinje neuron as
developed in Chapter 2 of this work for any neuron.
- - - -
247Llinas, R. Walton, K. & Lang, E. (2004). “Ch. 7 Cerebellum". In Shepherd, G. ed. The Synaptic
Organization of the Brain. New York: Oxford University Press
248Eccles, J. Ito, M. & Szentágothai, J. (1967) The cerebellum as a neuronal machine NY: Springer-Verlag
The Neuron 2- 315
The introduction of the Electrolytic Theory of the Neuron allows a re-examination of the Granit &
Phillips paper and resolution of most if not all of the questions and paradoxes left unresolved in that
paper. Specifically, the introduction of the three-terminal neuron with an internal three terminal active
amplifier is critical to understanding the data they acquired in 1956. They did not report the specific
location of their probe tip(s) with respect to their waveforms with the precision of Eccles et al.
316 Neurons & the Nervous System
Figure 2.10.3-1 displays a first attempt at a serape of a Purkinje neuron that can be used to interpret the
text of Granit & Phillips (Section 17.6.1.1). The voltage scale on the right is largely illustrative, but
based on an electrostenolytic supply of –154 mv as provided by the glutamate/GABA reaction (Section
3.2.2.3.3). The probe penetration scale is taken from the Eccles et al. paper of the next section. Granit &
Phillips employed two different probe strategies. Both probes moved vertically in this illustration, the
matrix probe within the interneuron space and the cell probe penetrating the intraneuron space of the
Purkinje neurons. The rounded corner box is focused on the location of the Activa within the lemma of
the neuron, presumably near the axon/soma interface.
This initial serape does not address the Purkinje neuron as a memory element due to its likely
employment of a four-layer synapse, consisting of a PNPN semiconductor. Such a synapse has a memory
storage capability (Section 17.7.2). It can be used to create a large scale memory in support of a large
scale database (Section 17.7.2 )
The probes of Granit & Phiiips were quite crude by current standards. They routinely employed a pair of
probes arranged 2.0 mm apart for stimulating neurons in the interposed nucleus. For recording from the
Purkinje neuron and its environment, they used 3M-KCl filled probes with a typical impedance of 5-20
Megohms + 3 pF. They did not state whether this shunt capacitance of this probe configuration was
compensated (Section 1.2.5.2.3). It was apparently not compensated as their pulse waveforms show
considerable overshoot. Phillips described the physical preparation of these probes249.
There are many individual situations discussed in words in the Granit & Phillips paper. It is difficult to
determine where to start relating the discussion to the serape. Their figure 7, frame 4 (left) and related
discussion appears to provide a consistent set of values that can be reinterpreted as the waveforms shown
in the above figure. Before proceeding, it is appropriate to note their cautions,
Figure 2.10.3-1 Initial Serape of 3-terminal Purkinje neuron with data from
Granit & Phillips and relying on the Electrolytic Theory of the Neuron. The
neuron contains a three terminal electrolytic semiconducting device, an Activa.
The scale of the figure does not allow precise representation of some features.
The figure does not address the crossbar switch associated with the dendritic
synapse. See text. Waveform data points from Granit & Phillips, 1956.
249Phillips, G. (1956a) Intracellular records from Betz cells in the cat Quart J exp Physiol vol 41, pp 58-69
The Neuron 2- 317
1. They do note under Methods, “The results to be described below are obtainable only if the cerebellum
is in perfect condition.”
2. They noted they considered plotting their data with increased negativity downward “unconventional.”
3. They note, “It has be be admitted at the outset that the antidromic identification of P-cells by fastigial
stimulation is inevitably less certain than the antidromic identification of spinal motoneurons by
stimulation of ventral roots.” But, they do not define what their specific term antidromic means. They
write in one place “in order to stimulate these cells antidromically or monosynaptically, tips of insulated
needles were placed in the cerebellar nuclei or in the arbor vitea above them.”
Combining several sources, “The arbor vitae lies within the center of the cerebellum and helps provide
valuable sensory information to the brain.” “The arbor vitae consists of white matter that allows
communication between different parts of the brain. Many of the supporting structures that connect with
the arbor vitae consist of gray matter.” “Within the arbor vitae exist four structures composed of gray
matter that provide inputs for the cerebellum -- the dentate, emboliform, globose and fastigial nuclei. The
four structures make up a larger network known as the interposed nucleus.” “The arbor vitae consists
primarily of myelinated axons that help to transmit nerve impulses through the body. A myelinated axon
has a white color with a slight pink tint. The pinkish tint comes from the myelin sheath that covers and
protects the axons. Myelin, which consists of protein and fatty materials, not only protects the axons from
damage, but it also serves to speed up the transmission of signals along the branches of the arbor vitae.”
The electrical parameters derived from the Granit & Phillips paper and relied upon in preparing the
serape can be presented in tabular form.
Purkinje Neuron parameters used in the Serape
Voltage value (mV) Cell condition Est. collector (axon) range
net VD-VP<12.7 cutoff –154 mV
>12.7 & <17.4 class B –140 to –120 mV
Threshold 17.4
Above thresh. Positive feedback rises rapidly to saturation
Peak act. Pot. –47.5 (podaplasm saturated –65
Act. Pot. width 1.0–1.5 ms
Condition @1.5 ms refractory –140
Figure 7 (frame 4, left) suggests a quiescent condition for the Purkinje neuron when the podoplasm
terminal (base of the activa) is in the range between 0 mV and –12.76 mV (with the dendroplasm
presumed at 0 mV potential). If a stimulus is provided to the dendroplasm of the Purkinje neuron, either
via the synapse or by charge withdrawal from the dendrolemma, the voltage of that plasma will rise
positively. Until the voltage difference between the dendroplasm and the podaplasm exceeds 12.76 mV,
the Activa will remain in cutoff. When the charge withdrawn from the dendroplasm, impulsively or via a
finite duration pulse, the Activa will begin to conduct charge from the axoplasm into the podaplasm.
This will make the axoplasm become more positive and the podaplasm become more negative. The
Activa is now operating in the Class Banalog amplifier mode. The result is an increase in the voltage
between the dendroplasm and the podaplasm. When this voltage becomes greater than 17.37 mV, the
Activa now enters a high gain mode due to the positive internal feedback due to the impedance in the
podaplasm circuit. For every incremental positive rise in the dendroplasm to podaplasm, the axoplasm
becomes more positive and more charge leaves the axoplasm for the podaplasm increasing the positive
differential between the dendroplasm and the podaplasm, an effect called positive internal feedback.
The axoplasm becomes more positive as fast as the current capacity of the Activa will support. until the
podaplasm potential reaches approximately –47.5 mV and the axoplasm reaches approximately –65 mV.
The voltage drop across the output circuit of the Activa is now approximately 17.5 mV, known as the
saturation potential of the Activa. Under saturation conditions, the amplification, known as the gain, of
the Activa goes to zero. However, it is still in the + feedback mode. As the potential on the podaplasm
begins to decay due to its time constant, TP, the differential voltage between the dendroplasm and the
podaplasm decreases, the axoplasm voltage decreases and the + feedback drives these two potentials
back toward their initial conditions as shown. Under these conditions, the axoplasm has produced a peak
positive going “action potential” of nominally 55 mV during an interval of 1.0-1.5 msec from the start of
the + feedback operation. Simultaneously, it has produced an internal negative going “pseudo action
potential” of 30 mV in the podaplasm.
If a researcher probing the Purkinje neuron, or any stage 3A neuron, is not careful, they may
interrogate the podaplasm instead of the axoplasm and report a negative going pseudo action
318 Neurons & the Nervous System
potential instead of the actual positive going action potential. The podaplasm generally occupies a
larger closed lemma than does the initial axon segment.
Note the time constant of the dendroplasm is generally longer than the podaplasm, resulting in a
refractory period shown as extending to a nominal 3.0 milliseconds on the time scale provided.
As the podaplasm begins to ramp up, the Purkinje neuron goes from cutoff into class B operating mode
(linear amplification) until it reaches the action potential generating threshold at –17.37 mV. At –17.37
mV, the neuron encounters positive feedback and immediately goes into monopulse oscillation, rising to
its saturate potential of –47.5 mV. It can be presumed that the axoplasm was near –154 mV during
cutoff, went into the range of –140 to –120 during class B operation and dropped to about –65 mV at the
peak of its positive going monopulse output (a quiescent to peak amplitude monopulse of about +90 mV).
These are reasonable values for any neuron operating as a stage 3A analog to monopulse converter.
Granit & Phillips further note relative to this waveform,
“Occasionally there is a ‘rebound’ increase in the frequency of discharge following the pause of an
inactivation response.”
This is an non-specific statement; it may be a characteristic of the phase code used to generate the pulse
stream, the IRIG code (Section 9.3.1).
2.10.3.3 Potential Purkinje neuron Circuit as defined by Marr, 1969
Marr attempted to bound the parameters of a circuit containing only a single Purkinje neuron and its
associated circuitry using a stochastic model of neural operations. He did not provide any significant
figures related to his largely conceptual model based on the earlier exploratory research of Eccles et al. in
1967. His results are largely consistent with this work, which expands on the work of Ito of 1984 in
Section 2.10.3.5.
His paper is limited to the motor aspects of cerebellum operations. There are some terminology
differences,
he defines a dual task for his single Purkinje circuit, (2a) learning and (2b) maintenance; whereas the
normal operation of the cerebellum equates to his maintenance and learning remains learning (which
occurs as a default loop, Section 17.2.5).
he defines a codon as a subset of a collection of active mossy fibers; whereas this work defines such a
group of mossy fibers as the specific input to a decoder (glomeruli) addressing a specific set of parallel
fibers.
he describes the synapse between the parallel fibers and the dendritic branchlets whereas this work
assigns the label crosspoint, or cruciform synapse for a synapse at this location.
he defines the cruciform synapse as a two-state device whereas here the same device is defined as a
four-layer semiconductor device of the PNPN type which is also a two-stable states.
Marr summarized his theory, including a set of predictions in item ,
“1. A detailed theory of cerebellar cortex is proposed whose consequence is that the cerebellum learns to
perform motor skills. Two forms of input/output relation are described, both consistent with the cortical
theory. One is suitable for learning movements (actions), and the other for learning to maintain posture
and balance (maintenance reflexes).
2. It is known that the cells of the inferior olive and the cerebellar Purkinje cells have a special
one-to-one relationship induced by the climbing fibre input. For learning actions, it is assumed that:
(a) each olivary cell responds to a cerebral instruction for an elemental movement. Any action
has a defining representation in terms of elemental movements, and this representation has a
neural expression as a sequence of firing patterns in the inferior olive; and
(b) in the correct state of the nervous system, a Purkinje cell can initiate the elemental movement
to which its corresponding olivary cell responds.
3. Whenever an olivary cell fires, it sends an impulse (via the climbing fibre input) to its corresponding
Purkinje cell. This Purkinje cell is also exposed (via the mossy fibre input) to information about the
context in which its olivary cell fired; and it is shown how, during rehearsal of an action, each Purkinje
cell can learn to recognize such contexts. Later, when the action has been learnt, occurrence of the
context alone is enough to fire the Purkinje cell, which then causes the next elemental movement. The
action thus progresses as it did during rehearsal.
The Neuron 2- 319
4. It is shown that an interpretation of cerebellar cortex as a structure which allows each Purkinje cell to
learn a number of contexts is consistent both with the distributions of the various types of cell, and with
their known excitatory or inhibitory natures. It is demonstrated that the mossy fibre-granule cell
arrangement provides the required pattern discrimination capability.
5. The following predictions are made.
(a) The synapses from parallel fibres to Purkinje cells are facilitated by the conjunction of
presynaptic and climbing fibre (or post-synaptic) activity.
(b) No other cerebellar synapses are modifiable.
(c) Golgi cells are driven by the greater of the inputs from their upper and lower dendritic fields.
6. For learning maintenance reflexes, 2 (a) and 2 (b) are replaced by
2'. Each olivary cell is stimulated by one or more receptors, all of whose activities are usually
reduced by the results of stimulating the corresponding Purkinje cell.
7. It is shown that if (2') is satisfied, the circuit receptor > olivary cell > Purkinje cell > effector may
be regarded as a stabilizing reflex circuit which is activated by learned mossy fibre inputs. This type of
reflex has been called a learned conditional reflex, and it is shown how such reflexes can solve problems
of maintaining posture and balance.
8. 5(a), and either (2) or (2') are essential to the theory: 5 (b) and 5(c) are not absolutely essential, and
parts of the theory could survive the disproof of either.”
Item 8 when configured as 5(a) and (2'), constitutes the learning mode that allows the crucifprm synapse
to be set to one of its stable states.
Marr provided a summary of Purkinje circuit elements from Eccle et al. better than they provided.
“It is therefore convenient to set them down here.
Each Purkinje cell has about 200,000 (spine) synapses with the parallel fibres crossing its dendritic tree,
and almost every such parallel fibre makes a synaptic contact. The length of each parallel fibre is 2-3 mm
(1 mm each way), and in 1 mm down a folium, a parallel fibre passes about 150 Purkinje cells. Eccles et
al. (1967) are certain each fibre makes at least 300 (of the possible 450) synaptic contacts with Purkinje
cells, and think the true number is nearer 450. There is one Golgi cell per 9 or 10 Purkinje cells, and its
axon synapses (in glomeruli) with all the granule cells in that region, i.e. around 4500. There are many
granule cells (2-4 x 106 per mm3 of granule cell layer), each with (usually) 3-5 dendrites (called claws):
the average is 4-5 and the range 1-7. Each dendrite goes to one and only one glomerulus, where it meets
one mossy fibre rosette. It is, however, not alone: each glomerulus sees the termination of about 20
granule cell dendrites, possibly a Golgi cell descending dendrite, and certainly some Golgi axon
terminals, all from the same Golgi cell. Within each folium, each mossy fibre forms 20-30 rosettes,
giving a divergence of 1 mossy fibre to 400-600 granule cells within a folium. The mossy fibre often has
branches running to other folia, and in Fig. 2 below one can count 44 rosettes on one fibre.”
These values are the source of the values in the figures of Section 2.10.3.5.
Beginning in his section 3, he adopts statistical theory to describe the operation of the Purkinje neurons
and supporting circuitry. This contrary to this work that describes the CNS as fundamentally a
deterministic system.
However it may be acceptable for bounding the parameters of certain parameters ala Tsotsos (Section
15.2.2.1).
In his section 4 he describes the need for his codon size to be a variable. In his section 4.1.4, he notes,
“It will be assumed that a signal in a mossy fibre is represented by a burst of impulses lasting many tens
of milliseconds; and that a signal from a Purkinje cell is represented by a prolonged increase in its firing
rate. This is discussed later (5.0); for the moment, it is needed only to justify the fifth condition.”
The comments in section 4.1.4 are compatible with either the mossy or climbing fibers acting as
integrators and thus providing a means of keeping the Purkinje neuron output sensitive to the other
indexing means for a finite length of time.
His section 4.2 notes,
“The Golgi cells are inhibitory, can be driven by mossy fibres (through their descending dendrites) and
synapse exclusively with granule cells. Further, they are particularly notable for the speed of their
response (citing Eccles et al., 1967).”
In his section 5.0, he notes,
320 Neurons & the Nervous System
“The second point arises from the fact that Purkinje cells have a high resting discharge of 20-50
impulses/sec. (Eccles et al. 1967, p. 306).”
“Purkinje cells can sustain high rates of firing (greater than 400/sec, according to Eccles et al. 1967, p.
308): it is therefore reasonable to assume that a signal in a Purkinje cell axon is represented by a large
increase in the firing rate, and that the effector systems are only sensitive to such messages. This
assumption would have to be made for almost any theory of the cortex, since the Purkinje cells form the
only output.”
His section 5.1 makes a critical observation,
“The fundamental hypothesis for the mechanism of the change of effectiveness of a parallel
fibre-Purkinje cell synapse is that if a parallel fibre is active at about the same time as the climbing fibre
to a Purkinje cell with which that parallel fibre makes synaptic contact, then the efficacy of that synapse
is increased towards some fixed maximum value. ('At about the same time' is an intentionally inexact
phrase: the period of sensitivity needs to be something like 50-100 msec.)” [italics in original]
This makes a critical statement about a parameter related to the learning experience. It holds the
learning gate open for enough time for the parallel fibers to change their configuration multiple times
and thereby store multiple bits of data on multiple Purkinje neurons.
At the end of his section 5.1, he makes another significant observation concerning the cruciform synapses
that is the same recommendation of this work for future study,
“The other and rather dangerous place one might look for implications of the modification hypothesis is
in the comparison of electron-micrographs of cells supposed to have modifiable synapses with those
supposed not to. This will not be attempted, but it may be relevant that the Purkinje cells seem to be the
only ones in the cerebellum whose dendrites carry the characteristic tubular system which terminates
'abruptly' at the base of the spines (Eccles et al. 1967, p. 9).
The electron-micrographs of the cruciform may show various charge accumulations which would identify
their “state.”
Marr describes certain simplifying assumptions in section 5.2 through section 6.0 that relate to his
stochastic model only. Section 7& 8 also relates to the model assumed and won’t be addressed here.
There is a brief Addendum at the end of the paper that may be important.
The Marr paper deserves its reputation for a paper during the 1960's related to the cerebellum. It was
tragic the community lost such a mind so prematurely.
2.10.3.4 Interpreting a Purkinje cell based on the conflicting information with a
serape
There are at least three different morphological configurations of the Purkinje neuron based on the work
of the histological community. Three of these configurations are illustrate in Figure 2.10.3-2,
reproduced from Fig 17.6.1.3.
The Neuron 2- 321
In frame A, several texts have described the descending axon(s) of basket cells, although primarily
contacting the non-inverting dendritic tree of the Purkinje neuron, occasionally contacting the periphery
of the base of the neuron in the area normally associated with the signal inverting poditic terminal. In
frame B, the descending axon(s) of basket cells, are shown as contacting the pre-axon area of the neuron.
In both cases, the descending axon of the basket cell would be considered to be contacting the poditic
(base) terminal of the Activa of the Purkinje neuron. However, in the second case, the poditic lemma of
the neuron extends down to the end of the thin portion of the emanating structure to the point where the
axolemma completes the formation of the Activa. At this point, the axolemma subsequently becomes
myelinated and the signal transitions into the propagation mode of transmission.
In both cases, the descending basket axon synapses with the poditic terminal of the purkinje neuron
(figure 56 in Eccles et al.).
In frame C, as proposed by Szentagothai, the soma of the Purkinje neuron is isolated from any synapse
formation on its surface by a group of glia cells. In addition, the myelinated collaterals easily replace the
mossy cell axons in synapsing with the Purkinje neurons of a second crossbar switch (Section 17.7.2.2).
There is so much written about the operation of the Purkinje neuron in the presence of action potentials,
or other stimuli applied to individual neurites, in the absence of any null hypothesis as to its functional
role, that accounting for its operation as a memory unit is difficult (see Section 17.6.1). The only way to
account for the operation of the Purkinje neuron of the cerebellum in the light of its many inputs may be
to create a serape presentation (Section 9.2.4).
Figure 2.10.3-2 Potential histological forms of Purkinje neurons. A; the
simplest variant proposed for the Purkinje neuron. The primary and secondary
dendrites are isolated from the matrix by Bergmann cells. The descending
axons of basket cells synapse with the perimeter of the base of the neuron,
resulting in a inverting (inhibiting) input to the Activa. B; the next most
complicated variant. The primary and secondary dendrites are also isolated
from the matrix by Bergmann cells. However, the descending axons of basket
cells synapse with the protruding portion of the base, labeled the pre-axon by
Eccles et al. in 1967. C; as described by Szentagothai (1965a) with soma
isolated by glia cells and myelinated collaterals. Some of the collaterals may
not be myelinated. All secondary dendrites (dendritic branchlets) are in a
single plane. All dendrites are applied to the positive (excitatory) input to the
Activa; all basket cell signals are positive going action potentials applied to the
negative (inhibitory) input to the Activa.
322 Neurons & the Nervous System
2.10.3.5 Interpreting the cerebellum as a storage area for a database
Based on the comments above and in the subsections of Section 17.7.2.8, it is possible to define a Null
Hypothesis about the indexing strategy used in the cerebellum as illustrated in Figure 2.10.3-3 .from
Section 17.7.2.8.3 and expanded from Ito in 1984.
The figure identifies multiple Microzones that constitute individual crossbar switches.
The figure shows three degrees of indexing apparently employed in individual sections of memory array
of the cerebellum,
indexing by the dendritic branchlets at their intersection with the parallel fibers (derived from the
ascending fibers),
indexing by the climbing fibers at their synapses with the bulk dendrites prior to their arborization
(derived from the mossy fibers),
indexing by the basket cells at their synapses with the Purkinje neuron soma.
The interpretation of these indexing schemes is complicated by the ability of each synapse associated
with the climbing fibers and the basket neurons to be represented by multiple contacts (boutons) with
their target neurite. in order to achieve the desired serial impedance level associated with the overall
synapse.
The complex encoding at the dendritic branchlets at their intersection with the parallel fibers is
particularly difficult to describe because of the multiple complex synapses of the PNPN types which form
individual storage elements ( a.k.a. crosspoints or cruciform synapses).
The physical appearance of a crosspoint does not reflect its electrical circuit performance. When it
is in its high impedance state, it effectively rmoves that crosspoint from any effect on the
performance of that Purkinje neuron. It is only the crosspoints that are in their low impedance
state that participate in indexing.
This process greatly simplifies the indexing of the individual Purkinje neuron, but makes it impossible to
evaluate the circuit based on its physical appearance (morphology). Of the uncountable number of
crosspoints associated with a single dendritic branchlet, only a few may be in their low impedance state
and effect the performance of the indexing operation.
The Neuron 2- 323
Figure 2.10.3-3 Null Hypothesis of the indexing strategy employed in the
cerebellum to allow access to the information stored in long term memory.
The indexing shown here follows the sequence; region, word & bit selection.
This hypothesis follows the reported properties of the different neurons
provided primarily by Wright (2016). Llinas & Hillman provided data on the
basket neurons. Note Wright’s comment related to the climbing fibers and
their relation to an Escher drawing. The climbing fibers, CF, should probably
be drawn as in contact with the Purkinje neurons along the transverse axis,
TP. The CF only contact the root dendritic areas through conventional
synapses. The parallel fibers only contact the dendritic branchlets through
spines at cruciform synapses. The function of many types of interneurons
present in the cerebellum have not been included here.
2.10.3.6 Interpreting the Single Purkinje as a storage unit for a database
The circuit of the Purkinje neuron of Eccles et al. of 1967 is more complicated than that of Granit &
Phillips of a decade earlier. In turn, the indexing circuit of Ito of 1984 is more complicated still.
The fact that no electron-micrograph could be found showing the internal lemma within the
dendrite to dendritic arborization region makes it difficult to determine the internal electrical
configuration within the normal single dendrite of a Purkinje neuron. It makes it even more
difficult to determine the internal electrical configuration of the rare Purkinje neuron with two
distinct dendrites and their arborizations identified by Eccles et al. (Section 10.2.4.5).
The type of electron-micrograph needed is shown in Section 2.2.2.3.1 at 204,000X from Gigula, 1975.
Acquiring suitable micrographs at this magnification and covering the length and cross- section of a
branchlet is very difficult. The full length is not a requirement if the region near the root of a few spines
could be documented along with the region near the branchlet/dendrite interface could be documented.
The documentation only needs to be accomplished once.
324 Neurons & the Nervous System
Figure 2.10.3-4 Symbolic form of one Purkinje Neuron within a crossbar
memory. In this configuration, auxiliary Activa (active amplifiers) are
introduced at the junction between each Purkinje root dendrite and each
branchlet under control of the climbing fibers. This would require multiple
internal lemma in close proximity, isolating the root dendrite from the
branchlets. See text. The nucleus of the cell plays no role in signaling.
The following symbolic representation of a single Purkinje neuron in Figure 2.10.3-4, operating in the
normal (or maintenance) mode, will assume the presence of an Activa at the junction of each dendritic
branchlet with its parent dendrite. This conceptual Activa will be controlled by the climbing fibers
synapsing with the dendrite.
There may be an alternate configuration that provide an active control of the output voltage of the
cruciform synapse in order to establish its operating state (Section 17.7.4). In this alternative, the
climbing input is used to control the voltage of the cathode potential of the PNPN switch within the
cruciform synapse. This configuration supports both the learning mode and the normal operating mode.
By adjusting the voltage between the climbing fiber input and the relevant parallel fiber, the state of the
cruciform synapse can be changed to the low impedance condition (shown by the closed switches in the
figure. This configuration will be shown conceptually in the next figure, after the simpler form is
discussed.
The figure consists of two branchlets out of a very large number (shown at the center). Each is shown
connected to its portion of a crossbar switch (Section 17.7.4). The crosspoints, cruciform synapses, are
shown at the termination of a spine of the branchlet (shown here as a horizontal line) with one of the
parallel fibers. The status of the crosspoint is shown by the switches shown to the right of the termination
point. The dotted switches are shown to emphasize two things,
the fact that there was no cruciform synapse formed with the “a” parallel fiber and,
the fact that the status of the other switches cannot be determined by their morphological appearance.
There may be a diode (not shown) before the junction between the spines with the branchlet to improve
the “OR” performance of the summation point (although this capability may be built into the four-layer
diode of the cruciform synapse).
The Neuron 2- 325
Figure 2.10.3-5 Alternate Symbolic form of one Purkinje Neuron within a
crossbar memory. This representation uses a blotch to show a change in the
configuration between the soma of the Purkinje neuron and the crossbar
switch. Note the change in the label above the Activa within the soma to
indicate the Activa of the Purkinje cell is now operating as a driven stage 3A
monopulse oscillator. The circuitry within the blotch and the explicit diode
would apply to each of the spines of each branchlet. See text.
When considering the basket cells (Ba) and stellate cells (St) he decides to address them as all stellate
cells. In this work the opposite choice has been made, as apparent in the above figure. He also assets,
“Both types of cells synapse exclusively with Purkinje cells, and are powerfully inhibitory [as shown.”
Figure 2.10.3-5 demonstrates a proposed alternate symbolic configuration of the Purkinje neuron and its
associated circuitry capable of operating in both the normal operating mode and the learning mode. The
change places the input from the climbing fibers in shunt with each spine at its interface with the
branchlet and may require a diode as shown to isolate the spine and the cruciform synapse during the
learning process. All of the potentials on the spines are controlled by boutons of the same climbing fiber
axon. Only an electron-micrograph can determine whether this configuration, or the one above is
feasible; or whether another configuration is used in the biological version.
If the alternate configuration is closest to the biological neuron, it suggests the functional role of the
climbing fibers is limited to the learning mode where the switches are closed permanently (the low
impedance configuration) for a particular set of parallel fibers that are activated. Marr does not consider
the learning mode within the cerebellum, but does note on page 461,
“Hence, it could be argued that when the climbing fibre is active, that is when synaptic modification is
taking place . . .”
This indicates he would have been comfortable with the concept of the climbing fibers controlling the
state of the cruciform synapse during learning. He also asserts on page 441,
“Each climbing fiber makes extensive contact with the dendritic tree of a single Purkinje cell (p), and its
effect there is powerfully excitatory.”
When fully excited by the climbing fiber, the spline is at its lowest voltage relative to its associated
parallel fibers; thereby changing the cruciform synapse to its lowest impedance state where it latches (a
closed switch) as per Section 17.7.4.
326 Neurons & the Nervous System
The Neuron 2- 327
2.11 CHAPTER SUMMARY
2.11.1 The ACTIVA, an ELECTROLYTIC COMPONENT FOUND IN EVERY
NEURON
This chapter has shown how an active electrolytic semiconductor device, the Activa, can be formed
within and between living neurons. It has also shown how the Activa can be combined with other
electrolytic, but otherwise conventional electrical, circuit elements to form circuits called conexuses. It
has postulated that the neuron consists of multiple electrically isolated conduits.
At a larger scale, it has shown that the fundamental neural signaling path consists of a series of passive
electrical conduits interdigitated with conexuses containing Activa. This organization has shown that the
synapse between neurons and the conexuses within neurons are fundamentally alike. This chapter has
also postulated that the conexus is the fundamental physiological unit of the biological neural system
instead of the morphologically defined neuron.
All of the above functional elements have been described in their entirety using only electrical and
quantum-mechanical terminology and phenomenology. There has been no need to call upon chemistry to
describe the functional (signaling) aspects of the neuron. As in Chapter one, the biological membranes of
the neuron have remained impermeable to ions and small molecules of all types for signaling purposes.
Only the metabolic aspects of the neuron related to growth and respiration, and the generation of
electrolytic power have relied upon chemical processes.
All synapses are in fact active semiconducting devices acting as low loss current transfer devices
(see Section 2.4.3).
The discovery that all neurons and all synapses contained at least one active electrolytic
semiconductor device provided an entirely new foundation on which to build a broader
understanding of the neural system.
The chapter has also postulated that the electrical power required by the neuron is derived from an
electrostenolytic process. The chapter went into more detail concerning the electrical properties of the
active device found within all neurons, the Activa. It then described a series of electrical circuits formed
from the basic conexus within a neuron. Finally, the chapter described a series of functional electrolytic
circuit building blocks that can be easily formed from the basic conexus within a neuron. Subsequent
chapters will discuss how these building block circuits are actually used in a variety of common neurons.
The postulates offered in this chapter will be justified in greater detail in the following chapters.
However, the basic premise is clear, the neural system of all animals is electrolytically based. The
Electrolytic Theory of the Neuron provides a comprehensive and unrivaled explanation for the operation
of a wide variety of individual neurons and synapses, as well as the overall neural system.
2.11.1.1 Absence of variable resistors in biological circuits
The chemical theory, since the time of Hodgkin & Huxley, have included the symbol for variable
resistors without defining how these resistors varied.
It is important to reflect on the fact that the equivalent circuits of neural activity (in this work) have
completely avoided the symbol for a variable resistor with its implied external control mechanism. By
replacing these symbols by the more appropriate transistor symbol (or the diode symbol from which the
transistor symbol is derived), the element is recognized for its variable but completely programmed
change in impedance as a function of applied voltage.
It is also important to note that the electrical potential of the plasma enclosed by a membrane has been
changed relative to the matrix without any change in the permeability of, or the transport of any ions
across, the conduit membrane.
A change in plasma potential within a membrane to a more negative value with respect to its quiescent
value is seen to be caused by transistor action, involving an Activa, and not by the “excitability of the
membrane.” The instantaneous potential within a plasma is controlled by the flow of electrons through
328 Neurons & the Nervous System
type 2 (and higher types of lemmma). A corollary to this situation is that the ionic concentration of the
plasmas within and adjacent to a neural conduit do not change in the short term and play no role in the
signaling function.
No conventional, power dissipating, resistors are found within the neural system. The transport delays
associated with diffusion of charge through an electrolyte plays a role similar to that of a resistor in more
conventional (non-electrolytic) circuits.
As noted by Yau250 based on the data he presented from Luttgau, changes in the concentration of Ca2+ and
Mg2+ within the intracellular medium (plasma) do not affect the current versus voltage characteristic of
the typical plasma membrane in-vivo. Such changes would have negligible impact on the operation of the
reverse biased axonal plasma membrane.
2.11.1.2 Electrochemical Support by Region
The division of the external membrane of a conduit into regions with distinctly different electrical
characteristics appears to be a fundamental design parameter of the neural system. By making
adjustments in the molecular makeup of the individual bilayers of the regions of a membrane, unique
types of electrical parameters may be easily obtained for these regions.
2.11.1.3 Lack of Need for ions to pass through Membranes for Signaling
A totally unexpected result of the analysis in this work is the lack of a requirement for ions to pass
through the exterior membranes (generally type 1 and type 2) of the conduits of a neuron for signal
related purposes. It appears that the movement of ions through type 3 membranes is entirely for the
purposes of genesis and metastasis. The hydrophobic core of the type 1 and type 2 BLMs completely
blocks the short term flow of ions through the membrane. No ionic currents are required for the
signaling operation of the neurons.
2.11.1.4 Confirmation of the Switching Characteristic of the Oscillating Neuron
The use of the binary switching functions, h, m & n in the unsolved partial differential equations
developed by Hodgkin & Huxley, and used by most subsequent modelers, introduce arbitrary switching
points that are not otherwise identified in their numerical integrations. These switching points are the
nearly the same as those defined by explicit events in the Electrolytic model of the relaxation type
oscillations of a stage 3A neuron. The binary switching functions do not reflect the threshold voltage of
relaxation type oscillators!
2.11.2 TRANSITION FROM AN AXON-ONLY TO A JUNCTIONAL-TISSUE
MODEL
While an axon can be described as an axolemma enclosing an axoplasm, the axolemma exhibits access to
more than one “surrounding medium.” It is in communications with the surrounding extracellular
medium. It is also in communication with other intracellular media. Any equation describing the
electrical potential of the axoplasm must take all of the access ways into account.
The above analysis led further. It showed, as illustrated in [Figure 2.2.2-1], that the configuration of the
junctional-tissue between two neurons was largely indistinguishable from the configuration of the
junctional-tissue between the dendrite and the axon within a neuron. As a result of further analysis, to be
presented in Chapter 3, a stunning conclusion appeared. It became clear that the synapse was another
form of conexus built using the three-terminal Activa defined above.
2.11.2.1 Rationalizing the axon-only versus the junctional-tissue models
Since the constrained analyses of Hodgkin & Huxley in the 1950's, the axolemma of a neuron has been
considered the key active element in the neurological system. This axolemma has been modeled as a
two-terminal electrical network of varying degrees of complexity. However, these axon-only models
have not proven satisfactory and have not explained the roles of the other neurites of the neuron. A large
cadre of investigators have not been able to explicitly define the mechanism controlling the variable
250Yau, K. (1994) Phototransduction mechanism in retinal rods and cones, Invest. Ophthal. & Vis. Sci. Vol. 35,
no. 1, pp 9-32
The Neuron 2- 329
impedance(s) shown in these axon-only models. Finally, the two-terminal axon concept has not led to
progress in understanding the overall operation of the neural system. It has been unable to explain the
signaling mechanism found between neurons. It has also failed to explain the subtraction process
involved in creating the signals observed at the S-plane of the retina. This situation has led other authors
to question the adequacy of the basic two-terminal assumption associated with the axon only ideology.
It has also been common for authors to attempt to explain the operation of the neural system based
entirely on chemical processes. This appears to be primarily due to the academic training of the authors
and the ubiquity of certain chemicals near elements of the neural system. However, this ubiquity has not
provided insight into the mechanisms employing these chemicals. The current concept of
neurotransmitters is a particularly awkward one in the neuroscience literature. It can be questioned on
many grounds. The fundamental chemistry associated with signaling within a neuron will be explored
further in Chapter 4. It leads to a totally different view of the chemical role of the putative
neurotransmitters.
An alternate unconstrained analysis, summarized above and diagramed in Figure 2.1.1-1, has led to a
fundamentally different “junctional-tissue” ideology. At a top level, this ideology focuses on the
junctional-tissue between conduits within a neuron as the location of the active mechanism within the
neuron. At the next lower level, the ideology focuses on the junctional-tissue as forming a unique three-
terminal electronic component. At a functional level, this single three-terminal device is seen to be
ubiquitous throughout the neural system. This three-terminal device can be shown to be the biological
equivalent of the man-made transistor. It is a PNP type electrolytic liquid-crystalline semiconductor
devices named an Activa. This ideology expands to describe three-terminal Activas located at multiple
locations along each neural signal path. These locations are both within and between (outside) individual
neurons.
The three-terminal junctional-tissue ideology leads to radically different interpretation of the chemicals
found in and adjacent to the neurons. Many of them are bio-energetic materials associated with
metabolism in other parts of the body. They are particularly associated with the well-known glutamate
cycle of metabolism. These materials are well suited to participation in an electrostenolytic process at the
surface of the neurons designed to provide electrical power for signaling instead of chemistry-based
signaling. Section 2.7 will expand the chemical mechanisms available under the junctional-tissue
ideology that lead to a complete understanding of the synapse as presented in Section 2.4.
The following sections will proceed to define the detailed features and proposed operation of the
fundamental neuron containing an Activa. Chapter 3 will address neurons of greater functional
complexity. Chapter 5 will address the morphological packaging and physiological operation of
complete neurons based on the junctional-tissue ideology and the Activa hypothesis. Following these
chapters, the reader can make an independent judgement concerning the competitive merits between the
axon-only and the junctional-tissue ideologies. The material of Chapters 8 through 12 will describe the
operation of the entire neural system based on the junction tissue ideology and Activa hypothesis.
2.11.2.2 The junctional tissue as the conexus within a neuron
As developed above and expanded upon in Section 2.3, the performance of the individual bipolar
neurons suggests they contain a very simple electrical circuit (a conexus) that contains a single active
semiconductor device (an Activa) as its centerpiece. This assumption has proved to be entirely
satisfactory in the case of all signal manipulation neurons and has led to a detailed understanding of the
more complex types of neurons. Such semiconductor devices are described as three-terminal devices.
The fact they are three-terminal devices suggests the internal construction of the neuron is more complex
than previously recognized. Two of these terminals are connected to a dendritic conduit and an axon
conduit respectively. The third terminal is connected to a newly defined element, a poditic conduit. The
nature and characteristics of this conduit will be discussed briefly in [Section 2.2.6.1] and presented in
detail in Chapter 3.
Both projection neurons and many signal detection neurons are found to contain multiple active devices.
All of the Activas found within these neurons are found in areas composed of junctional tissue.
2.11.2.3 The junctional tissue as the conexus between neurons–the synapse
As suggested by [Figure 2.2.2-1(D)], the synapse between two neurons appears cytologically identical to
the conexus within a neuron. They both occur in areas of junctional-tissue. While there is a functional
difference between an internal conexus and the synapse, the difference is defined primarily by the
electrical biases supplied to the three terminals of the Activa within each conexus. The operation of the
synapse is described in detail in Section 2.4.
330 Neurons & the Nervous System
2.11.3 TRANSITION FROM A DUAL-ALKALI TO AN ELECTRON-BASED
MODEL
The previous sections have portrayed the neuron in an entirely different light than that proposed by the
Dual Alkali-ion Diffusion Theory. Under the junctional-tissue ideology, the operation of the neuron is
based entirely on the flow of electrons into and out of a variety of enclosed plasma conduits. These
conduits are impervious to the sodium and potassium ions of the Dual Alkali-ion Diffusion Theory.
Under this Electrolytic Theory based on the junctional-tissue ideology, the neuron is fundamentally an
electrolytic device (or circuit) capable of performing a variety of electrical signal manipulations similar to
man-made transistor circuits. This performance is achieved by exploiting the conexus (combined Activa
and other electrolytic circuit elements) within the neuron. It is the exploitation of the analog device, the
Activa, within the fundamental neuron that gives the neural system its great flexibility and overall
capacity.
The Dual Alkali-ion Diffusion Theory is unsustainable in the presence of the superior Electrolytic
Theory.
There have been many papers describing the shortcomings of the alkali ion current theory of the neuron.
Connors & Stevens251,252,253 explored the shortcomings of the Hodgkin & Huxley model. To achieve a
more rational fit between the data and the proposed flow of alkali ions, they introduced an additional A-
current that was transient. They noted an inward current persisted in the absence of sodium ions in the
artificial sea water (pg 16).
The Electrolytic Theory has explained the operation of a neuron in ways the Dual Alkali-ion Diffusion
Theory cannot even address. The following sections of this Chapter and Chapter 9 will exploit the
Electrolytic Theory even further to explain additional details of the operation of individual neurons.
Chapters 11 through 15 will exploit the Electrolytic Theory even further to explain the operation of the
entire neural system at a very detailed level.
251Connor, J. & Stevens, C. (1971) Inward and delayed outward membrane currents in isolated neural somata
under voltage clamp J Physiol vol 213, pp 1-53 (three papers)
252Connor, J. (1977) Time course separation of two inward currents in molluscan neurons Brain Res vol
119(2):487-92
253Connor, J. Walter, D. & McKown, R. (1977) Neural repetitive firing: modifications of the Hodgkin-Huxley
axon suggested from crustacean axons Biophysical J vol 18, pp 81-102
The Neuron 2- 331
Table of Contents 6 November 2023
2 The Functional Configuration of the Basic Neuron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Introduction.............................................................. 3
2.1.1 The fundamental chemically-based neuron of biology . . . . . . . . . . . . . . . . . . . . 4
2.1.1.1 An exhaustive review of neuron models –Borg-Graham,1998 . . . . . . 6
2.1.2 Modeling difficulties of the chemical theory of the neuron up to the current day
............................................................ 7
2.1.3 Roadmap and fundamental premises developed in this chapter . . . . . . . . . . . . . . 8
2.1.4 Analyses of membranes in the literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.4.1 Demonstration of impermeability of lemma to cations or water. . . . 12
2.1.4.2 A short history of putative pores, carriers & gates in bilayer
membranes........................................... 14
2.1.4.2.1 Rationalizing pores, carriers & gates discussion–types of
lemma ....................................... 15
2.1.4.3 Permeability of in-vivo lemma by diffusion &/or pores . . . . . . . . . . 15
2.1.4.3.1 Permeability of single bilayer in-vitro by diffusion and/or
pores ........................................ 16
2.1.4.3.2 Paula et al. papers in Bilayer Lemma Physical Chemistry
............................................. 19
2.1.4.3.3 A potential potassium pore in 3D-- . . . . . . . . . . . . . . . . 23
2.1.4.4 Preparation of synthetic bilayer membranes. . . . . . . . . . . . . . . . . . . 24
2.1.4.5 Liquid crystalline versus gel state in phospholipids . . . . . . . . . . . . . 26
2.1.4.6 Electrostatic properties of charged lipids . . . . . . . . . . . . . . . . . . . . . 30
2.1.4.7 Expanding the lemma nomenclature . . . . . . . . . . . . . . . . . . . . . . . . 32
2.1.4.7.1 Membranes of Escherichia coli–Lind . . . . . . . . . . . . . . . 32
2.1.4.7.2 Expanding the outer bilayer nomenclature . . . . . . . . . . . 33
2.1.4.7.3 Features of membranes & junctions–Pappas, 1975. . . . . 33
2.1.4.7.4 Bilayers as studied by 2H NMR & molecular
dynamics–Huber, 2002 . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.1.4.7.5 Potential lipids in type 2 lemma and the
photoreceptors–Crawford, 2013 . . . . . . . . . . . . . . . . . . . 40
2.1.4.7.6 Concentration of DHA in the Human brain & its
nutrition–Calder, 2016 . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.1.4.7.7 Raman Spectroscopy of DHA and related
lipids–Broadhurst,2018 . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.1.4.7.8 Expanded properties of DHA –Crawford, 2020 . . . . . . . 48
2.1.4.8 Apparatus for creating & evaluating bilayer lemma . . . . . . . . . . . . . 48
2.1.4.8.1 Creating symmetrical & asymmetrical membranes . . . . 48
2.1.4.8.2 The Langmuir trough– –lipid strength & thickness. . . . . 49
2.1.4.8.3 Scanning calorimetry–evaluating TC in lipid chains-
Quinn,1976 ................................... 49
2.1.4.8.4 2H & 13C spectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.1.4.8.5 Low-Temperature 2H NMR Spectroscopy of Phospholipid
Bilayers- Barry, 1991 ........................... 51
2.1.4.8.6 X-ray crystallography . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.1.4.8.7 X-Ray crystallography and DHA-Lor, 2015 . . . . . . . . . . 52
2.1.4.9 Evaluating the individual lemma found in neurons . . . . . . . . . . . . . 57
2.1.4.9.1 Test apparatus for evaluating whole individual neurons
............................................. 59
2.1.4.7.7 Concentration of DHA in the retina-Jeffrey, 2001 . . . . . 59
2.1.4.7.7 Percent content of DHA in neural tissue . . . . . . . . . . . . . 59
2.1.4.7.8 Comparison between PtdEth of the two schools . . . . . . . 69
2.1.4.7.9 Dry weight of a typical neuron vs types of lemma present
............................................. 70
2.1.5 Formation of islands and plates of lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
2.1.5.1 Applying AFM to natural type 2, 3 & 4 lemma roughness. . . . . . . . 73
2.2 The structural and electrical characteristics of the static (first order) neuron . . . . . . . . . . . 74
2.2.1 The fundamental cell membrane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
2.2.1.1 Local (cytological) uniformity of the neuron membranes. . . . . . . . . 80
2.2.1.2 Molecular level uniformity of the fundamental membrane. . . . . . . . 80
2.2.1.3 Charge transfer through the bilayer membrane– by “holes” . . . . . . . 81
2.2.1.3.1 The long chain molecules of the lemma as nematics. . . . 82
332 Neurons & the Nervous System
2.2.1.3.2 The Nobel Prize in Chemistry for 2000–semi-conductive
lipids ........................................ 83
2.2.1.3.3 The role of double bonds in semi-conductive lipids . . . . 83
2.2.1.3.4 An alternate family of potential phospholipids . . . . . . . . 87
2.2.1.3.5 Spacial parameters of the neural phospholipids ADD. . . 88
2.2.1.4 The Chemical theory of the plasmalemma at the end of 20t h Century)
.................................................... 90
2.2.1.5 The dipole potential of the biological bilayer membrane (BLM) . . . 92
2.2.2 Development of the functional structure of the neuron . . . . . . . . . . . . . . . . . . . 92
2.2.2.1 Evolutionary path from stem-cell to neuron . . . . . . . . . . . . . . . . . . . 92
2.2.2.2 Local view of neuron formation from a stem-cell. . . . . . . . . . . . . . . 93
2.2.2.3 The first order neuron, non-functional . . . . . . . . . . . . . . . . . . . . . . 96
2.2.2.3.1 Examples of lap joints & electrostenolytic mechanisms
............................................. 97
2.2.2.4 The configuration of the fully functional second order neuron . . . . 98
2.2.2.5 Preview of the fully functional neuron in a neural signal path . . . . . 98
2.2.2.6 Fully elaborated schematics of fundamental neurons . . . . . . . . . . . . 99
2.2.2.6.1 Examples of lap joints & electrostenolytic mechanisms
............................................ 100
2.2.2.7 Structural features of the second order fundamental cell . . . . . . . . 104
2.2.2.7.1 The molecular structure of the junction between two
membranes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
2.2.2.7.2 Spines along the dendrites of neurons. . . . . . . . . . . . . . 107
2.2.2.8 Electrical features of the second order fundamental cell . . . . . . . . 107
2.2.2.8.1 The electrical description of the conduit wall . . . . . . . . 107
2.2.2.9 Electrical features of the second order fundamental cell . . . . . . . . 108
2.2.2.9.1 Electrical description of the electrostenolytic process . 108
2.2.2.9.2 Electrical description of gap junction between two
membranes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
2.2.3 The three terminal biological transistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
2.2.3.1 Comparing the Activa to a man-made transistor. . . . . . . . . . . . . . . 113
2.2.3.2 The Ebers-Moll model and the Early Effect. . . . . . . . . . . . . . . . . . 114
2.2.3.3 The fundamental electrical parameters of the unit Activa . . . . . . . 114
2.2.3.3.1 The offset parameter, aka the Band Gap . . . . . . . . . . . . 114
2.2.3.3.2 The thermal parameter . . . . . . . . . . . . . . . . . . . . . . . . . 116
2.2.3.3.3 The reverse saturation parameter . . . . . . . . . . . . . . . . . 116
2.2.3.3.4 The forward transconductance . . . . . . . . . . . . . . . . . . . 116
2.2.3.3.5 The heavy doping of the forward biased PN of an
Activa–Quantum Tunneling. . . . . . . . . . . . . . . . . . . . . . 116
2.2.3.3.6 An alternate theory of charge transport along a lipid,
Molecular Charge Tunneling . . . . . . . . . . . . . . . . . . . . 120
2.2.3.4 Proposed use of a heavily doped forward biased PN in an Activa
................................................... 123
2.2.3.4.1 Estimates of the I-V characteristic of heavily doped forward
biased PN of an Activa . . . . . . . . . . . . . . . . . . . . . . . . . 123
2.2.3.4.2 Proposed symbol for an Activa exhibiting Esaki tunneling
at its Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
2.2.3.4.3 Options for a heavily doped PN (Esaki) diode achieving oa
EG ~50 mV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
2.2.3.4.4 Symbol of PtdIns showing multiple pi-bonds in multiple
cis-bonds .................................... 126
2.2.3.4.5 PtdIns using a heavily doped p-type semiconductor . . 128
2.2.3.4.6 Brief data on the double bond of organic chemistry . . . 129
2.2.3.4.7 PtdIns using a heavily doped n-type semiconductor . . 130
2.2.3.5 Confirmation of the Activa’s input characteristic . . . . . . . . . . . . . . 131
2.2.4 Defining the conexus within a static neuron . . . . . . . . . . . . . . . . . . . . . . . . . . 131
2.2.4.1 Defining the electrical circuits of a neuron. . . . . . . . . . . . . . . . . . . 132
2.2.4.1.1 Rectification, frequently misconstrued in literature. . . . 134
2.2.4.2 Defining the fundamental conexus within a neuron . . . . . . . . . . . . 135
2.2.3.4.2 The proposed I-V characteristic of a functional Activa MOVE
INTO 2.2.4.......................................... 135
2.2.4.2.1 Overlay of electronic circuitry and cytology of a neuron
............................................ 135
2.2.4.3 Defining the third operational terminal of & within a neuron . . . . 136
The Neuron 2- 333
2.2.4.3.1 Additional capability provided by the poditic
conduit/terminal –Differential input ............... 136
2.2.3.4.3 The pros\posed cross section of a functional Activa EMPTY. . . 137
2.2.4.4 Illustrating the neuron using electrical engineering symbology . . . 139
2.2.5 Preview of forms and amplifier capabilities found within neural systems . . . 141
2.2.5.1 Preview of neuron morphologies using electrolytic theory–ETN . . 141
2.2.5.2 The fundamental neural signaling path of biological systems . . . . 142
2.2.6 Details of the static electrical properties of neural conduits . . . . . . . . . . . . . . 143
2.2.6.1 Equivalent circuit of the axon element . . . . . . . . . . . . . . . . . . . . . . 144
2.2.6.2 Equivalent circuit of the dendritic element. . . . . . . . . . . . . . . . . . . 148
2.2.6.2.1 Background literature . . . . . . . . . . . . . . . . . . . . . . . . . . 148
2.2.6.2.2 Equivalent circuit in this work . . . . . . . . . . . . . . . . . . . 148
2.2.6.3 Equivalent circuit of the poditic element . . . . . . . . . . . . . . . . . . . . 149
2.2.7 Recent organic field effect transistor (OFET) and potentially bipolar junction
transistor devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
- - - -Optional...................................................... 150
2.2.7.1 Background from the recent literature . . . . . . . . . . . . . . . . . . . . . . 152
2.2.7.2 Difference in organic vs biological semiconductor devices . . . . . . 153
2.2.7.3 “Active” semiconductor device of Tybrandt et al. . . . . . . . . . . . . . 154
2.2.7.4 “Active” semiconductor devices of Okamato et al. & Mitsui et al.
................................................... 157
2.2.7.5 “Active” semiconductor devices of See et al. . . . . . . . . . . . . . . . . . 158
2.2.7.6 “Active” graphene semiconductor devices of Tsai & Willner ADD
................................................... 159
2.2.7.7 “Active” semiconductor devices of Dumitru et al. . . . . . . . . . . . . . 159
2.2.7.8 Potential FET semiconductor devices of Sigworth. . . . . . . . . . . . . 163
2.3 The electrical characteristics of the dynamic (second order) neuron . . . . . . . . . . . . . . . . 163
2.3.1 Background drawn from electrical circuit theory. . . . . . . . . . . . . . . . . . . . . . . 163
2.3.1.1 The interconnection of neural circuits . . . . . . . . . . . . . . . . . . . . . . 163
2.3.1.2 Analog (electrotonic) versus pulse (phasic) operation . . . . . . . . . . 166
2.3.1.3 Types of oscillators found in the neural system . . . . . . . . . . . . . . . 166
2.3.1.4 Electrical feedback as a powerful (but poorly understood) neural
mechanism.......................................... 167
2.3.2 The three-terminal Activa provides great circuit flexibility . . . . . . . . . . . . . . 167
2.3.2.1 Small signal versus large signal operation . . . . . . . . . . . . . . . . . . . 168
2.3.2.2 General operating characteristics of a simple neuron . . . . . . . . . . . 169
2.3.2.2 Dynamic operation of a conexus with transistor-action and a resistive
poda impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
2.3.2.2.1 Simple amplification . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
2.3.2.2.2 Thresholding circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
2.3.2.2.3 Basic arithmetic functions. . . . . . . . . . . . . . . . . . . . . . . 172
2.3.2.2.4 Threshold and pulse integration circuits . . . . . . . . . . . . 173
2.3.2.3 Individual temporal/frequency selective neural circuits . . . . . . . . . 174
2.3.2.3.1 The common low pass characteristic of neurons. . . . . . 174
2.3.2.3.2 The capabilities of a lead-lag network. . . . . . . . . . . . . . 174
2.3.2.3.3 Interference, an alternate frequency selective technique
............................................ 174
2.3.2.4 Multipoint probing of pyramid neurons . . . . . . . . . . . . . . . . . . . . . 175
2.3.3 Dynamic operation of a conexus with Transistor Action and feedback. . . . . . 175
2.3.3.1 The nature of feedback. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
2.3.3.2 Internal feedback in the circuit of a fundamental neuron . . . . . . . . 176
2.3.3.3 Evidence supporting the relaxation oscillator description . . . . . . . 178
2.3.4 Emulation and simulation of Activa and Activa circuits . . . . . . . . . . . . . . . . . 179
2.3.4.1 Emulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
2.3.4.1.1 Emulation of the first order Activa . . . . . . . . . . . . . . . . 179
2.3.4.1.2 Emulation of the second order Activa circuit . . . . . . . . 180
2.3.4.2 Simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
2.3.4.2.1 Large Sale Simulation of Brain using digital
circuitry–Modha, ca. 2013 . . . . . . . . . . . . . . . . . . . . . . . 181
2.4 The synapse– Concept versus functional reality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
2.4.1 Historical aspects: the electrolytic vs chemical neurotransmitter. . . . . . . . . . . 183
2.4.1.1 Requirement on a chemical neurotransmitter . . . . . . . . . . . . . . . . . 187
2.4.1.2 Requirement on an electrolytic neurotransmitter . . . . . . . . . . . . . . 188
2.4.1.3 The neurotransmitters, neuro-facilitators & neuro-effectors. . . . . . 188
2.4.2 Detailed history of the electrolytic and chemical synapses . . . . . . . . . . . . . . . 189
2.4.2.1 Definition of the neural synapses . . . . . . . . . . . . . . . . . . . . . . . . . . 192
334 Neurons & the Nervous System
2.4.2.1.1 Junctions in non-neural, epithelium, tissue–Gilula . . . . 193
2.4.2.1.2 Junctions between neurons . . . . . . . . . . . . . . . . . . . . . . 195
2.4.2.1.3 Junctions between neurons according to chemical theory
............................................ 195
2.4.2.1.4 Junctions between neurons and non-neural material . . . 197
2.4.2.2 Recent studies of the chemical synapse concept. . . . . . . . . . . . . . . 197
2.4.2.3 Summary framework of the electrolytic synapse. . . . . . . . . . . . . . 199
2.4.2.4 A reversible synapse challenges the chemical theory . . . . . . . . . . . 199
2.4.3 The Electrolytic (gap junction), Synapse style 1 . . . . . . . . . . . . . . . . . . . . . . . 201
2.4.3.1 Introduction EDIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
2.4.3.2 Recent empirical data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
2.4.3.3 The schematic of the electrolytic synapse . . . . . . . . . . . . . . . . . . . 204
2.4.3.3.1 The cytology of the synaptic disks . . . . . . . . . . . . . . . . 205
2.4.3.3.2 The electrolytic synapse as an “active” diode . . . . . . . . 206
2.4.3.4 Powering the electrolytic synapse. . . . . . . . . . . . . . . . . . . . . . . . . . 207
2.4.3.5 The amino acids as neuro-facilitator, not neurotransmitter . . . . . . 207
2.4.3.6 The gap junction is a barrier to ions EDIT to include EZ Water . . 207
2.4.3.6.1 Liquid-crystalline water–EZ water . . . . . . . . . . . . . . . 208
2.4.3.6.2 Test of solute-free phase in confined EZ water . . . . . 211
2.4.4 First documentation of the PNP Activa in a synapse ................. 212
2.4.4.1 Background–summary of facts leading to a PNP designation . . . . 212
2.4.4.2 The synapse as an active device, an ACTIVA . . . . . . . . . . . . . . . . 213
2.4.5 The PNPN Diode forming a Storage Unit used in Memory Circuits– Synapse
style 2 .................................................... 216
2.4.6 The Chemical or Paracrine Junction– Synapse style 3. . . . . . . . . . . . . . . . . . . 217
2.4.7 Morphogenesis of a synapse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
2.4.7.1 Potential electrophoretic formation of a synapse EMPTY . . . . . . . 218
2.4.7.2 Re-examining the initial connection between neurons . . . . . . . . . . 219
2.4.7.3 Re-examining the initial connection between neurons at the molecular
level............................................... 219
2.5 Neural applications of electrotonic, or analog, neurons . . . . . . . . . . . . . . . . . . . . . . . . . . 219
2.5.1 Morphologically bipolar cells of Stage 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
2.5.1.1 Topology of the morphologically bipolar cell . . . . . . . . . . . . . . . . 220
2.5.1.2 The Electrolytic Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
2.5.2 The lateral (differencing) cells of stages 2 through 6 . . . . . . . . . . . . . . . . . . . 223
2.5.2.1 The topography of the lateral cells . . . . . . . . . . . . . . . . . . . . . . . . . 223
2.5.2.1.1 The typical input structure of signal differencing neurons
............................................ 226
2.5.2.1.2 The electrolytic circuit of the lateral neuron . . . . . . . . . 226
2.5.2.3 Operation of the lateral neurons . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
2.5.3 The sensory neurons of stage 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
2.5.3.1 The functional properties of the generic stage 1 neuron. . . . . . . . . 228
2.5.3.2 The gain mechanism in a sensory neuron . . . . . . . . . . . . . . . . . . . . 230
2.5.3.3 The conventional sensory neuron schematic . . . . . . . . . . . . . . . . . 230
2.5.3.4 The excitation/de-excitation mechanism of sensory neurons–sources
................................................... 231
2.5.3.5 The E/D mechanism of sensory neurons–general case . . . . . . . . . . 231
2.5.3.6 The E/D mechanism of sensory neurons–Hodgkin Condition . . . . 234
2.5.3.7 The E/D mechanism in parametric stimulation. . . . . . . . . . . . . . . . 234
2.6 The pulse (phasic) and hybrid signaling neurons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
2.6.1 The Action Potential vs pseudo action potentials EDIT . . . . . . . . . . . . . . . . . 235
2.6.1.1 The nominal action potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
2.6.1.1.1 The refractory period of a relaxation oscillator. . . . . . . 241
2.6.1.1.2 The measured nonlinearity of the axon (collector) circuit of
the neuron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
2.6.1.2 The pseudo-action potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
2.6.1.2.2 The pseudo–action potentials of Mueller & Rudin . . . . 244
2.6.1.2.3 The pseudo–action potentials of endotherms in-vitro . 247
2.6.1.2.4 The pseudo–action potentials of the cardiocytes. . . . . . 247
2.6.2 The encoding (ganglion) neuron of the PNS, mid-brain & cortex . . . . . . . . . . 247
2.6.2.1 Signal input via the poditic conduit . . . . . . . . . . . . . . . . . . . . . . . . 251
2.6.2.2 The introduction of myelin in connection with the axon . . . . . . . . 251
2.6.2.3 Waveforms at the poditic terminal before and during pulse generation
................................................... 251
2.6.3 Electrical characteristics of pulse regenerators–Nodes of Ranvier . . . . . . . . . 254
The Neuron 2- 335
2.6.3.1 Introduction of the Node of Ranvier of the axon . . . . . . . . . . . . . . 254
2.6.3.2 The topology & cytology of the Node of Ranvier . . . . . . . . . . . . . 254
2.6.3.3 The circuit schematic of the Node of Ranvier . . . . . . . . . . . . . . . . 259
2.6.4 The decoding (stellite/stellate) neuron of the mid-brain and cortex. . . . . . . . . 260
2.6.4.1 Cytology of the stellite neuron . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
2.7 Other hybrid neurons, the hormonal, visceral & mobility interface . . . . . . . . . . . . . . . . . 261
2.7.1 The paracrine stage 7 neuro-effector neurons. . . . . . . . . . . . . . . . . . . . . . . . . 262
2.7.1.1 The paracrine stage 7 neuron interface with striate muscle . . . . . . 263
2.7.2 The endocrine stage 7 neuro-effector neurons–The hormonal system . . . . . . 264
2.7.2.1 The amino acids as progenitors of many hormones . . . . . . . . . . . . 265
2.7.3 The exocrine stage 7 neuro-effector neurons . . . . . . . . . . . . . . . . . . . . . . . . . 265
2.7.4 The hybrid cardiocyte of the cardiac system. . . . . . . . . . . . . . . . . . . . . . . . . . 265
2.7.4.1 The functional properties of the cardiocyte . . . . . . . . . . . . . . . . . . 267
2.7.4.1.1 The electrical characteristics of the cardiocytes. . . . . . 267
2.7.4.1.2 Is the cardiocyte a driven monopulse oscillator?. . . . . . 268
2.7.5 Special case of the giant (swimming) neuron (not only axon) of squid . . . . . 269
2.7.5.1 Problems with the H & H model–Frankenhauser & Huxley, 1964
................................................... 270
2.7.5.2 Hodgkin & Huxley never solved their differential equations . . . . . 271
2.7.5.3 Hodgkin & Huxley never identified the “charge carrier” in their Model
................................................... 272
2.7.5.4 cytology of the unsheathed axon of the giant neuron--Metuzals, 1983
................................................... 274
2.7.6 The special case of the eccentric cell of Limulus. . . . . . . . . . . . . . . . . . . . . . . 276
2.7.7 The mossy and climbing fibers of the cerebellum & hippocampus . . . . . . . . . 276
2.7.7.1 The neural anatomy relating to the cerebellum. . . . . . . . . . . . . . . . 277
2.7.7.1.1 Anatomy of the climbing fibers entering the cerebellum
............................................ 280
2.7.7.1.2 Anatomy of the mossy fibers entering the cerebellum. . 281
2.7.7.1.3 Details of the synaptic structure of the Purkinje cells . . 282
2.7.7.1.4 Early Simulation of Purkinje cells–Rapp, 1994 . . . . . . 283
2.7.7.1.5 The unusual axonal structure of the Purkinje cells . . . . 284
2.7.7.2 The neural anatomy relating to the hippocamus EMPTY. . . . . . . . 284
2.7.7.2.1 Anatomy of the climbing fibers entering the hippocampus
EMPTY..................................... 284
2.7.7.2.2 Anatomy of the mossy fibers entering the hippocampus
............................................ 284
2.7.7.2.3 Mossy fiber sprouting & recurrent excitation in the
hippocampus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
2.7.7.2.4 Details of the synaptic structure of the Purkinje cells EDIT
............................................ 285
2.8 Other important features of neurons and neural paths EMPTY . . . . . . . . . . . . . . . . . . . . 285
2.8.1 Merging and bifurcating signal paths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
2.8.1.1 Merging and bifurcation in the analog signal domain . . . . . . . . . . 286
2.8.1.2 Merging and bifurcation in the pulse signal domain. . . . . . . . . . . . 286
2.8.2 Relationship of nuclei to conduits and sheaths . . . . . . . . . . . . . . . . . . . . . . . . 286
2.8.3 Biasing and the non-uniformity of axoplasm potential . . . . . . . . . . . . . . . . . . 287
2.8.4 Confirmation of the physical circuit and analytical models . . . . . . . . . . . . . . . 287
2.8.4.1 Confirmation of the switching characteristic of the oscillating neuron
................................................... 288
2.8.5 Specialized regions of outer lemma of a neuron . . . . . . . . . . . . . . . . . . . . . . . 288
2.8.6 Neural pathway genesis and growth cones. . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
2.8.6.1 ADD Potential neurogenesis mechanisms EMPTY . . . . . . . . . . . . 290
2.9 Mathematical and computer modeling of neurons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
2.9.1 Modeling difficulties up to the current day . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
2.9.1.1 Major problems with the McCulloch & Pitts mathematical neuron
................................................... 292
2.9.1.2 An alternate realistic model of the mathematical neuron . . . . . . . . 292
2.9.2 Major problems with subsequent mathematical neurons . . . . . . . . . . . . . . . . . 294
2.9.2.1 Analytical models spanning the last 60 years . . . . . . . . . . . . . . . . . 294
2.9.3 The NEURON– a computational model with mixed roots . . . . . . . . . . . . . . . 295
2.9.3.1 Modification of the symbology in the program, NEURON . . . . . . 296
2.9.3.2 Recommendation regarding the software program, NEURON . . . 297
2.10 Analyses of the neuron literature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
2.10.1 Neurons of the peripheral nervous system. . . . . . . . . . . . . . . . . . . . . . . . . . . 298
2.10.1.1 Generic stage 1 sensory neuron . . . . . . . . . . . . . . . . . . . . . . . . . . 298
336 Neurons & the Nervous System
2.10.2 Neurons of the central nervous system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
2.10.2.1 Multipoint probing of neurons . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
2.10.2.1.1 Multipoint probing of pyramid neurons by Williams &
Stuart....................................... 300
2.10.2.1.2 A Multi-segment math model of Pyramid neurons–Bahl,
2012........................................ 302
2.10.2.1.3 Multipoint probing of Purkinje neurons in cerebellum
............................................ 304
2.10.2.1.4 Dendrite signal projection velocities. . . . . . . . . . . . . . 306
2.10.2.2 Simultaneous Multipoint probing of neurons . . . . . . . . . . . . . . . . 309
2.10.3 Purkinje & other neurons of stage 5C, the cerebellum. . . . . . . . . . . . . . . . . . 312
2.10.3.1 Background related to the cerebellum . . . . . . . . . . . . . . . . . . . . . 313
2.10.3.2 Interpreting a Purkinje cell of Granit & Phillips (1956) with a serape
................................................... 314
2.10.3.3 Potential Purkinje neuron Circuit as defined by Marr, 1969 . . . . 318
2.10.3.4 Interpreting a Purkinje cell based on the conflicting information with
a serape ............................................ 320
2.10.3.5 Interpreting the cerebellum as a storage area for a database. . . . . 322
2.10.3.6 Interpreting the Single Purkinje as a storage unit for a database . 323
2.11 CHAPTER SUMMARY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
2.11.1 The ACTIVA, an ELECTROLYTIC COMPONENT FOUND IN EVERY
NEURON.................................................. 327
2.11.1.1 Absence of variable resistors in biological circuits . . . . . . . . . . . 327
2.11.1.2 Electrochemical Support by Region . . . . . . . . . . . . . . . . . . . . . . . 328
2.11.1.3 Lack of Need for ions to pass through Membranes for Signaling
................................................... 328
2.11.1.4 Confirmation of the Switching Characteristic of the Oscillating
Neuron............................................. 328
2.11.2 TRANSITION FROM AN AXON-ONLY TO A JUNCTIONAL-TISSUE
MODEL................................................... 328
2.11.2.1 Rationalizing the axon-only versus the junctional-tissue models
................................................... 328
2.11.2.2 The junctional tissue as the conexus within a neuron. . . . . . . . . . 329
2.11.2.3 The junctional tissue as the conexus between neurons–the synapse
................................................... 329
2.11.3 TRANSITION FROM A DUAL-ALKALI TO AN ELECTRON-BASED
MODEL................................................... 330
The Neuron 2- 337
Chapter 2 List of Figures 11/6/23
Figure 2.1.1-1The generic schema of a biological neuron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Figure 2.1.2-1 Framework for modeling the neuron. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Figure 2.1.4-1 Bare and hydrated ions. Dimensions in nanometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Figure 2.1.4-2 Comparing the dependence of K+ and H+ permeability on diametervs length. . . . . . . . 18
Figure 2.1.4-3 Permeability coefficients of potassium ions and halides. . . . . . . . . . . . . . . . . . . . . . . . . 21
Figure 2.1.4-4 Calculated permeability coefficient for a single bilayer . . . . . . . . . . . . . . . . . . . . . . . . . 22
Figure 2.1.4-5 Physical characteristics of synthetic and natural bilayer membranes . . . . . . . . . . . . . . . 25
Figure 2.1.4-6 Free energies of small anesthetics across the water–POPC interface . . . . . . . . . . . . . . . 27
Figure 2.1.4-8 Electrostatic properties & structure of selected phospholipid. . . . . . . . . . . . . . . . . . . . . 31
Figure 2.1.4-9 Ramachandran Plots for PDPC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Figure 2.1.4-10 “Instantaneous configuration of the SDPC lipid bilayer . . . . . . . . . . . . . . . . . . . . . . . 37
Figure 2.1.4-11 Composite frames showing NMR of POPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Figure 2.1.4-12 “Phospholipids in 3D energy-minimized configuration . . . . . . . . . . . . . . . . . . . . . . . . 42
Figure 2.1.4-13 Clarification of Crawfords use of “Double bonds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Figure 2.1.4-14 Single layer plasma lemma showing the two bilayers. . . . . . . . . . . . . . . . . . . . . . . . . . 44
Figure 2.1.4-15 Calder (2016) nomenclature used for DHA discussion . . . . . . . . . . . . . . . . . . . . . . . . 45
Figure 2.1.4-16 Four configurational representations of DHA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Figure 2.1.4-17 Schematic of a method for producing asymmetrical lipid bilayers . . . . . . . . . . . . . . . . 48
Figure 2.1.4-18 Differences between different levels of unsaturation . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Figure 2.1.4-19 Diagrammatic representation of the structure of two phospholipid bilayers. . . . . . . . . 51
Figure 2.1.4-20 “The first moment (M,)of the 2H NMR spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Figure 2.1.4-21 Structural models of diPALM-PC & PALM, DHA-PE used in Martin et al. paper . . . 53
Figure 2.1.4-22 “Transmission solution small angle X-ray scattering (SAXS) data for DPPC/DHA-PE
......................................................................... 55
Figure 2.1.4-23 Electron micrograph of the photoreceptor and nuclear laminates of the bullfrog. . . . . 56
Figure 2.1.4-24 Expanded cross section through a human retina to show circuitry . . . . . . . . . . . . . . . . 58
Figure 2.1.4-25 An exploded view of the baseline photoreceptor cell . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Figure 2.1.4-26 “The metabolic pathway of conversion of α-linolenic acid to DHA. . . . . . . . . . . . . . . 65
Figure 2.1.4-27 Phosphoglycerides, before condensation with the suffix to form a phosphotidyl(suffix
amino acid)................................................................ 67
Figure 2.1.4-28 Full name of phosphatidyl ethanolamine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Figure 2.1.4-29 Comparison between PtdEth, or EPG, of two schools . . . . . . . . . . . . . . . . . . . . . . . . . 69
Figure 2.1.5-1 Analogy between the dendritic outer wall and the earth’s crust . . . . . . . . . . . . . . . . . . . 73
Figure 2.2.1-1 Ordered amphiphilic materials in aqueous solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Figure 2.2.1-2 Options in interdigitation of bilayer membranes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Figure 2.2.1-3 En face view of a gap junction in a neuron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Figure 2.2.1-4 The conductivity range achieved in conjugated carbon molecules . . . . . . . . . . . . . . . . . 83
Figure 2.2.1-5 Fatty acyl residues ( R) commonly found in membrane lipids . . . . . . . . . . . . . . . . . . . . 84
Figure 2.2.1-6 Spatial dimensions related to double bonds in lipid tail . . . . . . . . . . . . . . . . . . . . . . . . . 86
Figure 2.2.1-7 Four configurational representations of DHA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Figure 2.2.2-1 The differentiation of a stem-cell into a variety of neurons . . . . . . . . . . . . . . . . . . . . . . 92
Figure 2.2.2-2 Cytological evolution of a cell to 1st and 2nd order neuron . . . . . . . . . . . . . . . . . . . . . . . 95
Figure 2.2.2-3 Subcellular fraction of gap junctions isolated from rat liver. . . . . . . . . . . . . . . . . . . . . . 97
Figure 2.2.2-4 A composite neuron–Synapses may form on different elements of a neuron . . . . . . . . . 99
Figure 2.2.2-5 A more fully elaborated schematic of a fundamental neuron . . . . . . . . . . . . . . . . . . . . 101
Figure 2.2.2-6 Schematic of a complete visual sensory neuron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Figure 2.2.2-7 Caricature of a gap junction as it appears in cross section . . . . . . . . . . . . . . . . . . . . . . 105
Figure 2.2.2-8 Structure of the Activa at the atomic level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Figure 2.2.2-9 Electrical representations of a gap junction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Figure 2.2.3-1 Three terminal active biological device, the Activa . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
Figure 2.2.3-2 Band gaps of EZ Water & bulk water compared with Germanium and Silicon . . . . . . 115
Figure 2.2.3-3 “Energy-band diagrams in a heavily doped p-n diode for a forward bias . . . . . . . . . . . 118
Figure 2.2.3-4 The I-V Diagram resulting from tunneling in a forward-biased diode . . . . . . . . . . . . . 119
Figure 2.2.3-5 A tunnel diode I-V characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Figure 2.2.3-6 I-V characteristic for Bi2Se3 for various band gaps . . . . . . . . . . . . . . . . . . . . . . . . . . 120
Figure 2.2.3-7 (No caption in original) Comparing diode & resistive circuits . . . . . . . . . . . . . . . . . . . 121
Figure 2.2.3-8 EZ Water vs bulk water band gap as used in an Activa, a Node of Ranvier OR synapse.
........................................................................ 125
Figure 2.2.3-9 Proposed symbols for doped PNP activa based on standard symbols . . . . . . . . . . . . . 126
Figure 2.2.3-10 PtdIns shown with four double cis-bonds.................................. 127
Figure 2.2.3-11 “Unsaturated fatty acids, lipids.” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
Figure 2.2.3-12 The sigma-pi model of a double bond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Figure 2.2.3-13 Template for demonstration of proposed band gap of the Activa. . . . . . . . . . . . . . . . 131
338 Neurons & the Nervous System
Figure 2.2.4-1 Input impedance and output characteristic of common base configured Activa . . . . . . 133
Figure 2.2.4-2 Overlay of electronic circuitry of a fundamental neuron on its topography . . . . . . . . . 136
Figure 2.2.4-3 Transfer characteristic of a common emitter configured Activa. . . . . . . . . . . . . . . . . . 136
Figure 2.2.4-4 Differential input structure of a typical lateral neuron . . . . . . . . . . . . . . . . . . . . . . . . . 138
Figure 2.2.4-5 The role of glutamate and GABA in powering the neuron . . . . . . . . . . . . . . . . . . . . . . 140
Figure 2.2.5-1 Fundamental morphological forms of neurons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
Figure 2.2.5-2 Fundamental functional form of the neuron and its electrical variations . . . . . . . . . . . 143
Figure 2.2.6-1 Illustration of the various electrical equivalent circuits representing individual specialized
regions .................................................................. 146
Figure 2.2.6-2 Electrical equivalent circuit of the poditic conduit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
Figure 2.2.7-1 Hierarchy of potential CWA sensory equipment ADD. . . . . . . . . . . . . . . . . . . . . . . . . 150
Figure 2.2.7-2 Typical drain characteristic & transfer curve for a common source n-channel MOSFET
........................................................................ 151
Figure 2.2.7-3 An organic bipolar junction transistor, BJT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
Figure 2.2.7-4 The IBJT as an addressable delivery point for modulation of neuronal cell signaling
........................................................................ 156
Figure 2.2.7-5 Schematic of an OFET with polycrystalline channel . . . . . . . . . . . . . . . . . . . . . . . . . . 158
Figure 2.2.7-6 PAA-gated pBTTT-C14 OFET performance curves . . . . . . . . . . . . . . . . . . . . . . . . . . 161
Figure 2.3.1-1 Typical quiescent point and operating range of various neurons . . . . . . . . . . . . . . . . . 164
Figure 2.3.2-1 A circuit diagram showing the separation of signal and bias terminals . . . . . . . . . . . . 168
Figure 2.3.2-2 Operating characteristics of typical conexus in grounded base configuration . . . . . . . 170
Figure 2.3.2-3 Addition and multiplication in ladder networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
Figure 2.3.3-1 Operating characteristics of the Activa with internal feedback. . . . . . . . . . . . . . . . . . . 177
Figure 2.3.3-2 Axoplasm patch-clamp potential measured using parametric stimulation . . . . . . . . . . 178
Figure 2.3.4-1 Nominal # of neurons & synapses in mouse, rat, cat, monkey & human CNS . . . . . . . 182
Figure 2.4.1-1 Early and updated electrolytic synapse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
Figure 2.4.2-1 Caricatures of the chemical and electrolytic junctions . . . . . . . . . . . . . . . . . . . . . . . . . 191
Figure 2.4.2-2 Comparing synapses at different magnification of adult cat . . . . . . . . . . . . . . . . . . . . . 193
Figure 2.4.2-3 “Thin section of the tight junction between rat hepatocytes . . . . . . . . . . . . . . . . . . . . . 194
Figure 2.4.2-4 Chemical theory representation of a gap junction synapse . . . . . . . . . . . . . . . . . . . . . . 196
Figure 2.4.2-5 The ortho- (normal) and anti-dromic operation of a synapse . . . . . . . . . . . . . . . . . . . . 200
Figure 2.4.3-1 Overlay of electronic circuitry of a fundamental synapse on its topography . . . . . . . . 202
Figure 2.4.3-2 The electrolytic synapse showing signaling and support functions . . . . . . . . . . . . . . . 205
Figure 2.4.3-3 Fundamental structure of a synaptic disk of a photoreceptor pedicel. . . . . . . . . . . . . . 206
Figure 2.4.3-4 The I-V characteristic of a synapse as an “active” diode . . . . . . . . . . . . . . . . . . . . . . . 207
Figure 2.4.3-5 EZ water is liquid crystalline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
Figure 2.4.3-6 Glass rod lifts up stiff EZ layer at water air interface . . . . . . . . . . . . . . . . . . . . . . . . . . 210
Figure 2.4.3-7 Electrical potential measured at different distances from the gel surface located at 0.
........................................................................ 211
Figure 2.4.4-1 Electron micrograph showing the base region of the PNP synapses. . . . . . . . . . . . . . . 214
Figure 2.4.5-1 The physical arrangement of the electrolytic synapse style 2 . . . . . . . . . . . . . . . . . . . . 217
Figure 2.5.1-1 The topology of the bipolar cell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
Figure 2.5.2-1 Electron micrograph of a pyramid cell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
Figure 2.5.2-2 The cytological organization of a pyramid cell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
Figure 2.5.2-3 The input topography of a typical differencing (lateral) cell . . . . . . . . . . . . . . . . . . . . 226
Figure 2.5.2-4 Topology and circuit diagram of the lateral cell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
Figure 2.5.3-1 Generic sensory neuron cytology and schematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
Figure 2.5.3-2 Circuit diagram of generic sensory neuron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
Figure 2.5.3-3 The complete impulse solution to the E/D Equation for the transduction process . . . . 231
Figure 2.5.3-4 The complete impulse solution to the E/D Equation . . . . . . . . . . . . . . . . . . . . . . . . . . 232
Figure 2.6.1-1 Measured action potentials vs temperature for rat & human motor neurons. . . . . . . . . 238
Figure 2.6.1-2 Features of action potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
Figure 2.6.1-3 Steady state current-voltage curves of a Node of Ranvier . . . . . . . . . . . . . . . . . . . . . . 242
Figure 2.6.1-4 Time course of membrane potential following a short parametric shock . . . . . . . . . . . 243
Figure 2.6.1-5 Current-voltage characteristic of a bilayer of sphingomyelin . . . . . . . . . . . . . . . . . . . 245
Figure 2.6.2-1 Ganglion cell topology and circuit diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
Figure 2.6.2-2 Pulse to Pulse intervals of ganglion cells as a function of excitation . . . . . . . . . . . . . . 250
Figure 2.6.2-3 Nomenclature used by Bishop et al. in discussing the extracellular LGN . . . . . . . . . . 252
Figure 2.6.3-1 Node of Ranvier topology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
Figure 2.6.3-2 Node of Ranvier with dimensions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
Figure 2.6.3-3 Node of Ranvier isolated in living tissue by dissection. . . . . . . . . . . . . . . . . . . . . . . . 257
Figure 2.6.3-4 “Longitudinal section through the node-paranode region of a large myelinated . . . . . 259
Figure 2.6.4-1 Fundamental stage 3 pulse decoding neuron. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
Figure 2.7.1-1 Preliminary table of neuro-effector actions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
Figure 2.7.1-2 Schematic of the neuro-effector/myocyte interface for striate muscle . . . . . . . . . . . . . 264
The Neuron 2- 339
Figure 2.7.4-1 Proposed electrolytic circuit of a cardiocyte (myocyte) . . . . . . . . . . . . . . . . . . . . . . . . 266
Figure 2.7.4-2 Electrical operating characteristic of a cardiocyte . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
Figure 2.7.5-1 The “action potential” solved by numerical means by Frankenhauser & Huxley . . . . . 271
Figure 2.7.5-2 Fully implemented electrophysiological/histological Neuron. . . . . . . . . . . . . . . . . . . . 273
Figure 2.7.5-3 Unsheated Giant Axon of Squid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
Figure 2.7.7-1 The anatomy of the cerebellum of human for discussion . . . . . . . . . . . . . . . . . . . . . . . 278
Figure 2.7.7-2 Perspective view of a folium of the cerebellum showing Purkinje cells ADD . . . . . . . 279
Figure 2.7.7-3 The climbing fibers entering the cerebellum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
Figure 2.7.7-4 The mossy fibers entering the cerebellum ADD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
Figure 2.7.7-5 Details of the climbing fiber/Purkinje cell interface ADD . . . . . . . . . . . . . . . . . . . . . . 282
Figure 2.9.1-1 Framework for modeling the neuron ADD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
Figure 2.9.1-2 The falsifiable model of McCulloch & Pitts (A) vs a realistic model (B). . . . . . . . . . . 293
Figure 2.9.2-1 Suggested revision of the baseline neuron in NEURON. . . . . . . . . . . . . . . . . . . . . . . . 297
Figure 2.10.1-1 Generic stage 1 sensory neuron receptor (auditory. . . . . . . . . . . . . . . . . . . . . . . . . . . 299
Figure 2.10.1-2 Physiological map of the stage 1 visual sensory receptor related to adaptation . . . . . 300
Figure 2.10.2-1 A potential map of a pyramidal type neuron. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302
Figure 2.10.2-2 Montage of signal projection within and action potential generation in a CA1 pyramidal
neuron of the hippocampus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
Figure 2.10.2-3 Simultaneous patch clamp with soma stimulus, human cerebral cortex ex vivo . . . . . 310
Figure 2.10.2-4 The symbol a Truth Table for XOR symbolic logic . . . . . . . . . . . . . . . . . . . . . . . . . . 311
Figure 2.10.2-5 A typical XOR circuit implemented in binary logic . . . . . . . . . . . . . . . . . . . . . . . . . . 311
Figure 2.10.3-1 Initial Serape of 3-terminal Purkinje neuron with data . . . . . . . . . . . . . . . . . . . . . . . . 316
Figure 2.10.3-2 Potential histological forms of Purkinje neurons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
Figure 2.10.3-3 Null Hypothesis of the indexing strategy employed in the cerebellum. . . . . . . . . . . . 323
Figure 2.10.3-4 Symbolic form of one Purkinje Neuron within a crossbar memory . . . . . . . . . . . . . . 324
Figure 2.10.3-5 Alternate Symbolic form of one Purkinje Neuron within a crossbar memory . . . . . . 325
340 Neurons & the Nervous System
(Active) SUBJECT INDEX (using advanced indexing option)
100 billion....................................................................... 115
1010............................................................................ 151
3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23, 42, 47, 117, 158, 285, 290, 302
3-D ............................................................................ 158
50%................................................................. 40, 46, 53, 70, 71
60%...................................................................... 15, 33, 218
8 million ........................................................................ 220
95% . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1, 6, 111, 181, 186, 219, 234, 293, 295, 296, 301
98%............................................................................ 230
99.5% .......................................................................... 206
99%.................................................................... 182, 183, 187
acetylcholine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154, 155, 189, 199, 262-265
actin................................................................ 218, 240, 289, 290
action potential . . 5, 6, 8, 58, 148, 165, 166, 178, 189, 196, 198, 235-239, 243, 244, 247, 250-252, 254,
255, 260, 261, 269-271, 273, 280, 286-289, 291, 294-298, 301, 304, 306-311, 318
Activa . 1, 4-6, 9, 10, 15, 30, 59, 61, 73, 78, 96, 98, 99, 102-108, 110-116, 123, 125, 126, 131-137, 139,
141-143, 145, 146, 148-150, 152, 155, 163, 165-168, 170-180, 186, 187, 190, 197,
200, 203-206, 208, 212, 213, 216, 220, 221, 223, 226, 228, 230, 237, 239, 241-243,
249, 251, 254, 255, 257, 260, 261, 267, 268, 271-274, 283, 286, 287, 293, 297, 299,
302, 306, 308, 313, 316, 317, 321, 324, 325, 327-330
activa at the atomic level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
active diode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186, 200, 204, 206, 212, 293
acuity........................................................................... 130
adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61, 179, 180, 190, 230, 236, 299, 300
adaptation amplifier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61, 179, 180, 230, 236, 300
Alarm mode...................................................................... 237
amercine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180, 223, 224, 226
ammonia........................................................................ 264
amphipathic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29, 73, 78, 90
amplification . . . . 6, 14, 108, 134, 136, 148, 149, 158, 159, 166, 168, 171, 176, 178, 203, 212, 227, 230,
254, 273, 293, 317, 318
amygdala........................................................................ 217
anisotropic........................................................................ 82
apoptosis......................................................................... 63
arborization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99, 282, 283, 300, 304, 322, 323
archaic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6, 59, 72, 93, 99, 139, 181, 186, 284, 313
arginine......................................................................... 262
atomic force microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32, 288
attention. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4, 14, 63, 135, 171, 179, 294, 314
average velocity................................................................... 298
axon segment. . . . . . . . . . . . . . . . . . . 6, 102, 146, 182, 193, 201, 238, 254, 255, 259, 286, 287, 298, 318
axoplasm . . . 3, 98, 105, 106, 108, 109, 139, 142, 144-146, 149, 163-166, 171, 172, 178, 179, 187, 188,
191-193, 199, 200, 203-207, 212, 220-222, 228, 230, 237-239, 243, 250, 251, 254,
260-262, 264, 265, 267, 269, 271-274, 286, 287, 306, 308, 309, 313, 317, 318, 328
band gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113-116, 119, 123-126, 131, 132, 244
BAPA .......................................................................... 199
Bayesian ......................................................................... 14
BBB........................................................................ 264, 265
bifurcation................................................................... 286, 294
bilayer . . . 3, 11-16, 18-20, 22-26, 28-30, 32-35, 37, 38, 41, 43, 44, 47-50, 52, 68, 70, 72-82, 84, 87, 90-
93, 97, 100, 104, 106, 108, 120, 122, 135, 143, 144, 153, 157, 204, 206, 212, 220, 230,
243, 245, 263, 288
bilayer membrane . . . . . . . . . . . . . . . . . . 11, 14, 15, 24, 32, 48, 80, 84, 92, 106, 108, 135, 144, 157, 220
bilayers . . . 12-16, 18-20, 22, 23, 25-27, 29, 30, 32, 34, 38, 42, 44, 48, 49, 51, 52, 70, 73-83, 86, 87, 89-
92, 106, 108, 153, 244, 328
billion ...................................................................... 109, 115
binding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24, 188, 198, 201, 263
The Neuron 2- 341
bipolar . . 9, 58, 59, 131, 141, 149, 150, 152, 154, 157, 172, 218, 220-223, 226, 237, 248, 250, 251, 261,
276, 329
bistratified........................................................................ 58
bi-stratified . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59, 99, 141, 223, 226, 293
boundary layer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30, 146, 149
bouton................................................................... 73, 218, 285
Brownian motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35, 82, 105, 106, 149, 207
cable theory................................................................... 14, 296
Calcium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83, 247, 265, 303, 304, 306, 310
calibration....................................................................... 187
cardiocyte . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144, 236, 265-268, 301
Central Nervous System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62, 187, 188, 203, 237, 283, 300
cerebellum. . . . 1, 9, 182, 183, 213, 220, 276-281, 284, 300, 304, 305, 312-314, 317, 318, 320-323, 325
cerebrum.................................................................. 1, 300, 301
cholinergic....................................................................... 157
cis-. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35, 40, 41, 46, 69, 86, 88, 126, 127
class A.................................................................. 239, 273, 309
class B...................................................................... 317, 318
climbing fibers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276, 277, 280, 281, 284, 319, 322-325
coaxial cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6, 296, 298
collateral........................................................................ 280
commissure.................................................................. 235, 301
common-base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155, 172, 175, 237
common-emitter .................................................................. 155
compensation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9, 184, 244, 307
complex neurons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10, 59, 141, 168, 301
computation.................................................................. 270, 309
computational . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3, 7, 8, 172, 288, 291, 295
computational anatomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
conduction velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258, 289
conexus . . 116, 131, 132, 135, 136, 141-143, 163, 166-168, 170, 171, 173, 175, 177, 179, 199, 201-204,
206, 228-230, 255, 327-330
confirmation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131, 213, 241, 252, 287, 288, 328
coordinate bond. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72, 73, 150
coordinate chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73, 263
cross section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58, 81, 105, 112, 137, 146, 258, 263, 272
crossbar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316, 321, 322, 324, 325
cross-section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82, 204, 209, 230, 263
CRUCIAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9, 74, 91, 218, 290, 299
cruciform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1, 216, 281, 318, 320, 322-325
cubic equation................................................................ 294, 295
cutin........................................................................ 110, 114
DACB...................................................................... 150, 184
data base......................................................................... 10
database. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1, 10, 63, 281, 300, 313, 316, 322, 323
Debye .......................................................................... 159
decoder ......................................................................... 318
dendrolemma. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100, 103, 228, 229, 317
desmosome.................................................................... 33, 34
determinants ..................................................................... 301
dihedral.......................................................................... 35
diode . . . . 1, 4, 9, 15, 43, 70, 73-75, 79, 104, 107-114, 116-119, 121-123, 125, 126, 132, 134, 135, 143-
145, 154, 163, 170, 172, 175, 180, 186, 189, 200, 201, 203-207, 212, 216, 220, 230,
242-244, 250, 269, 293, 324, 325, 327
dipole potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30, 75, 92
disparity.......................................................................... 24
DNA ........................................................................... 159
dopamine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15, 139, 184, 189, 203, 217
double bond. . . . . . . . . . . . . . . . . . . . . . . . . . . 11, 26, 32, 40, 41, 50, 51, 68, 69, 71, 83-88, 129, 130, 151
double layer...................................................................... 159
dynamic range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 165, 246, 267
E/D ................................................................ 231, 232, 234, 289
eccentric cell..................................................................... 276
Electrolytic Theory of the Neuron. . . 1, 33, 34, 41, 48, 189, 200, 203, 212, 213, 216, 217, 219, 237, 252,
272, 274, 283, 284, 300, 309, 315, 316, 327
electromagnetic propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6, 298
342 Neurons & the Nervous System
electrometer...................................................................... 210
electrostenolytic process . . . . . 15, 72, 73, 94, 97, 101, 104, 108, 109, 139, 144, 149, 165, 166, 195, 205,
220, 230, 272, 281, 299, 300, 327, 329
electrostenolytics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72, 102, 288
endocrine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15, 92, 93, 100, 191, 192, 217, 262, 264, 265, 293
endothermic animals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237, 247
eNOS........................................................................... 262
equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18, 98, 165, 274
ergic............................................................................ 283
escape pulse...................................................................... 269
evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40, 74, 92, 95, 192, 199, 294
exocrine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92, 93, 191, 192, 262, 265, 293
exothermic animals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232, 247
expanded . . . . 8, 12, 48, 52, 58, 90, 93, 163, 165, 191, 195, 216, 225, 226, 278, 281, 293-295, 299, 322,
329
external feedback. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167, 293, 294
EZ water . . . . . . . . . . . 32, 114-116, 119, 123, 125, 126, 130-132, 191, 195, 197, 205-207, 209-212, 219
fanciful names.................................................................... 276
fasciculus........................................................................ 290
feedback . 59, 167, 175-177, 218, 220, 227, 228, 235, 237-239, 242, 243, 249, 254, 255, 259, 261, 269,
277, 285, 287, 292-294, 317, 318
feedforward...................................................................... 277
Fermi level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117, 122, 126
fluorescent....................................................................... 308
fMRI........................................................................... 219
four layer diode..................................................................... 1
Fourier transform................................................................... 79
four-layer diode................................................................. 9, 324
free energy........................................................................ 35
freeze-fracture................................................................ 134, 205
free-running. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238, 240, 250, 276
GABA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4, 72, 109, 139, 140, 186, 188, 189, 199, 230, 283, 293, 316
GABA-ergic ..................................................................... 283
gamma.......................................................................... 124
ganglion neuron. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1, 58, 235, 250, 251, 254, 260
gap junction. . 34, 79, 80, 97, 104, 105, 109-111, 113, 132, 182, 189, 191, 194-197, 199, 201, 204, 207,
208
General Wave Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
genetics.......................................................................... 62
glia......................................................................... 218, 321
glomeruli................................................................ 282, 318, 319
glutamate. . . . . . . . . . . . . 4, 15, 93, 102, 139, 140, 183, 185, 188, 197-199, 201, 207, 283, 308, 316, 329
glycol........................................................................ 71, 154
glycolysis........................................................................ 102
GR.............................................................................. 31
Grotthuss..................................................................... 81, 208
GWE........................................................................... 298
Helmholtz double layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Helmholtz layer................................................................... 115
Hermann cable.................................................................... 296
hippocampus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198, 276, 284, 285, 307
Hodgkin Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232, 234, 287, 295, 298
hole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38, 81, 82, 91, 101, 108, 152, 153, 191, 199, 208, 301
hole conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108, 208
hole transport. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38, 82, 101, 152, 153, 301
homogeneous................................................................ 24, 77, 91
hormone. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15, 70, 184, 192, 262
hydrogen bond. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29, 73, 120, 153, 208, 211
hyperpolarization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166, 171, 301, 305
hypophysis............................................................... 199, 264, 265
hypothalamus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199, 264, 265
ice ................................................................. 106, 115, 130, 131
in vitro. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1, 218, 290, 301, 305
in vivo............................................................... 19, 218, 289, 290
inhomogeneous.................................................................... 91
The Neuron 2- 343
inositol. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31, 60, 64, 71, 129
intelligence ...................................................................... 292
interaxon........................................................................ 254
internal feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . 167, 175-177, 220, 235, 242, 249, 254, 255, 259, 317
interneuron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165, 201, 316
interval-duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265, 268
inverting . . . . . . . . . . . . 5, 15, 107, 138-140, 166, 168, 173, 221, 225, 226, 228, 277, 283, 302, 311, 321
in-vitro. . . . . . . . . . . . . . . . . . . 7, 16, 55, 74, 107, 134, 166, 237, 238, 243, 244, 247, 268, 281, 291, 305
in-vivo . . 1, 15, 25, 115, 131, 134, 166, 172, 180, 187, 189, 191, 200, 204, 236, 243, 247, 267, 268, 290,
309, 313, 314, 328
ion-pump........................................................................ 274
IRIG ........................................................................... 318
iso-leucine................................................................... 262, 266
IUPAC....................................................................... 49, 153
Kirchoff’s Laws. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134, 168
Langmuir. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25, 48, 49, 120, 165
Langmuir trough . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25, 48, 49
latency.......................................................................... 234
lateral geniculate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248, 251
learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281, 293, 318-320, 324, 325
learning mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281, 319, 324, 325
Limulus......................................................................... 276
liquid-crystal................................................................... 1, 129
liquid-crystalline . . . . 1, 3, 9, 12, 16, 26, 29, 34, 81, 82, 91, 115, 129, 151, 154, 191, 196, 206, 208, 210,
212, 329
locomotion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7, 243, 269, 270, 291, 292
long term memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1, 313, 323
Lord Kelvin................................................................... 14, 301
lysine........................................................................... 266
L-Dopamine ..................................................................... 139
marker.......................................................................... 208
Maxwell.................................................................... 6, 14, 298
Medulla......................................................................... 205
MEG....................................................................... 307, 308
metabotropic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184, 185, 190, 199
microtubule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103, 218, 289
midbrain ........................................................................ 217
mobility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12, 82, 151-153, 157, 158, 208, 261
mode switching................................................................... 176
modulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144, 156, 160, 198, 260
molecular biology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25, 49
monopolar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141, 172, 219, 220, 237, 250, 276
monopulse . 6, 138, 206, 236-239, 247, 249, 252, 254, 259, 268, 269, 271, 273, 276, 287, 301, 308, 309,
318, 325
monopulse oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138, 238, 252, 254, 268, 276, 325
morphogenesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93, 216, 218, 219, 294
mossy fibers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276, 277, 281, 283-285, 318, 322
multiple probe.................................................................... 201
multipolar ................................................................... 141, 218
muscarinic....................................................................... 263
myelin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11, 143, 235, 251, 254, 257, 258, 286, 289, 317
myelinated. . . 5, 6, 165, 166, 219, 237, 238, 252, 254, 259, 260, 270, 271, 276, 280, 281, 283, 287-289,
292, 296, 300-302, 312, 317, 321
Myelination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243, 248, 264, 292, 297, 298, 304
myosin.......................................................................... 218
narrow band...................................................................... 115
nematic .......................................................................... 82
neurite . . . 72, 107, 136, 182, 188, 201, 204, 205, 207, 218, 219, 223, 226, 228, 243, 282, 283, 289, 297,
300, 322
neurites . . . . . . . . . 6, 72, 201, 204, 218, 220, 226, 228, 269, 281-283, 295, 296, 298, 300, 302, 321, 328
neurogenesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219, 254, 289, 290
neuromodulator............................................................... 191, 203
neurotransmitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10, 111, 154, 183-189, 199, 207, 208, 293
neuro-effector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11, 184, 189, 199, 217, 261-265
neuro-facilitator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15, 139, 140, 188, 189, 207
neuro-inhibitor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15, 139, 140, 186, 189, 293
344 Neurons & the Nervous System
nicotinic......................................................................... 263
nitric oxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199, 262, 265
nNOS........................................................................... 262
Nobel Prize................................................................... 83, 123
Node of Ranvier . . 6, 8, 9, 59, 78, 123, 125, 132, 141, 142, 178, 197-199, 235, 237, 238, 242, 254-260,
283, 286, 287, 291, 298
noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172, 206, 207, 232, 258
non-inverting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5, 15, 138-140, 168, 173, 221, 277, 283, 302, 321
n- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47, 71, 80, 111, 113, 120, 130, 151, 212, 216
n-type. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80, 111, 113, 130, 216
OCT............................................................................ 277
Ohm’s Law ...................................................................... 134
oligodendroglia................................................................... 286
orbital ...................................................................... 129, 130
orbitals...................................................................... 129, 130
OSC........................................................................ 158, 159
oskonation........................................................................ 30
oskonatory........................................................................ 33
out of plane...................................................................... 149
out-of-plane....................................................................... 97
pain........................................................................ 178, 288
paracrine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15, 92, 155, 190-192, 199, 203, 217, 262, 263, 293
parametric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8, 178, 234, 237, 238, 241, 243, 244, 269, 287, 296, 309
parvocellular..................................................................... 248
patch-clamp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178, 200, 273, 306, 307, 314
pedestal..................................................................... 247, 260
pedicel...................................................................... 172, 206
pedicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58, 183, 205, 243, 254, 260, 264, 283, 297
pericrine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15, 92, 262, 265
PET........................................................................ 154, 219
phase velocity.................................................................... 298
pheromone........................................................................ 93
piezoelectric ................................................................. 231, 232
pituitary gland.................................................................... 264
plasticity........................................................................ 285
pnp. . . . . . . . . . . . . . . . . . . . . . 1, 59, 82, 111-114, 125, 126, 152, 154, 155, 171, 180, 212-214, 216, 329
PNPN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1, 9, 183, 216, 217, 316, 318, 322, 324
poda. . . . . . . . . . . . . . . . . . . . . . . . . 149, 171, 173, 175-177, 226-228, 239, 249, 250, 255, 259, 261, 297
podites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6, 107, 148, 204, 269, 283, 300
poditic . . 5, 59, 99, 135, 136, 139, 141, 144, 149, 165-168, 173, 220, 223, 224, 226, 228, 242, 243, 251,
252, 254, 257, 260, 265, 268, 287, 293, 296, 297, 300, 302, 321, 329
polyelectrolyte.................................................................... 159
POSS........................................................................... 226
Pretectum........................................................................ 286
probe compensation................................................................ 244
propagation velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251, 289
protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32, 40, 79, 114, 178, 184, 289, 301
pseudo-action potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247, 296
PtdSer ........................................................................... 63
pulse-to-pulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250, 251, 254, 269
Purkinje cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213, 214, 216, 220, 277, 279-283, 314, 318-320, 325
pyramid cell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223, 225, 252, 300
pyramid neuron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1, 300, 301, 303
P-channel........................................................................ 151
p-type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80, 91, 111, 113, 128
quantum-mechanical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10, 79, 105, 106, 109, 110, 135, 231, 244, 327
quiescent . . 94, 134, 145, 163-166, 170-172, 200, 206, 207, 220-222, 228, 230, 231, 237, 238, 250, 252,
259, 260, 265, 267, 287, 317, 318, 327
Q-channel ....................................................................... 250
rafts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15, 55-57, 288, 289
reading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51, 158, 159, 243, 260
rectifier..................................................................... 132, 134
refractory period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237, 241, 243, 286, 309, 318
residue...................................................................... 140, 262
resonance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32, 77, 118, 210
The Neuron 2- 345
reversible synapse................................................................. 199
roadmap........................................................................ 8, 92
roughness................................................................... 32, 72, 73
S potential................................................................... 251, 252
saturation. . . . . . . . . . . . . . . . . . . 83, 87, 90, 114, 116, 133, 134, 165, 170, 171, 180, 237, 238, 271, 317
Schwann cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193, 274, 286
seam ............................................................................ 33
second messenger.................................................................. 30
semi-metallic water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82, 105, 106, 111, 113, 149, 204-208, 255
serape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314, 316, 317, 320, 321
signature sequence.................................................................. 24
simple neurons..................................................................... 59
smooth muscle................................................................ 195, 262
spinal cord................................................................... 185, 188
spines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99, 107, 283, 320, 323-325
stage 1 . . . . . . . . . . . . . . . . . 8, 123, 139, 182, 201, 221, 224, 228, 230, 231, 235, 236, 291, 292, 298-300
stage 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57, 70, 98, 131, 220, 223, 235, 236, 247, 265, 300
stage 3 . . 5, 6, 8, 11, 59, 107, 139, 141, 143, 148, 163, 165, 173, 183, 203, 206, 219, 226, 235, 236, 240,
242, 243, 247, 251, 254, 260, 261, 276, 280, 283, 291, 292, 294-297, 300, 301, 305
stage 3A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5, 6, 138, 241-243, 252, 300, 312, 317, 318, 325, 328
stage 3B................................................................... 6, 276, 283
stage 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57, 70, 99, 107, 175, 223, 235-237, 247, 300
stage 5................................................................... 70, 172, 235
stage 5c......................................................................... 312
stage 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182, 201, 270, 292
stage 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15, 173, 182, 183, 186, 187, 192, 197, 217, 236, 261-265, 269
stage 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144, 236, 265, 267
stellate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7, 135, 141, 223, 224, 260, 283, 325
stellate neuron................................................................ 224, 260
stellite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173, 235, 236, 260, 261
stellite neuron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235, 260, 261
stratified . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5, 6, 59, 99, 137, 141, 223, 226, 293
stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159, 231, 265, 290
style 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182, 183, 201, 203, 216, 217
style 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9, 183, 203, 216, 217
style 3 ...................................................................... 183, 217
surface tension.................................................................. 16, 80
synapse . 1, 6-9, 59, 73, 78, 98, 99, 107, 115, 123, 125, 142, 164, 165, 179, 182-187, 189-192, 194-208,
210, 212, 213, 216-220, 224, 235, 248, 255, 257, 260, 262, 263, 265, 273, 276, 277,
282-286, 293, 295, 297, 301, 302, 316-322, 324, 325, 327-329
synapse style 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182, 183, 201
synapse style 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9, 183, 216, 217
synapse style 3................................................................ 183, 217
syncytium ....................................................................... 166
Template . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120, 131, 179, 181, 271
thalamic reticular nucleus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
thalamus ................................................................ 174, 181, 190
three-terminal . . . 1, 3, 5, 6, 9, 10, 112, 136, 139, 144, 167, 173, 186, 200, 201, 205, 212, 243, 247, 252,
272, 274, 277, 284, 293, 294, 297, 315, 328, 329
threshold . . 6, 107, 153, 159, 165, 173-175, 181, 237-239, 241, 252, 269, 271, 273, 287, 292, 293, 297,
298, 308, 309, 317, 318, 328
tight junction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34, 104, 194, 201
tinnitus.......................................................................... 172
topography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136, 148, 202, 223, 226
topology . . . . . . . . . 11, 135, 143, 148, 174, 220, 221, 225, 227, 228, 248, 249, 254, 255, 259, 260, 295
torsion........................................................................... 47
transcendental functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
transduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92, 93, 129, 190, 228, 231, 232
transistor action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10, 74, 111, 112, 135, 146, 175, 203, 230, 294, 327
translation................................................................... 187, 199
trans-............................................................................ 86
Tsotsos ..................................................................... 313, 319
Turing.......................................................................... 292
twitch........................................................................... 183
two-port......................................................................... 292
346 Neurons & the Nervous System
type 1. . 12, 15, 19, 24, 44, 70, 73, 85, 86, 90, 93, 101, 104, 105, 107, 135, 143, 145, 146, 196, 220, 229,
328
type 2. . . 11, 15, 30, 32, 40-44, 56, 63, 69, 70, 72, 73, 76, 83, 86, 88-90, 94, 95, 101-105, 108, 109, 111,
116, 119, 123, 126, 129, 132, 135, 139, 143-146, 153, 163, 171, 203, 204, 212, 217,
220, 228-230, 258, 264, 272, 274, 328
type 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12, 14, 15, 24, 56, 70, 73, 93, 101, 102, 104, 108, 135, 328
type 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15, 73, 82, 92, 109
type I............................................................................ 15
voltage clamp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59, 178, 243, 270, 330
voxel........................................................................... 220
white matter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71, 282, 317
Wikipedia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35, 80, 123, 128, 129
write/read........................................................................ 216
X-ray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12, 29, 49, 52, 53, 77-79