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Schematic representation of the voltage-clamp arrangement, illustrating a single myelinated nerve fibre lying over three insulating gaps separating four fluidifilled pools A, B, C and E. D represents the inside of the fibre at the node of Ranvier.

Schematic representation of the voltage-clamp arrangement, illustrating a single myelinated nerve fibre lying over three insulating gaps separating four fluidifilled pools A, B, C and E. D represents the inside of the fibre at the node of Ranvier.

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1. Voltage-clamp studies were carried out on single rabbit myelinated nerve fibres at 14 degrees C with the method of Dodge & Frankenhaeuser (1958). 2. A method was developed to allow the ionic currents through the modal membrane to be calibrated exactly under voltage-clamp conditions by measuring the resistance of the internode through which the c...

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... fine needles into a fan of interwoven fibres (see Stampffi & Hille, 1976). A single fibre with three nodes visible was isolated by cutting away surrounding fibres leaving it attached at its two ends to the undissected portions of the trunk. It was transferred under Locke to a nerve chamber with four pools, A, B, C, E, separated by partitions (see Fig. 1). The node was positioned to lie in the A pool and Vaseline seals were applied to the surface of the three partitions. The fluid level was then lowered to expose the seals and remove conducting pathways between pools. The preparation was allowed to stabilize at 14 0C for 15-20 min before kinetic measurements were begun Single fibres ...
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... of the internodes and from the unknown properties of the cut end of the fibre. In the present experiments, where go, values for rabbit and frog nerve fibres are compared, a series of measurements was devised to determine directly the internode resistances RDE, RCD and the resting nodal resistance, BAD, for each fibre, as illustrated in Fig. ...
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... action potential in a rabbit fibre Fig. 2A shows a membrane action potential in a rabbit node at 14 0C in response to a rectangular pulse of current injected between E and A (Fig. 1). The action potential has a threshold of about 30 mV, lasts 3 msec, and reaches a height of 110 mV. For comparison, a frog action potential at 14 0C is shown in Fig. 2B; the duration, of about 3 msec, is similar to that calculated by Frankenhaeuser (1965) for toad node at 10 0C. It is apparent that at the same temperature, a rabbit and ...
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... series of equally spaced depolarization steps starting from the holding potential. -80 mY. and ending at + 55 mV. B, the corresponding family of ionic currents in a frog node generated by a similar series of depolarizations. C7, a family of sodium currents calculated on the basis of the Hodgkin-Huxley parameters for sodium current in rabbit node (Fig. 7, 10), with values of E~5 and j>, from the fibre in A. D, addition of 12 mM-TEA-Cl to the Ringer bathing the frog node. Note that delayed rectification (potassium current) is present in the frog node but absent in the rabbit node. Ends of rabbit and frog fibres cut in 160 and 120 mM-KCl respectively. B and D are from two different frog ...
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... not study tail currents or use multiple pulse experiments to characterize Tm and Th (and thus, ah and 8lm) over the hyperpolarizaing and low depolarizing potential range, we have chosen to fit only the fib and am curves and use them together with the fitted curves for m. (E) and ha) (E) to derive the corresponding values for ah (E) and 8m (E). Fig. 10 shows the values obtained for 8lh (E) and am (E) at 14 C. respectively. These expressions are similar to those used by Frankenhaeuser & Huxley (1964). Note that the curves for aZm and j8h are extrapolated to somewhat more negative membrane potentials than those used ...
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... passive nodal parameters for axon 17 (Table 1), together with a value of 2pF for the membrane capacitance determined in the same fibre from the measured membrane time constant, were used to calculate a non-propagating rabbit action potential to compare with the observed action potential obtained from the same axon as shown in Fig. 11. Except that it has a slightly smaller amplitude and a S. Y. CHIU, J. M. RITCHIE, R. B. ROGART AND D. STAGG broader duration, the computed action potential is essentially similar to the observed potential at 14 'C. Fig. 12 illustrates the computed ionic currents underlying a rabbit action potential and the similar currents computed for ...
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... non-propagating rabbit action potential to compare with the observed action potential obtained from the same axon as shown in Fig. 11. Except that it has a slightly smaller amplitude and a S. Y. CHIU, J. M. RITCHIE, R. B. ROGART AND D. STAGG broader duration, the computed action potential is essentially similar to the observed potential at 14 'C. Fig. 12 illustrates the computed ionic currents underlying a rabbit action potential and the similar currents computed for frog, using our own kinetics for frog sodium current and using those for potassium currents taken from Hille (1971 b). Comparison of the time courses of ionic currents underlying the frog and rabbit action potential at 14 ...
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... nerve, the outward current responsible for repolarizing the membrane in rabbit nerve at 14 0C consists of only one ionic component, the passive leak: potassium currents are virtually absent. A family of voltage-clamp current records for a rat node at 37 0C published by Nonner & StAmpfli (1969) also shows the absence of potassium current (see also Fig. 12. Comparison of the computed time courses of the ionic currents underlying rabbit and frog action potential at 14 'C. Note the existence of two peaks in the time course of I., during the frog membrane action potential and the existence of only the initial peak for I,. in the rabbit. Note also that the repolarizing current is leak plus ...

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... Using the EONS SENN model with the original parameters used for deriving exposure guidelines by Reilly & Diamant, thresholds were calculated for 5 MCDs (Hodgkin & Huxley, 1952;Frankenhaeuser & Huxley, 1964;Chiu, et al., 1979;Sweeney, et al., 1987;Schwarz & Eikhof, 1987;Schwarz, et al., 1995). The model labels and abbreviations are given in Table 1 and further information about them can be found in Tarnaud et al. (Tarnaud, et al., 2018). ...
Preprint
Occupational exposure limit values (ELVs) for body internal electric fields can be derived from thresholds for action potential generation. These thresholds can be calculated with electrostimulation models. The spatially extended nonlinear node model (SENN) is often used to determine such thresholds. An important part of these models are the membrane channel dynamics describing the ionic transmembrane currents. This work shows how ELVs change significantly with different ion channel dynamics (up to a factor of 22). Furthermore, two more detailed double-cable models by Gaines et al. (MRG-Sensory and MRG-Motor) are also considered in this work. Thresholds calculated with the SENN model (with Frankenhaeuser-Huxley membrane channel dynamics) and the MRG models are compared for frequencies between 1 Hz and 100 kHz and temperatures between 22 °C and 37 °C. Results show that MRG thresholds are lower than SENN thresholds. In the context of occupational ELVs, using the double cable model would lead to approximately ten times lower limit values. Therefore, future exposure guidelines should take the influence of different electrostimulation models into account when deriving ELVs. Highlights Different membrane channel dynamics change derived exposure limit values by more than one order of magnitude. Double-cable models result in a reduction of derived exposure limit values by one order of magnitude. Lower temperatures reduce the action potential thresholds at frequencies below 300 Hz.
... TRAAK and TREK-1 are localized to nodes of Ranvier, the small gaps between myelinated regions of axons where the action potential is regenerated during saltatory conduction [9][10][11] . In contrast to the classically studied squid giant axon, from which the canonical model of the molecular basis for the action potential was derived, mammalian axons can completely lack voltage-gated K + channels at nodes 12 . Instead, TRAAK and TREK-1 contribute to the large nodal leak K + conductance that sets the resting potential, repolarizes the membrane in an action potential, and maintains voltage-gated Na + channel availability to facilitate high-frequency spiking [9][10][11] . ...
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TRAAK, TREK-1, and TREK-2 are mechanosensitive two-pore domain K+ (K2P) channels that contribute to action potential propagation, sensory transduction, and muscle contraction. While structural and functional studies have led to models that explain their mechanosensitivity, we lack a quantitative understanding of channel activation by membrane tension. Here, we define the tension response of mechanosensitive K2Ps using patch-clamp recording and imaging. All are low-threshold mechanosensitive channels (T10%/50% 0.6-2.7 / 4.4-6.4 mN/m) with distinct response profiles. TRAAK is most sensitive, TREK-1 intermediate, and TREK-2 least sensitive. TRAAK and TREK-1 are activated broadly over a range encompassing nearly all physiologically relevant tensions. TREK-2, in contrast, activates over a narrower range like mechanosensitive channels Piezo1, MscS, and MscL. We further show that low-frequency, low-intensity focused ultrasound increases membrane tension to activate TRAAK and MscS. This work provides insight into tension gating of mechanosensitive K2Ps relevant to understanding their physiological roles and potential applications for ultrasonic neuromodulation.
... The notion behind ionic cable theory is to incorporate the density distribution of specific proteins subdivided into two classes, carriers and pores (ion channels), into passive cable models of neural processes by distributing these specific voltage-dependent ionic currents discretely. In particular, we will consider an all Na + system like that found in rabbit myelinated axons (Chiu et al., 1979) or pyramidal dendrites in the electrosensory lateral-line lobe of weakly electric fish (Turner et al. 1994) with discrete loci of Na + channels or hotspots as active point sources of transmembrane current, imposed on a homogeneous (non-segmented) leaky cable structure with each hotspot assumed to occupy an infinitesimal region containing a small cluster of fast pores called Na + channels in the presence of ion fluxes due to active transport processes, such as Na + -Ca 2+ exchanger and Na + -pump imbedded in the lipid bilayer membrane as proteins specialized as slow carriers. ...
... Equation (1) can be cast in terms of non-dimensional space and time variables, X = x/λ and T = t/τm, respectively, where λ = (Rmd/4 ρi) 1/2 and τm = RmCm are, respectively, the space and time constants in cm and msec. Thus Eqn (1), after using δ(λX) = δ(X)/λ , becomes where T > 0, 0 < X < L, l is the physical length in cm, L = l/λ is the electrotonic length, X = x/λ represents loci along the cable of ionic current, expressed in terms of the dendritic space constant λ, and I is the nonlinear transient Na + transmembrane current density per unit membrane surface of cable (µA/cm) (expressed as a sink of current since by convention inward current is negative and outward is positive) based upon the H-H gate formalism and the constantfield equation (Chiu et al., 1979;Dodge & Frankenhaeuser, 1959;Frankenhaeuser & Huxley, 1964): ...
... This is especially prevalent at hotspots when spatial ionic concentration changes are expected to be large (Qian & Sejnowski 1989). In addition to a barrier, there are 'membrane gates' controlling the flow of Na + (ionic) current, with the time-dependent gating having a lower power for activation from the standard H-H model (Chiu et al. 1979;Dodge & Frankenhaeuser, 1959;Frankenhaeuser & Huxley, 1964). ...
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We derive an approximate analytical solution of a nonlinear cable equation describing the backpropagation of action potentials in sparsely excitable dendrites with clusters of transiently activating, TTX-sensitive Na+ channels of low density, discretely distributed as point sources of transmembrane current along a continuous (non-segmented) passive cable structure. Each cluster or hot-spot, corresponding to a mesoscopic level description of Na+ ion channels, included known cumulative inactivation kinetics observed at the microscopic level. In such a reduced third-order system, the ‘recovery’ variable is an electrogenic sodium-pump and/or a Na+-Ca2+ exchanger imbedded in the passive membrane, and a high leakage conductance stabilizes the system. A nonlinear cable equation was used to investigate back-propagation and repetitive activity of action potentials, exhibiting characteristics of the modified Hodgkin-Huxley kinetics (in the presence of suprathreshold input). In particular, a time-dependent analytical solution was obtained through a perturbation expansion of the non-dimensional membrane potential (Φ) for all voltage dependent terms including the voltage dependent Na+ activation μ) and state-dependent inactivation (η) gating variables and then solving the resulting system of integral equations. It was shown that back-propagating action potentials attenuate in amplitude with the frequency following experimental findings and that the discrete and low-density distributions of transient Na+ channels along the cable structure contribute significantly to their discharge patterns. A major significance of integrative modelling is the provision of a continuous description of the non-dimensional membrane potential (Φ) as a function of position.
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... Moreover, the kinetics of fast Na ? conductance [17], ion pumps [18], K ? reversal potential [19], input impedance [20], and axon geometry [21,22] are also potential factors affecting the super-and subnormal periods. ...
... In the multi-compartment MRG axon model, the afterpotentials include both DAP with a decreased stimulus threshold and AHP with an increased stimulus threshold. This variability of the recovery cycle is consistent with previous studies [8][9][10][17][18][19][20][21][22]. Further, multiple factors have been identified to contribute to the recovery cycle pattern, such as passive discharging of the internodal axolemma [22], activation of persistent Na ? ...
... current [58,59], dynamics of fast Na ? conductance [17], temperature [13,14], ion pump [18], input impedance [20], fiber diameter [21], and internodal distance [8,9]. In particular, McIntyre et al. [31] suggest that the variation in recovery cycle pattern represents the nonlinear interactions of above multiple factors, which is not caused by single factor. ...
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The axons exhibit depolarizing and hyperpolarizing afterpotentials, which result in complicated patterns of recovery cycle and influence the activation of subsequent action potential (AP) with deep brain stimulation (DBS). Our objective is to examine the spike initiation at axonal afterpotentials. We use biophysical models to simulate the afterpotentials and apply two-pulse conditioning-test paradigm to measure the stimulus threshold in recovery cycle. We analyze the phase plane portraits and interactions of ionic currents at spike threshold to determine the spike initiating dynamics associated with the recovery cycle. We show that the afterpotentials alter the net current at voltage threshold of subsequent AP, which results in the changes in spike threshold. The difference between spike threshold and afterpotentials determines the stimulus threshold for evoking subsequent AP, which governs the recovery cycle pattern. Our simulations provide a biophysical basis of the spike initiation at the afterpotentials, which is important for interpreting the activity-dependent modulations of axonal excitability. The predictions should be considered when understanding the frequency-dependent firing patterns in the axon with DBS.
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... The original H-H model has two voltage-gated currents, sodium and potassium, and a leakage current (Hodgkin & Huxley, 1952;Zhang et al., 2014). The CRRSS model contains only the voltage-gated sodium and the leakage current, since there are almost no potassium currents in mammalian nodes of Ranvier (Chiu et al., 1979;Schwarz & Eikhof, 1987;Schwarz et al., 1995). ...
... First we tested depolarizing and hyperpolarizing pre-pulsing options with rectangular stimulus waveform for selectivity. Then, we introduced eight different stimulus waveforms (Espay et al., 2016;Grill, 2015), with and without the hyperpolarization pre-pulse (HPP) (Chiu et al., 1979). We hypothesized that using non-rectangular stimulus waveforms may shift the SD curves in a way to achieve higher levels of selectivity than the classical rectangular waveform in the presence of electrophysiological diversity. ...
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... In this research work, a combined one dimensional (1D) functional model of various dorsal nerves in the human foot is proposed and constructed. The combined functional dorsal nerve model (CFDNM) incorporates the modified unmyelinated Hodgkin-Huxley (UHH) [22] and the myelinated Chiu, Ritchie, Rogert, Stagg and Sweeney (MCRRSS) [23] electrophysiological nerve models. These models were employed to construct and propagate action potential using grid based finite difference method to obtain the Bidomain model solution in SUSSN and MLN respectively. ...
... These electrophysiological nerve models were utilized to determine action potential in a single grid point of the desired SUSSN of the skin of the foot and interconnected dorsal MLN respectively. Equations (1) and (2) are the mathematical equations and their parameters employed in both UHH [22] and MCRRSS [23], implemented in CellML. ...
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The nerves in the skin surface of the foot are comprised of unmyelinated smaller somatic nerves and larger myelinated sensory nerves. Current diagnostic methods are unable to evaluate combined nerve conduction velocity (NCV) from both unmyelinated smaller somatic nerve (USSN) and myelinated larger nerves (MLN) respectively. Computational models may provide an alternative tool to determine the NCV of the combined nerve. Therefore, a combined functional dorsal nerve model (CFDNM) of the various dorsal nerves along with its associated nerve ending of the human foot is proposed and constructed. The combined dorsal nerve model consists of synthetic USSN (SUSSN) and dorsal MLN of the foot. The unmyelinated as well as myelinated electrophysiological nerve models were used to simulate selected SUSSN and MLN of the foot by injecting an external stimulus at the most distal part of SUSSN of the foot through the use of bidomain model. Results from our work demonstrated that the action potential propagated from the most distal part to proximal part of distinct dorsal nerves of the foot, e.g., the simulated NCV of the combined intermediate dorsal cutaneous nerve (IDCN) of the foot was 28.4 m s⁻¹. The CFDNM will provide a vital tool for diagnosis initially small fibre neuropathy (SFN) by computing NCV in the prospective studies.
... Contrary to non-myelinated axons, in myelinated axons of warm blooded animals the potassium current is of negligible intensity [14]. An equation missed by the authors (Chiu, Ritchie, Rogart, and Stagg) was reconstructed by Sweeney in 1987 and consequently this model, which is of the HH type, was named CRRSS model [15][16][17]. ...
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... The distinct distribution of ion channels in the node of Ranvier of mammalian myelinated nerve fibres was detected more than 40 years ago: Na + channels are located in the nodal axolemma and, surprisingly, voltage-dependent Kv1 channels to the juxta-paranodal axolemma (Chiu & Ritchie, 1981). Instead of delayed-rectifying K + current as in the squid giant axon and the frog node of Ranvier, time-and voltage-independent nodal 'leakage' current was shown to repolarize the action potential in the mammalian node (Chiu et al. 1979;Brismar, 1980;Schwarz & Eikhof, 1987). The recent identification of the K + -selective 'leakage' channels, such as TRAAK and TREK-1 channels, has opened a new field of research, since almost all research into K2P activators and inhibitors has been done on K2P channels heterologously expressed in artificial expression systems. ...
... The authors recognized the small amplitude of the outward K + currents but did not pursue this observation further. About 10 years later the observation of small delayed rectifying outward K + currents was confirmed by recordings from the node of Ranvier of rat (Brismar, 1980) and rabbit (Chiu et al. 1979;Chiu & Ritchie, 1981) myelinated nerve fibres. The authors discovered that in the mammalian myelinated nerve fibre Na + channels (Na v 1.6) are located to the nodal axolemma, whereas delayed-rectifying voltage-dependent Kv1 channels are absent in the node, but located to the juxta-paranode (Chiu & Ritchie, 1981). ...
... The authors discovered that in the mammalian myelinated nerve fibre Na + channels (Na v 1.6) are located to the nodal axolemma, whereas delayed-rectifying voltage-dependent Kv1 channels are absent in the node, but located to the juxta-paranode (Chiu & Ritchie, 1981). It was also recognized that the leakage current in the mammalian node is larger than in the frog node by a factor of 4-5 (Brismar, 1980) and that its magnitude is sufficient to repolarize the action potential (Chiu et al. 1979). ...
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In myelinated nerve fibres, action potentials are generated at nodes of Ranvier. These structures are located at interruptions of the myelin sheath, forming narrow gaps with small rings of axolemma freely exposed to the extracellular space. The mammalian node contains a high density of Na⁺ channels and K⁺‐selective leakage channels. Voltage‐dependent Kv1 channels are only present in the juxta‐paranode. Recently, the leakage channels have been identified as K2P channels (TRAAK, TREK‐1). K2P channels are K⁺‐selective ‘background’ channels, characterized by outward rectification and their ability to be activated, e.g. by temperature, mechanical stretch or arachidonic acid. We are only beginning to elucidate the peculiar functions of nodal K2P channels. I will discuss two functions of the nodal K2P‐mediated conductance. First, at body temperature K2P channels have a high open probability, thereby inducing a resting potential of about −85 mV. This negative resting potential reduces steady‐state Na⁺ channel inactivation and ensures a large Na⁺ inward current upon a depolarizing stimulus. Second, the K2P conductance is involved in nodal action potential repolarization. The identification of nodal K2P channels is exciting since it shows that the nodal K⁺ conductance is not a fixed value but can be changed: it can be increased or decreased by a broad range of K2P modulators, thereby modulating, for example, the resting potential. The functional importance of nodal K2P channels will be exemplified by describing in more detail the function of the K2P conductance increase by raising the temperature from room temperature to 37°C. image