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On cell surface deformation during an action potential
Christian Fillafera, Matan Mussela,b, Julia Muchowskia, Matthias F. Schneidera
aTechnical University of Dortmund
Department of Physics
44227 Dortmund
Germany
bUniversity of Augsburg
Department of Physics
86159 Augsburg
Germany
1Address correspondence to: Dr. Matthias Schneider
Technische Universität Dortmund
Medizinische und Biologische Physik
Otto-Hahn-Str. 4
44227 Dortmund
tel: +49-231-755-4139
email: matthias-f.schneider@tu-dortmund.de
Keywords: action potential; Chara; mechanical; membrane; cell surface
Abstract
Action potentials (AP) are considered to be electrical phenomena. However, non-electrical changes at
the cell surface have been reported and resulted in contradictions with the classical theory. The evidence
presented herein corroborates that an AP is not a purely electrical phenomenon. It is demonstrated that
excitation of plant cells (Chara braunii internodes) is accompanied by out-of-plane displacements of
the cell surface in the micrometer range (~1–10 µm). The onset of cellular deformation coincides with
the depolarization phase of the AP. The mechanical pulse (i) propagates with the same velocity as the
electrical pulse (within experimental accuracy; ~10 mm s-1), (ii) is reversible, (iii) in most cases of
biphasic nature (109 out of 152 experiments) and (iv) presumably independent of actin-myosin-motility.
The existence of transient mechanical changes in the cell cortex is confirmed by micropipette aspiration
experiments. A theoretical analysis demonstrates that this observation can be explained by a reversible
change in the mechanical properties of the cell surface (transmembrane pressure, surface tension and
bending rigidity). Taken together, these findings contribute to the ongoing debate about the physical
nature of cellular excitability.
Significance Statement
Ever since the controversy between Galvani and Volta in the early 19th century, excitation processes in
cells and tissues have been considered to be of an electrical nature. Several lines of evidence (see e.g.
(1, 2)) suggest that this conclusion was premature. It is demonstrated herein that an action potential is
associated with a significant deformation of the cell; i.e., a change in its mechanical properties. These
observations are not predicted by the present electrical theory and demonstrate the relevance and
importance of additional macroscopic variables for understanding cellular excitation.
Introduction
Action potentials (AP) are intriguing phenomena that appear in many biological systems (neurons,
myocytes, excitable plant cells, etc.). For a long time, it has been believed that these pulses are of an
electrical nature. The mathematical description of APs was based on the view that the excitable
membrane can be fully represented by an equivalent circuit (3). However, this approach has come under
substantial criticism. The debate has been stirred up by Tasaki (4–12) and has been extended mainly
through the works of Kaufmann (2, 13) and Heimburg (1, 14). One of the central points of criticism of
the electrical framework is that it neither contains nor predicts non-electrical manifestations of the AP.
These pulse components, however, exist and include optical (4), thermal (15), magnetic (16) as well as
mechanical (5–8, 17) changes at the cell surface. The latter have been studied with a variety of highly
sensitive techniques (piezoelectric benders, interferometry, AFM). At first, the inherently soft nature of
nervous tissue preparations combined with the sheer minuteness of the movements posed difficulties
and led to varying results (5–7, 17). Nevertheless, more recent studies are in agreement and indicate that
the mechanical pulse in cylindrical axons is of biphasic nature with expansion followed by contraction
(~1–10 nm) (8, 18). In parallel, there exists a biphasic intracellular pressure wave (18). Intriguingly,
neither the mechanism behind the mechanical pulse component nor its relation to the electrical events
are currently understood. Aside from APs in axons, other excitation phenomena in biology are also
associated with mechanical changes. Deformations were reported, for instance, in muscle cells (19) as
well as during spreading depression waves in cortical tissue (20). It must be of central interest to
investigate if these phenomena can be explained by a unified theory.
While there exists firm evidence that an AP is not only an electrical but also a mechanical pulse, several
open questions remain. Even in well-cleaned axons the cell surface is covered by extracellular matrix
and Schwann cells (9). This makes it difficult to observe and study the excitable membrane directly.
Moreover, if this sheath is stiffer than the underlying cell membrane it will lead to significant attenuation
of mechanical signals. Thus, the actual mechanical changes during an AP may be larger than anticipated.
Herein, we attempt to contribute to these open problems. Mechanical changes are investigated during
AP propagation in plant cells. Internodes from Charophytes are well suited for this purpose. These cells
are large (diameter !0.5—1 mm; length !1—15 cm), easy to handle and have a long-standing history
in excitable cell research (21, 22). In Charophytes, comparatively large radial and axial deformations
have been reported during an AP (~100 nm (6, 23)). As in the case of axons, the mechanical pulse is
biphasic and consists of expansion followed by contraction (24). Herein, we demonstrate that “freeing”
the excitable membrane from the constraints of the plant cell wall reveals even larger surface
displacements in the micrometer range. A theoretical analysis indicates that these deformations during
an AP are due to reversible changes in the mechanical properties of the cell surface (transmembrane
pressure, surface tension, bending rigidity).
Results
Cell surface deformations during an AP. In a native Chara cell, the plasma membrane is tightly pressed
against the cell wall by a turgor pressure (!6·105 N m-2 (25)) (Fig. 1a). However, by changing the
extracellular osmotic pressure it was possible to progressively reduce turgor until the plasma membrane
detached from the cellulose sheath – a process known as plasmolysis (Fig. 1b) (26, 27). During this
procedure, the protoplast did not retract uniformly. In certain regions (e.g., at the nodes) the membrane
still adhered to the cell wall whereas in other areas it detached entirely. Initially, the shape of a
plasmolysed cell was irregularly wavy. As time progressed, the protoplast equilibrated, assumed an
unduloid-like form, and eventually fragmented*.
Figure 1. Cell surface deflection during an action potential (AP). (a) In Chara, the cytoplasm (cp) is marginalized by
the tonoplast (to)-covered vacuole (vac). The cellular cortex consists of the cell wall (cw), cell membrane (cm), cortical
cytoskeleton (cc), chloroplasts (chlo) and subcortical actin bundles (ab) (see (28)). (b) When turgor was reduced by
changing the external osmotic pressure, cm separated from cw. Deflections (dashed arrow) of the projection edge of the
protoplast surface (prot) were tracked by light microscopy. (c) Upon excitation of an AP the cell surface underwent a
biphasic, reversible deflection (stimulus indicated by arrow; top trace: membrane potential; bottom trace: kymograph of
surface deflection). (d) Membrane potential pulse (black) and out of plane displacement of the cell surface (red); note:
an initial inward movement is followed by expansion.
Chara cells did not lose excitability in the course of plasmolysis. Thus, it was possible to stimulate APs
and to study if deflections of the cell surface occur. For this purpose, randomly chosen regions of the
protoplast edge were tracked by light microscopy (Fig. 1b). In the absence of electrical stimulation only
minor drift of the edge was observed (Fig. S1). In contrast, a distinct surface displacement occurred
* This process was described previously (28) and resembles a pearling instability that develops at a very slow pace; in the
medical/biological literature this phenomenon is sometimes referred to as beading or varicose. Physically, it is related to the
Plateau-Rayleigh instability
upon excitation of an AP (in 142 out of 152 cases; N=30 cells) (Fig. 1c and Video S1 and S2). The
maximum deflection was more often outward (95 cases) than inward (47 cases) and typically in the 1—
10 µm range (Fig. S1). In the majority of experiments a brief displacement (≤1 s) with opposite
directionality preceded the maximum deformation (109 cases; Fig. 1d and Video S2). Such biphasic
displacements were also reported in fully turgid cells, albeit with 10—100x lower amplitudes (24). In
general, the amplitudes and time courses of the deformations were quite variable at different locations
along the protoplast projection edge (Fig. S1). This variation will be explained in a forthcoming
manuscript.
Correlation between membrane potential and surface displacement pulse. The AP propagation
velocity calculated from the mechanical displacement (8.2±2.4 mm s-1; n=26 pulses in N=4 cells), within
experimental accuracy, agreed with that based on the electrical pulse (9.6±2.0 mm s-1; Fig. S2). In most
experiments the surface displacement slightly trailed the membrane potential pulse (Fig. 1d). However,
since the electrical measurement is by default not as localized as a mechanical measurement, the delay
between the electrical and mechanical pulse may be a measurement artifact. Future studies could
circumvent this difficulty, for instance, by using fluorescent imaging which allows for localized
monitoring of the membrane potential as well. In any case, it was evident that the mechanical
deformation outlasted the electrical component (Fig. 1c). The membrane potential pulse in a
plasmolysed cell usually had a duration of ~10—20 s, whereas the surface deflection relaxed on
timescales that were an order of magnitude longer (!0.5—5 min). The latter agrees with observations
in fully turgid Charophytes (23, 24).
Involvement of actin-myosin-motility in surface displacement. Actin and myosin are present in
Characean cells, but their types and roles differ as compared to muscle cells (29). In Chara, coherent
sliding of myosin-coated organelles on actin filaments leads to directional streaming of the cytoplasm
(velocities up to 100 µm s-1). During an AP, streaming is temporarily arrested and recovers within
several minutes (29). This demonstrates that there exists a coupling between membrane excitation and
actin-myosin-motility (excitation-cessation-coupling). Furthermore, the relaxation time of cytoplasmic
streaming to normal velocities after stoppage (>1min) is of a similar order of magnitude as that of the
surface deformation (cf. Fig. 1 and Ref. (24)). Thus, stoppage of streaming or a coincident process in
the cytoskeleton may be involved in the observed deformations.
We attempted to investigate this possibility. It was reported that membrane excitation can be uncoupled
from streaming if extracellular Ca2+ is replaced with Mg2+ (30). This approach, however, was not
feasible, because plasmolysis in the absence of Ca2+ led to rupture of the Chara cell membrane. In a
subsequent series of experiments, cytochalasin D (CytD) was employed. This substance interferes with
and arrests cytoplasmic streaming by a presently unknown mechanism (31). Cytochalasins also
uncouple membrane excitation and contraction in muscle cells (i.e. the membrane is excitable, but
contractility is impaired (32)). Thus, it was expected that treatment with CytD will abolish the cell
surface deformation in Chara if the latter is dependent on actin-myosin motility. When a Chara cell was
incubated with CytD, it remained excitable but streaming came to a halt. This is analogous to the effects
of CytD on muscle cells. However, when an AP was triggered, the surface deformation of the Chara
cell persisted (Fig. 2). The time scales of this deflection were similar and the amplitudes were slightly
larger as compared to native cells. In combination with observations in muscle cells (32), these results
suggest that actin-myosin-motility is not involved in surface deformation during an AP in Chara.
Figure 2. Effect of cytochalasin D on surface deflection during an action potential (AP). (top) Displacement of
the cell surface upon excitation of an AP in artificial pond water (APW) and (bottom) in APW + 50µM cytochalasin
D. Stimulus indicated by arrow. Vertical scale bars represent 20 µm.
Micropipette aspiration at rest and during an AP. To better understand the mechanism of the cell
surface displacement, micromechanical tests were carried out. A small incision (length !500 µm) was
made in the cell wall of a plasmolysed Chara internode. Through this opening it was possible to directly
access the cell surface (see Fig. 1a and Ref. (28)).
Figure 3. Cell mechanical changes during an action potential (AP). (a) Aspiration of Chara cell membrane into
a micropipette (membrane projection indicated by m, protoplast surface by p). Note: the cell membrane is peeled off
the dense array of chloroplasts (also see Video S3). (b) During an AP the membrane underwent a reversible cycle of
motion into and out of the pipette at constant suction pressure. (c) Suction pressure (Δp) prior to stimulation of an
AP was “clamped” at 0<Δp<Δpcap (see text for definition of Δpcap). Membrane potential record (top) and aspirated
length (Lp; bottom) during an AP. (d) Initial phase of membrane motion into pipette (n=6 experiments in N=4 cells;
individual traces (black) and average (red)). See text for additional data and statistics. Unlabeled scale bars represent
10 µm.
Micropipette aspiration was used to study the mechanical properties of this surface. For a cylindrical
cell that is aspirated into a pipette, the surface tension† (σ) is given by the Young-Laplace law
" # $% &
'(
)*
'+
,-
with .% the pressure difference between extracellular medium (%/01) and pipette (%(), and '+ and '(
as the radii of the cell cylinder and the pipette respectively (33). The cortical tension of the cell in the
resting state "2341 (i.e., before excitation) was determined from the pressure difference (.%+5() that is
required to aspirate a membrane projection with length (6() equal to the pipette radius (i.e., when a
hemispherical membrane cap was aspirated (34)). In plasmolysed Chara cells, "2341 was 0.0670.01 mN
m-1 (n=4 experiments in N=3 cells; .% !10 N m-2, '+!150 µm, '(!10 µm). This value of membrane
tension is in good agreement with that of other excitable systems, for instance, Nitella protoplasmic
droplets (!0.05 mN m-1 (35)) and molluscan neurons (!0.04 mN m-1 (36)).
For aspiration experiments during an AP, the pipette touched the cell surface and a slight suction
pressure was applied (8 9 .% 9 .%+5(; see Fig. 3 and Methods for details). Once the position of the
membrane projection within the pipette had remained relatively steady, an AP was stimulated and
propagated past the aspiration site. Although the pipette pressure was held constant, 6( increased upon
arrival of the AP in all experiments conducted (n=22; N=9 cells; Fig. 3, Video S3). In some cases, a
short “inward dip” occurred prior to this movement (Fig. 3d). The membrane projection either moved
into the pipette irreversibly (Fig. S3) or reached a maximum and relaxed back to its initial position (Fig.
3c and Video S3). Since cell surface deflections in absence of a pipette were reversible (Fig. 1), it seems
likely that irreversibility was a concomitant of the aspiration procedure (37). In general, reversibility
prevailed (14 out of 22 cases).
Mechanical analysis of micropipette aspiration during an AP. In a typical aspiration experiment, the
surface forces, which are applied by the surface tension " and the bending rigidity :;<balance the
pressure difference between the extracellular medium and the interior of the pipette (.%). This triplet of
surface properties (.%; "; := represents the mechanical state of the system in a 3d-phase space. The
† For a bilayer membrane that behaves as a closed system: σ=γ-π where γ is the interfacial tension that results from contact of
the bilayer with the aqueous environment and π is the surface pressure in the membrane plane. The natural state of a lipid
bilayer is defined as γ=π in which case σ should vanish. Usually, however, it is nonzero (33).
objective of this section is to identify the conditions under which the balance of forces of a weakly
aspirated cell is disrupted, such that the system is progressively aspirated (Fig. 3). This was achieved by
calculating the aspiration length (6() that minimizes the elastic energy of the cell surface for different
values of the mechanical parameters (for details see Eq. (7) in Materials and Methods).
An example of the energy as a function of 6( is provided for three values of the surface tension with the
other parameters (.% and :) held constant (Fig. 4a). This graph demonstrates the existence of a critical
value of ", that flattens the energy function. From there, an increase of surface tension stabilizes the
weakly aspirated state (6(# 8), while a decrease of "<leads to an instability; i.e., 6( increases with time,
which means that the cell is aspirated into the pipette.
The phase space of the system consists of two regimes: one in which the weakly-aspirated state is stable
and one where it is not. A state is unstable when the surface tension and bending rigidity are insufficient
to balance the pressure difference (34). A 2d-slice in the .% ) " plane of the phase-space is depicted in
Fig. 4b. Weakly aspirated states are stable below the dashed line (instability line). The estimated resting
state of a plasmolysed Chara cell is located in this regime and is marked by a grey ellipse. A transition
across the line into the unstable regime (from stable 6(# 8 to 6(> 8) can be induced, for example, by
increasing $% by ~5 N m-2, decreasing " by ~50% or decreasing : by 2-3 orders. The effect of the latter
is much smaller, and requires a close proximity of the initial state to the instability line. The short inward
motion of a weakly aspirated cell at the beginning of an AP (Fig. 3d) may be induced by a parameter
change with opposite directionality (i.e., a decrease in $% or an increase in " or :). These findings are
in line with a more elaborate calculation conducted for a different domain of the parameter space (37).
Figure 4. (a) The energy E as a function of aspiration length Lp for three values of the surface tension reveal that the
weakly aspired state (6(# 8) can be stable, critical and unstable. Other parameters were held constant: : # *8,-?@; $% #
AB
CD; <'(#*8<EF and ; %(# G<HIJ. For convenience, the energy was scaled to zero at an aspiration length of zero (6(#
8). In addition, it was normalized by the mean thermal energy at room temperature (&8/K), to indicate that the elastic
energy stored in the surface is considerably larger. (b) The instability line in the ∆p–σ phase space. Weakly aspirated
states are located below the line. The estimated resting state of the cell is depicted by the grey ellipse (its size represents
the experimental error). Decreasing : effectively shifts the instability line in the direction of the arrow. The three states
studied in (a), are depicted as small diamonds in (b).
Discussion
It has been documented by several independent investigators, that APs are accompanied by cellular
deformations (4–12, 17, 18, 23, 24). In axons, the latter are typically on the scale of 1—10 nm, whereas
in fully turgid Charophytes they reach ~100 nm. Herein, it was demonstrated that the actual motions of
the cell surface may be 1—2 orders of magnitude larger than these previously reported values. In Chara,
separation of the plasma membrane from the cell wall reveals micron-sized displacements that were
readily observable by light microscopy. These results confirm the assertion that sheathing material
and/or cells significantly attenuate mechanical changes at the surface of an excitable cell. In order to
better understand the mechanism behind this cellular deformation, micropipette aspiration experiments
were carried out. A theoretical analysis of these data indicated that a reversible change in the mechanical
properties of the surface (%/01; "; :) takes place during an AP. This provides a basis to discuss potential
mechanism that underlie the cell surface deformation:
Cell surface displacement due to a change in transmembrane pressure. Since hydrostatic pressure
does not change during excitation of a cell, significant transmembrane pressure deviations should only
arise if the chemical potential of water in the intra- or extracellular space is altered. The chemical
potential depends on several parameters that define the thermodynamic phase state of water
(temperature, concentration of solutes, etc.). To the best of our knowledge, non-ionic changes of the
chemical potential have remained widely unexplored during cellular excitation. It is often assumed that
the solute concentration is the most likely parameter to change. Any variations of solute concentration
in the intra- or extracellular compartments will lead to a chemical potential gradient for water and thus
to a change in osmotic pressure. This gradient will be equilibrated by transfer of water (osmosis) if the
membrane is sufficiently permeable. In the classical theory of excitability (the Hodgkin and Huxley
model), transmembrane flux of ions is a central mechanism, and cell surface displacements in neurons
have been interpreted based on osmosis (38). Others, however, have argued against this assertion (9,
18). A main contradiction emerged from voltage clamp experiments. There, it is assumed that
transmembrane flux of ions can be monitored directly in the form of (ionic) currents (21). Ionic currents
are low during hyperpolarization (~30 µA cm-2) and high during depolarization (~1 mA cm-2) (39). If
ionic fluxes were the cause of the mechanical response, one would therefore expect larger displacements
during depolarization as compared to hyperpolarization. However, the opposite was observed (18). This
constitutes a central problem that has to be kept in mind.
In Chara, an AP is associated with an efflux of KL, and MN from the cell (O APG Q *8,?<FRLSTFU (40)).
Thus, the cell surface may experience a transient osmotic pressure change corresponding to an increase
in the extracellular pressure. However, if the efflux of solute is homogenous across the surface, this
pressure change will occur inside as well as outside the pipette and thus .% should remain unchanged.
Furthermore, an AP in Chara should be followed by a slight decrease of cell volume (25). In the simplest
case, this would lead to a uniform inward movement of the cell surface. Experimentally, however,
inward as well as outward deflections were observed (Fig. S1). In combination with arguments by others
(9, 18), this underlines that the mechanical changes are not readily explained by ion flux-induced
osmosis. In any case, a more detailed consideration of cellular geometry and of the properties of the
surface are required.
Cell surface displacements due to changes in surface tension and/or bending rigidity. In a 1945 paper,
Hodgkin and Huxley considered several potential mechanisms of the nerve action potential (41). One
implied a cooperative change of orientation of lipid dipoles. This possibility was rejected, because such
a process should notably alter the electrical membrane capacitance (KC) – a parameter that at that time
was assumed to be constant during an AP. In subsequent studies, it was demonstrated, however, that the
assumption of constancy of KC had been premature (42). This may have led to misinterpretations, for
example, because dynamic capacitive currents were ruled out in the original works (2). Based on this
point and others, a criticism of the electrical theory was formulated by Kaufmann (2, 13) and more
recently by Heimburg (1, 14). These authors proposed that an AP is a pulse propagating in the quasi 2-
dimensional membrane interface. Such a reversible (adiabatic) phenomenon must be associated with
transient changes in forces and fluctuations of all thermodynamic observables of the system (electric
field, pressure, temperature, surface area etc.). More recently, others have elaborated on this proposition
(1, 14, 43–45). It was demonstrated that linear (43) as well as non-linear, self-stabilizing pulses (solitary
waves) (44, 45) can be excited in lipid monolayers – the simplest model system of a cell membrane.
These pulses indeed manifest in all thermodynamic variables (e.g. electrical, thermal, optical, etc.) (46–
48). This is also the case for APs (3, 4, 12, 15, 18). If one compares the solitary waves in protein-free
lipid monolayers at the water-air interface with action potentials, additional similarities exist (threshold,
amplitude saturation, etc.). Thus, the thermodynamic theory predicts a lateral pressure pulse (related to
the surface tension) as well as a change in mechanical susceptibilities (area compressibility and bending
rigidity) during cellular excitation. The biphasic mechanical changes during an AP in Chara (Figs. 1—
3) may be the consequence of pulse-associated changes in "<and/or :<of the excitable medium. The
present analysis of micropipette aspiration results suggests that the observed phenomenology (Fig. 3)
could be explained by a sufficient decrease in surface tension by ~50 % and/or bending rigidity by ~2
orders. Such changes are not unrealistic, as a decrease in surface tension by ~10% was demonstrated in
lipid monolayer pulses (43) and during phase transitions in lipid bilayers : can be reduced by 1—2
orders of magnitude (49). For most state changes, however, " and : will change simultaneously. For
example, when a fluid lipid membrane is compressed isothermally into the phase transition regime, the
lateral pressure as well as : increase. In order to understand the particular relations between " and : in
Chara, it will be necessary to obtain state diagrams of the excitable medium. The latter could be the
plasma membrane or a more extensive cellular interface. It has been reported, for example, that cellular
excitation spreads to the vacuole (21), which indicates that the latter may be the case.
On the relation between the electrical and mechanical events. In Chara, the cell surface deformation
relaxes on time scales that are roughly an order of magnitude longer than the membrane potential pulse
(30—300 sec versus 5—10 sec). The mechanical relaxation time agrees fairly well with the duration of
the relative refractory period (> 60 sec at room temperature (50)). Thus, the surface deformation
dynamics may reveal information about relaxation of the excitable medium, which is not readily
apparent from the membrane potential record. Relaxation of the surface deformation in squid giant axons
– which closely coincides with the electrical pulse in native cells – also appears to be prolonged under
certain conditions, for instance, upon exposure of the axon to TEA (a treatment which extends the
membrane potential pulse in time (11)). An even slower, yet otherwise very similar, mechanical
displacement pulse occurs during spreading depression (SD) waves in cortical tissue (20). This
similarity is intriguing, because an SD wave involves synchronous activity of millions of cells. The
overall phenomenology in Chara internodes is also reminiscent of that of muscle fibers where cellular
shortening lags behind and outlasts the electrical pulse (19).
In principle, there are three potential relations between the membrane potential pulse and the cellular
deformation: (i) the mechanical and electrical components are two aspects of the same phenomenon
(i.e., they are coupled), but the mechanical component relaxes on longer timescales. From a
mathematical point of view, such behavior of variables is common in coupled differential equations.
From a physical point of view, a phase shift between two aspects of the same phenomenon is also
common, for instance, for particle displacement and pressure in a sound wave. (ii) The cell surface
deformation is an independent phenomenon triggered by the AP. In that case, it should be possible to
induce it in absence of membrane excitation. Up to date, this was neither observed by us nor by others
(6, 8, 18, 23, 24). An involvement of actin-myosin contractility, as has been proposed previously for
axons (51), is not obvious in Chara (c.f. Fig. 2). The present work did not address if a volume phase
transition in the gel-like “ectoplasm-plasmalemma complex” may be involved (10). For axons, there
exists evidence that the cortical cytoskeleton may not be essential for the mechanical pulse (18), as
removal of cell cortical filaments resulted in a more pronounced deformation. (iii) Finally, the
mechanical pulse may consist of two components (one on the timescales of the AP and an additional
(triggered) component).
Conclusions
The present work demonstrated that an AP is associated with a significant surface deformation (~1—10
µm) in plasmolysed Chara cells. This deformation co-propagates with the electrical signal, is biphasic
(69% of cases), reversible and relaxes at a slower rate compared to the membrane potential pulse. Due
to the magnitude of the displacements as well as the slow time scales of the pulse, this preparation is
well suited to study the physical origin of cell mechanical changes during excitation. Falsifiable
predictions were made concerning the surface property changes (%/01; "; :) that may be involved. Future
work should aim at understanding the coupling between the electrical and the mechanical signal. Finally,
it will be important to investigate if interfacial pulses in cell membrane models (lipid monolayer) and
action potentials in excitable cells can receive a unified theoretical explanation.
Materials and Methods
Materials. All reagents were purchased from Sigma-Aldrich (St. Louis, MO, USA) and were of
analytical purity (≥99%). Glass capillaries were obtained from Sutter Instrument (Novato, CA, USA).
Cell cultivation and storage. Chara braunii cells were cultivated in glass aquariums filled with a layer
of 2-3 cm of New England forest soil, quartz sand and deionized water. The cells were grown under
illumination from an aquarium light (14W, Flora Sun Max Plant Growth, Zoo Med Laboratories Inc.,
San Luis Obispo, CA, USA) at a 14:10 light:dark cycle at room temperature (~20°C). Prior to use, single
internodal cells were stored for a minimum of 12 h in a solution containing 0.1 mM NaCl, 0.1 mM KCl
and 0.1 mM CaCl2.
Plasmolysis of Chara internode. A single internodal cell (3-6 cm long) was placed on a plexiglass frame
into which compartments (~2 x 5 x 10 mm; h x w x l) had been milled. The bottom of the frame consisted
of a glass coverslip. Small extracellular sections (length ~5 mm) of the cell were electrically isolated
against each other with vacuum grease (Dow Corning Corporation, Midland, MI, USA). The grease also
provided structural support for the cell during plasmolysis. Artificial pond water was added (APW; 1
mM KCl, 1 mM CaCl2, 5 mM HEPES, 110 mM D-sorbitol; pH set to 7.0 with NaOH). This APW was
replaced gradually with APW of higher osmolarity (regulated by addition of D-Sorbitol; initial: ~120
mOsm kg-1; final: ~270 mOsm kg-1). Addition of ~0.5% bovine serum albumin to the final APW was
crucial to minimize adhesion between aspiration pipette and cell membrane. After an equilibration time
of 30-60 min, the plexiglass chamber was fixed on the microscope stage. A waveform generator (Agilent
33250A; Agilent, Santa Clara, CA, USA) in combination with a stimulus isolation unit (SIU5; Grass
Technologies, Warwick, RI, USA) was used to trigger APs.The membrane potential in one of the
compartments far from (1-5 cm) the stimulation site was monitored by intracellular recording.
Deflections of the edge of the cell surface are presented as kymographs. In brief, the intensity profile
along a line (see Fig. 1) was extracted from every frame of the video recordings (framerate: 10-40 s-1)
and was assembled in ImageJ (Version: 1.46r; http://imagej.nih.gov/ij) using the macro ImageJ
Kymograph (by J. Rietdorf and A. Seitz). Brightness and contrast of the final kymographs was adjusted.
Prominent features in the intensity profile correspond to cell membrane and protoplast edge respectively
(Fig. 1). The latter is particularly contrast rich due to the presence of chloroplasts. The membrane
potential recording was temporally synchronized with video microscopy by an LED flash into the optical
path of the inverted microscope (Olympus IX71). The time difference between the membrane potential
pulse and the mechanical displacement was calculated by depicting deviations in both signals. The
criterion for the time of arrival at the measurement site was defined as a deviation of the signal from
baseline by three times the standard deviation of baseline variance.
Micropipette aspiration during an AP. A hypodermic needle was used to make a small incision in the
cell wall cylinder of a plasmolysed Chara internode (26). The medium in the first compartment was
replaced with 150 mM KCl to facilitate membrane potential recording via the K+-anesthesia technique.
Glass pipettes were pulled to a needle tip (P-97 micropipette puller; Sutter Instrument, Novato, CA,
USA) and were broken after scoring with a second pipette to obtain a flat tip. The pipette was filled with
APW and was connected to a water column whose height was regulated by a micromanipulator. The
typical technical requirements and procedures for micropipette aspiration can be found in the literature
(33, 34). When aspirating the membrane of plasmolysed protoplasts, however, one deals with a less
defined cellular geometry. Oftentimes, the convoluted protoplast shapes made it difficult to observe the
region in which the aspiration pipette touched the cell membrane (because a lobe of protoplast obscured
the initial 10-50 µm of the pipette). In such cases, it was possible to reveal the membrane projection by
aspirating it beyond the overlapping region. However, this procedure prolonged the experiment and in
general required higher suction pressures. To ensure comparability of the results, we resorted to the
following procedure: Care was taken to find a position of the protoplast edge, at which the point of
contact between pipette and protoplast surface was directly observable. The pipette was slightly pressed
against the membrane and a suction pressure was applied. This pressure was insufficient 8 9 $% 9
$%+5( to aspirate a membrane projection that is longer than the pipette radius VWP XP ; 6(> '(=. The
negative pressure required to meet this condition was in the range of ~103-104 mN m-2 V'(!*8<EF=P<For
measurements of the membrane potential, a Ag/AgCl electrode was looped through the water column
into the pipette (PS-2132; 50Hz sample rate; PASCO scientific, Roseville, CA, USA).
Mechanical model of micropipette aspiration. Complex aspiration scenarios have been studied
previously (37, 52). However, these works were carried out in a different context, at a different regime
of the parameter space and did not directly focus on the question posed herein. During an AP, the
aspirated Chara cell does not reach a new stable mechanical state. Thus, our focus is only on identifying
the stability conditions for the weakly aspired state (zero aspiration). Such compromise allows the use
of a simplified spherical geometry. The model assumptions are: (i) only the simplest surface
contributions are considered: surface tension (") and the linear regime of the bending rigidity (:) (53).
(ii) At equilibrium, there are no internal flows in the bulk or along the surface; i.e., statics implies that
", :, and $% are constants‡. Their dependence on geometrical factors (e.g., surface area) was neglected,
because the focus was on the initiation of the instability and not on determining the final strongly-
‡ In principle, these parameters should be coupled to one another by a state equation.
aspirated state. (iii) A simplified geometry of a spherical cell was considered instead of the cell-wall-
bounded cylinder, because it allows a rather simple analytic expression of the energy function. The
simplification is reasonable because the cell volume is much larger than the aspirated segment, Y+3ZZ >
*8[Y
54(. The volume of the sphere was matched to that of a plasmolysed Chara cell by setting ' #
*8U'(, with '(#10 \m. The model geometry is depicted in Fig. 5, although not to scale (the pipette
radius is a hundred times smaller than the cell radius). (iv) Changes in cell volume during an AP were
neglected since ]^
^O*8,_ (25). (v) The pressure inside the pipette %( was assumed constant, %(#
G<HIJP
Figure 5. Geometry of the aspiration model (not to scale; in the calculations R/Rp~102).
The favorable shape was calculated by minimizing the elastic energy function
` # ab cd e:
&b &f Ucd e %b cY<<<V*=
with A, the surface area, H, the mean curvature of the surface and Y, the cell volume. For the
simplified geometry considered, the energy function is
` # "d e :g+02h e %/01Y4(ie %(Y
54( ) %jkY1/1P<<<V&=
The area and curvature contributions to the energy are respectively
d # &l'(
Ue &l'(6(e &l'U* e mno p ; VA=
g+02h # ql q * e mno p e 6(
'(
e q ; Vq=
with
ors p t '(
'P<<<<Vu=
The volume contribution is partitioned into Y4(i the volume of the part of the cell outside of the pipette
(shaded area in Fig. 4a), Y
54( the volume enclosed in the pipette, and Y1/1 # Y4(ie Y
54( (52).
Y4(i#&l
A'v* e mno p e l
A'(
U'mno p
Y
54( #&
Al'(
ve l'(
U
<<<VG=
The assumption of a constant cell volume simplifies the energy expression into
` # "d e :g+02h e.%Y4(ieTRwxy; z
with .% # %/01 ) %(.
Acknowledgements
We wish to thank K. Kaufmann for talks and personal discussions, which have inspired us to conduct
the present experiments. The interested reader is particularly encouraged to consult K. Kaufmann’s
writings from the 1980s. We also acknowledge discussions with S. Shrivastava and crafting of
measurement chambers by D. Campbell. CF is grateful for funding by the Max Kade Foundation
(http://maxkadefoundation.org/). MFS would like to acknowledge financial support by the German
Science Foundation (DFG) as well as the research unit SHENC.
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Supporting information
Supporting figures
Figure S1. Cell surface deflection during an action potential (AP). (a) Under control conditions
(no excitation of an AP) only a slight drift of the protoplast projection edge was observed. A
representative kymograph is shown. Vertical scale bar represents 10 µm. Average drift of projection
edge during 10 min ≪1µm (ntotal=134 experiments). (b) Upon propagation of an AP across the field of
view, the cell surface deflected. At random points on the protoplast, varying amplitudes and directions
of the displacement were observed (see kymographs). Horizontal and vertical scale bars apply to all
kymographs. The latter represents 10 µm. (c) Frequency histogram of maximal displacement of
projection edge during an AP (ntotal=135 experiments in 24 cells).
Figure S2. Pulse propagation velocities. Propagation velocity of action potentials in plasmolysed
Chara braunii internodal cell as calculated from electrical and mechanical component respectively.
The plotted values are averages (±standard deviation) of n=6-7 measurements per cell.
Figure S3. Irreversible membrane aspiration during an AP. An AP was excited under condition
Lp>0 where the membrane had initially been separated from the protoplast by aspiration (i.e. in the
unstable regime). (a) Recording of membrane potential (arrow indicates stimulus artifact). (b)
Concurrent with the depolarizing phase of the AP the aspirated membrane (m) deflected into the
pipette. Kymograph shown is a representative example. See text for detailed statistics. Scale bar
represents 10 µm.
Supporting movie legends
Video S1. Cell surface deflection during an action potential (AP). A typical plasmolysed Chara
cell. The protoplast appears as a dark tube within the cell wall cylinder. Upon stimulation of an AP (9
s mark; ~0.5 cm from observation site), a dynamic deflection of the cell surface occurs (arrows are
guides to the eye). Note: biphasic and reversible nature of displacement; transient stoppage of
cytoplasmic streaming during AP; field of view ~200 x 110 µm
Video S2. Close-up view of cell surface deflection during an AP. An AP is excited electrically (0.5
s mark; ~2 cm from the observation site). Note: biphasic and reversible nature of the displacement as
well as a slight lateral shift of the cell surface; video speed switches from real time to time lapse at 12
s mark; field of view ~35 x 35 µm.
Video S3. Micromechanical testing during an AP. A low suction pressure (insufficient to aspirate
the membrane) is applied to a Chara cell via a micropipette. This suction pressure is kept constant
during the time course of the experiment. When an AP is excited (2.5 s mark), the membrane
projection deflects into the pipette. Note: deflection is fully reversible; video speed switches from real
time to time lapse at 7 s mark; field of view: ~165 x 90 µm.
