Cell Surface Deformation during an Action Potential

Abstract

The excitation of many cells and tissues is associated with cell mechanical changes. The evidence presented herein corroborates that single cells deform during an action potential. 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 action potential. The mechanical pulse: 1) propagates with the same velocity as the electrical pulse (within experimental accuracy, ∼10 mm s⁻¹), 2) is reversible, 3) in most cases is of biphasic nature (109 out of 152 experiments), and 4) is 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.

Introduction

Action potentials (APs) 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 a purely electrical nature. The mathematical description of APs was based on the view that the excitable membrane can be fully represented by an equivalent circuit (1). However, this approach has come under criticism. The debate has been stirred up by Tasaki (2, 3, 4, 5, 6, 7, 8, 9, 10) and has been extended mainly through the works of Kaufmann (11, 12) and Heimburg and Jackson (13, 14). One of the central points of criticism of the electrical framework is that it neither contains nor predicts nonelectrical manifestations of the AP. These pulse components, however, exist and include optical (2), thermal (15), magnetic (16), and mechanical (3, 4, 5, 6, 17) changes at the cell surface. The latter have been studied with a variety of highly sensitive techniques (piezoelectric benders, interferometry, AFM). The inherently soft nature of nervous tissue preparations combined with the sheer minuteness of the movements posed difficulties and led to varying results (3, 4, 5, 17, 18). Nevertheless, more recent studies are widely in agreement and indicate that the mechanical pulse in cylindrical axons consists of either expansion (18) or expansion followed by contraction (∼1–10 nm) (10, 19, 20). In parallel, there exists a biphasic intracellular pressure wave (19). 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 most prominently in muscle cells (21) but also during spreading depression waves in cortical tissue (22). It must be of central interest to investigate whether these phenomena have the same underlying mechanism.

Although 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 (7). 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. Intracellular material, such as the cortical cytoskeleton, could have a similar effect (19). Thus, the actual mechanical changes during an AP may be larger than anticipated. It is important to resolve this question, because the magnitude of the displacement allows conclusions about the underlying electro-mechanical coupling mechanism. Suggested mechanisms include a rotation of phospholipids (11), a thickness change of the cell membrane during an order transition (14, 23), a phase transition in the ectoplasm (8), and capacitance changes (19). 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 longstanding history in excitable cell research (24, 25). In Charophytes, comparatively large radial and axial deformations have been reported during an AP (∼100 nm (4, 26)). 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 can be attributed to reversible changes in three mechanical properties of the cell surface (transmembrane pressure, surface tension, bending rigidity).

Materials and Methods

Materials

All reagents were purchased from Sigma-Aldrich (St. Louis, MO) and were of analytical purity (≥99%). Glass capillaries were obtained from Sutter Instrument (Novato, CA).

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 (14 W, Flora Sun Max Plant Growth; Zoo Med Laboratories, San Luis Obispo, CA) at a 14:10 light/dark cycle at room temperature (∼20°C). Before 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 × 5 × 10 mm; h × w × 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, Midland, MI). 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 (model No. 33250A; Agilent, Santa Clara, CA) in combination with a stimulus isolation unit (SIU5; Grass Technologies, Warwick, RI) 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 was extracted from every frame of the video recordings (framerate: 10–40 s⁻¹) and was assembled in the software ImageJ (V.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. 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 (model No. IX71; Olympus, Melville, NY). Thereby, it was possible to estimate the time difference between the membrane potential pulse and the mechanical displacement. The criterion for the time of arrival of a pulse at the measurement site was defined as a deviation of the signal from baseline by three times the spreading depression 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 plasmolyzed Chara internode (27). 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) 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. For measurements of the membrane potential, an Ag/AgCl electrode was looped through the water column into the aspiration pipette (PS-2132, 50 Hz sample rate; PASCO Scientific, Roseville, CA). The typical technical requirements and procedures for micropipette aspiration can be found in the literature (28, 29). When aspirating the membrane of plasmolyzed protoplasts, one deals with a comparatively irregular cellular geometry. 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 at 0 < Δp < Δp_cap to aspirate a membrane projection that is longer than the pipette radius (i.e., L_p > R_p). The negative pressure required to meet this condition was in the range of ∼10³–10⁴ mN m⁻² (R_p ∼ 10 μm). The system was allowed to equilibrate for several 10s of seconds. Subsequently, two spatially distant electrodes (several millimeters to a centimeter away) were used to trigger an action potential that propagated past the aspiration site.

Mechanical model of micropipette aspiration

Complex aspiration scenarios have been studied previously (30, 31). However, these works were carried out in a different context, in 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: 1) only the simplest surface contributions are considered, i.e., surface tension (σ) and the linear regime of the bending rigidity (κ) (32). Although we have focused here on the simplest elastic description of a cell surface, additional parameters may also change during an AP (e.g., spontaneous curvature, in-plane shear rigidity, and surface compressibility). It may be worthwhile to investigate a more elaborate model of cell surface elasticity in future work. 2) At equilibrium, there are no internal flows in the bulk or along the surface; i.e., statics implies that σ, κ, and Δp are constants. In principle, these parameters should be coupled to one another by a state equation. 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 aspirated state. 3) 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, V_cell > 10⁶ V_asp. The volume of the sphere was matched to that of a plasmolyzed Chara cell by setting R = 10² R_p, with R_p = 10 μm. The model geometry is depicted in Fig. 1, although not to scale (the pipette radius is 100-times smaller than the cell radius). 4) Changes in cell volume during an AP were assumed to be negligible because ΔV/V ∼ 10⁻⁴ (33). 5) The pressure inside the pipette p_p was assumed constant. The favorable shape was calculated by minimizing the elastic energy function

$$E=\mathit{\sigma }\int dA+\frac{\kappa }{2}{\int \left(2H\right)}^{2}dA+p\int dV,$$ (1)

where A is the surface area, H is the mean curvature of the surface, and V is the cell volume. For the simplified geometry considered, the energy function is

$$E=\mathit{\sigma }A+\kappa g_{\text{curv}}+p_{\text{out}}{V}_{\text{sph}}+p_p{V}_{\text{asp}}-p_{\text{in}}{V}_{\text{tot}}.$$ (2)

The area and curvature contributions to the energy are, respectively,

$$A=2\pi R_p^2+2\pi R_p{L}_p+2\pi R^2\left[1+\text{cos}\left(\alpha \right)\right],$$ (3)

$$g_{\text{curv}}=4\pi \left\{4\left[1+\text{cos}\left(\alpha \right)\right]+\frac{L_p}{R_p}+4\right\},$$ (4)

with

$$\text{sin}\left(\alpha \right)\equiv \frac{R_p}{R}.$$ (5)

The volume contribution is partitioned into V_sph as the volume of the part of the cell outside of the pipette (shaded area in Fig. 1), V_asp as the volume enclosed in the pipette, and V_tot = V_sph + V_asp (31):

$$\begin{array}{l}{V}_{\text{sph}}=\frac{2\pi }{3}{R}^3\left[1+\text{cos}\left(\alpha \right)\right]+\frac{\pi }{3}{R}_p^{2}R\text{cos}\left(\alpha \right),\hfill \\ V_{\text{asp}}=\frac{2}{3}\pi R_p^3+\pi R_p^2.\hfill \end{array}$$ (6)

The assumption of a constant cell volume simplifies the energy expression into

$$E=\sigma A+\kappa g_{\text{curv}}+\Delta p{V}_{\text{sph}}+\text{const,}$$ (7)

with Δp = p_out – p_p.

Figure 1.

Geometry of the aspiration model (not to scale; in the calculations R/R_p ∼ 10²). To see this figure in color, go online.

Results

Cell surface deformation 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 (33)) (Fig. 2 a). However, by increasing the extracellular osmolarity it was possible to progressively reduce turgor until the plasma membrane detached from the cellulose sheath—a process known as plasmolysis (Fig. 2 b) (27, 34). 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 plasmolyzed cell was irregularly wavy. As time progressed, the protoplast equilibrated, assumed an unduloidlike form, and eventually fragmented. This process was described previously (28) and resembled 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. Chara cells did not lose excitability in the course of plasmolysis. There were also no signs of variation potentials that have been observed in plants upon deleterious manipulations (35). 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. 2 b). In the absence of electrical stimulation, only minor drift of the edge was observed (Fig. S1). In contrast, a distinct surface displacement occurred upon excitation of an AP (in 142 out of 152 cases; N = 30 cells) (Fig. 2 c; Movies 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. 2 d; Movie S2). Such biphasic displacements have also been reported in fully turgid cells, albeit with 10–100× lower amplitudes (20). 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 discussed in a forthcoming article.

Figure 2.

Cell surface deflection during an 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 (42)). (b) When turgor was reduced by increasing the extracellular osmolarity, 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) Given here is the membrane potential pulse (black) and out-of-plane displacement of the cell surface (red); note: an initial inward movement is followed by expansion. To see this figure in color, go online.

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. 2 d). However, because 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 that allows for localized monitoring of the membrane state. In any case, it was evident that the mechanical deformation outlasted the electrical component (Fig. 2 c). The membrane potential pulse in a plasmolyzed 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 (20, 26). It is of interest to note that the first derivative of the displacement with respect to time (i.e., the out-of-plane velocity of the membrane) correlates fairly well with the membrane potential pulse (Fig. S3). This indicates that the two pulses are not independent phenomena.

Involvement of Ca²⁺ and actin-myosin-motility in surface displacement

Actin and myosin are present in Characean cells, where coherent sliding of myosin-coated organelles on actin filaments leads to directional streaming of the cytoplasm (velocities up to 100 μm s⁻¹) (36). During an AP, streaming is temporarily arrested (excitation-cessation-coupling) and recovers within several minutes. This resembles the relaxation timescales of the surface deformation as observed herein (see Fig. 2 and (20)). Thus, the cellular events that trigger stoppage of streaming (probably an increase of intracellular Ca²⁺ (37)) or a coincident process in the cytoskeleton may be involved in the observed deformations. We attempted to investigate these possibilities. It has been reported that membrane excitation can be uncoupled from the cessation of streaming by replacing extracellular Ca²⁺ with Mg²⁺ (38). This approach, however, was not feasible, because plasmolysis in the absence of Ca²⁺ led to rupture of the Chara cell membrane. Another technique that was proposed to uncouple membrane excitation from streaming in Nitella—addition of manganese chloride (5 mM) to the external medium (39)—was also not successful, as it led to spontaneous activity and deterioration of the cell. We finally attempted to gradually reduce the extracellular concentration of Ca²⁺ by addition of a chelating agent (EGTA, 0.1–2 mM). In this concentration range, the stoppage of cytoplasmic streaming during an AP persisted. Upon addition of increasing amounts of EGTA (10 mM), the membrane potential record started to fluctuate, streaming became irregular, and the cell exhibited signs of deterioration. The replacement of extracellular Ca²⁺ by other cations (Mg²⁺, Mn²⁺, Ba²⁺) was also studied with Nitella translucens, but it was not possible to achieve a plasmolyzed and excitable state.

In a subsequent series of experiments, cytochalasin D (CytD) was employed. Cytochalasins have been reported to uncouple membrane excitation and contraction in muscle cells (i.e., the membrane is excitable, but contractility is impaired (40)). These substances also interfere with and arrest cytoplasmic streaming by a presently unknown mechanism (41). Thus, we hypothesized 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, cytoplasmic streaming came to a halt but the cell remained excitable. This is analogous to the effects of CytD on muscle cells. When an AP was triggered under these conditions, the surface deformation of the Chara cell persisted (Fig. 3). The timescales of the deflection were similar and the amplitudes were slightly larger as compared to native cells. This is in contrast to the observation of diminished contractility of muscle cells upon addition of CytD (40). These results provide some indication that actin-myosin-motility may not be involved in the surface deformation during an AP in Chara.

Figure 3.

Effect of cytochalasin D on surface deflection during an AP. (Top) Shown here is the displacement of the cell surface upon excitation of an AP in artificial pond water (APW) and (bottom) in a different cell that had been incubated with APW + 50 μM cytochalasin D. (Arrow) Stimulus is indicated. 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 plasmolyzed Chara internode. Through this opening it was possible to directly access the cell surface (see Fig. 2 a and (42)). 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

$$\sigma =\Delta p{\left(\frac{2}{R_p}-\frac{1}{R_c}\right)}^{-1},$$

with Δp as the pressure difference between extracellular medium (p_out) and pipette (p_p), and R_c and R_p as the radii of the cell cylinder and the pipette, respectively (28). The cortical tension of the cell in the resting state σ_rest (i.e., before excitation) was determined from the pressure difference (Δp_cap) that is required to aspirate a membrane projection with length equal to the pipette radius (i.e., when a hemispherical membrane cap was aspirated (29)). In plasmolyzed Chara cells, σ_rest was 0.06 ± 0.01 mN m⁻¹ (n = 4 experiments in N = 3 cells; Δp ∼10 N m⁻², R_c ∼ 150 μm, R_p ∼ 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 (43)) and molluscan neurons (≈0.04 mN m⁻¹ (44)).

For aspiration experiments during an AP, the pipette touched the cell surface and a slight suction pressure was applied (0 < Δp < Δp_cap; see Fig. 4 and Materials and Methods for details). Once the position of the membrane projection at the pipette tip had remained relatively steady, an AP was induced several millimeters to centimeters away and propagated past the aspiration site. Although the pipette pressure was held constant, L_p increased upon arrival of the AP in all experiments conducted (n = 22, N = 9 cells; Fig. 4; Movie S3). In some cases, a short outward dip occurred before this movement (Fig. 4 d). The membrane projection either moved into the pipette irreversibly (Fig. S4) or reached a maximum and relaxed back to its initial position (Fig. 4 c; Movie S3). In general, reversibility prevailed (14 out of 22 cases). Because cell surface deflections in the absence of a pipette were reversible (Fig. 2), it seems likely that irreversibility was a concomitant of the aspiration procedure (30).

Figure 4.

Cell mechanical changes during an AP. (a) Shown here is 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 Movie S3). (b) During an AP, the membrane underwent a reversible cycle of motion into and out of the pipette at constant suction pressure. Aspirated membrane cap is indicated by a dashed arrow. (c) Suction pressure (Δp) before stimulation of an AP was clamped at 0 < Δp < Δp_cap (see text for definition of Δp_cap). Shown here is the membrane potential record (top) and aspirated length (L_p; bottom) during an AP. (d) Shown here is the initial phase of membrane motion into the 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. To see this figure in color, go online.

Mechanical analysis of micropipette aspiration during an AP

In a typical aspiration experiment, the surface forces, which consist of the surface tension σ and the bending rigidity κ, balance the pressure difference between the extracellular medium and the interior of the pipette (Δp). This triplet of surface properties (Δp, σ, κ) represents the mechanical state of the system in a 3D-phase space. The 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. 4). This was achieved by calculating the aspiration length (L_p) that minimizes the elastic energy of the cell surface for different values of the mechanical parameters (for details, see Eq. 7). An example of the energy as a function of L_p is provided for three values of the surface tension with the other parameters (Δp and κ) held constant (Fig. 5 a). This graph demonstrates the existence of a critical value of σ, which flattens the energy function. From there, an increase of surface tension stabilizes the weakly aspirated state (L_p = 0), whereas a decrease of σ leads to an instability; i.e., L_p increases with time, which means that the cell is aspirated into the pipette.

Figure 5.

(a) The energy E as a function of aspiration length L_p for three values of the surface tension reveal that the weakly aspired state (L_p = 0) can be stable, critical, or unstable. Other parameters were held constant: κ = 10⁻¹⁹ J, Δp = 3N/m², R_p = 10 μm. For convenience, the energy was scaled to zero at an aspiration length of zero (L_p = 0). In addition, it was normalized by the mean thermal energy at room temperature (20°C), to indicate that the elastic energy stored in the surface is considerably larger. (b) Shown here is the instability line in the Δp−σ phase space. Weakly aspirated states are located below the line. The estimated resting state of the cell is depicted by the gray ellipse (its width reflects the experimental error in the measurement of σ_rest, whereas its height reflects the experimental error in the aspiration pressure that sets the weakly aspirated state). Decreasing κ effectively shifts the instability line in the direction of the arrow. The three states studied in (a) are depicted as small diamonds in (b).

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 (29). A 2D slice in the Δp−σ plane of the phase-space is depicted in Fig. 5 b. Weakly aspirated states are stable below the instability line (dashed line). The estimated resting state of a plasmolyzed Chara cell is located in this regime and is marked by a gray ellipse. A transition across the line into the unstable regime (from stable L_p = 0 to L_p > 0) can be induced, for example, by increasing Δp by ∼5 N m⁻², decreasing σ by ∼50%, or decreasing κ 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. 4 d) can be induced by a parameter change with opposite directionality (i.e., a decrease in Δp or an increase in σ or κ). These findings are in line with a more elaborate calculation conducted for a different domain of the parameter space (30).

Discussion

It has been documented by several independent investigators that excitation of cells and tissues is accompanied by a deformation. Mechanical pulses with micrometer amplitudes have been reported in myocytes (1) and during spreading depression waves (22). During an AP in single axons, the deformations are typically on the scale of 1–10 nm (10, 18, 19), whereas in fully turgid Charophytes they reach ∼100 nm (4, 20). Herein, it was demonstrated that sheathing material may attenuate these motions. When the plasma membrane of a Chara cell was separated from the rigid external cell wall, considerably larger biphasic displacements were observed (1–10 μm compared to ∼100 nm; Fig. 2). An obvious difference as compared to axons is that membrane potential and displacement are not in phase (Fig. 2 d; (20) as compared to (18, 19)). In Chara internodes, the derivative of displacement roughly correlates with voltage (Fig. S3).

On the relation between the electrical and mechanical events

There are at least three possible relations between the membrane potential pulse and the cellular deformation: 1) the mechanical and electrical components belong to the same phenomenon (i.e., one observes two aspects of the action potential). An objection to this viewpoint comes from the different behavior in time of membrane potential and the surface deformation. In Chara, the cell surface recovers its shape on timescales that are roughly an order-of-magnitude longer than the membrane potential pulse (30–300 s vs. 5–10 s). A difference in time course, however, does not necessarily mean that one deals with decoupled phenomena. Such behavior of variables is common, for example, in coupled differential equations. The mechanical relaxation time agrees fairly well with the duration of the relative refractory period (>60 s at room temperature (45)). Thus, it could be that the mechanical observable reflects state changes of the excitable medium in a more direct manner as compared to the electrical one. This first option will be falsified if the same deformation can be induced in absence of an AP. 2) The cell surface deformation is an independent phenomenon triggered by the AP. This is equivalent to the view of excitation-contraction coupling in muscle cells. There, an AP at the plasma membrane is believed to trigger cellular shortening via a process that involves intracellular polymers (1). This shortening lags behind and outlasts the electrical pulse (21). Similarly, an AP in Chara couples to an intracellular process based on actin/myosin (cytoplasmic streaming). The recovery time of streaming (several minutes (36)) also outlasts the membrane potential pulse. This second option will be falsified, if the deformation persists upon removal of intracellular filaments (e.g., by intracellular perfusion (19)). 3) A third alternative is that the cell surface deformation consists of two mechanical components (one being the mechanical aspect of an AP and an additional triggered component). In the following, potential mechanisms that could underlie the cellular deformation are discussed.

Potential involvement of Ca²⁺ and cytoskeleton in cell surface deformation

An increase in the intracellular Ca²⁺ concentration has been implicated in many cellular events such as the stoppage of cytoplasmic streaming in Charophytes, muscle contraction, etc. It has been argued that the stoppage of cytoplasmic streaming during an AP in Nitella can be eliminated by various protocols that reduce the concentration of Ca²⁺ in the extracellular medium (38, 39, 46). By using these techniques, it should have been possible to investigate the role of Ca²⁺ influx in the cellular deformation. However, it was found herein and by others that these techniques cannot be readily applied to all Chara and Nitella cells (39, 46).

Cytoskeletal motility as in muscle cells is probably not involved in the cell mechanical changes in Chara. Cytochalasin D interferes with contractility in muscle (40) and inhibits actin-myosin based streaming in Chara (41). The cell surface deformation, however, persisted in presence of this substance (Fig. 3). Still, the role of cytoskeletal filaments (e.g., by polymerization/depolymerization, etc.) in the mechanical events warrants further investigations.

Cell surface deformation due to a change in transmembrane pressure

Significant transmembrane pressure deviations should only arise if the chemical potential of water in the intra- or extracellular space is altered. A chemical potential difference will be equilibrated by transfer of water (i.e., osmosis) if the membrane is sufficiently permeable. In the classical theory of excitability, transmembrane flux of ions is a central premise. Therefore, cell surface displacements in neurons and plant cells have usually been interpreted as cell volume changes based on osmosis (20, 47). In nerve fibers, transmembrane flux of ions was estimated from radiotracer studies to be on the order of 10⁻¹¹ mol cm⁻² impulse⁻¹ (1, 7). In Chara, an influx of Ca²⁺ and an efflux of Cl⁻ and K⁺ occurs during an action potential. The influx of Ca²⁺ (∼4⋅10⁻¹⁴ mol cm⁻² impulse⁻¹) (37) is believed to be orders-of-magnitude smaller as compared to the efflux of Cl⁻ and K⁺ (∼4⋅10⁻⁹ mol cm⁻² impulse⁻¹) (48). The main consequence of these events in Chara should be an increase in extracellular osmolarity during an AP. This is equivalent to an increase in extracellular pressure (p_out). The cell could deform as a consequence of this transmembrane pressure difference. If the chemical potential difference for water is equilibrated by efflux from the cell, the pressure difference will decrease and in parallel to this, the cellular volume will be reduced.

Although a chemical potential difference for water could underlie the cellular deformations as observed herein, we deem it necessary to point out open problems. In the simplest case, i.e., if the cell membrane is highly permeable to water and if no significant transmembrane pressure acts on the surface (47), one expects uniform shrinkage. Experimentally, however, inward as well as outward deflections of the cell surface were observed (Fig. S1). This indicates that a more comprehensive consideration of cellular geometry and of the mechanical forces that govern the surface is required. Another open problem regarding an ion-based mechanism of the deformation in excitable cells emerged from voltage-clamp experiments (19). Ionic currents are low during hyperpolarization (∼30 μA cm⁻²) and high during depolarization (∼1 mA cm⁻²) (49), yet larger displacements were found during hyperpolarization of squid axons (19).

Finally, it must be emphasized that an osmotic mechanism implies a change in cell volume. To the best of our knowledge, there is little evidence that corroborates that this is the case. One study with Charophytes has indicated that volume decreases slightly during an AP (33). However, more experimental evidence, in particular from neuronal preparations, is required. It has to be kept in mind that cellular deformations can also occur at constant volume. As an analogy, one may imagine a droplet of water sitting on a surface. The droplet will deform at constant volume if, for instance, its surface tension is changed by addition of a small amount of surfactant.

Cell surface displacements due to changes in surface tension and/or bending rigidity

It was proposed by Kaufmann (11, 12) and more recently by Heimburg and Jackson (13, 14) that an AP is a propagating change of state in the quasi 2D 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, it was indeed demonstrated that linear (50) as well as nonlinear, self-stabilizing pulses (solitary waves) (51, 52) can be excited in lipid monolayers—the simplest model system of a cell membrane. These pulses manifest in all thermodynamic variables (e.g., electrical, thermal, optical, etc.) (53, 54, 55). This is also the case for APs (1, 2, 10, 15, 19). 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 mechanical changes during an AP in Chara (Figs. 2, 3, and 4) may be the consequence of pulse-associated changes in σ and/or κ of the excitable medium. For an acoustic pulse in a 2D continuum, a biphasic response is expected because of mass conservation (11). The analysis presented here of micropipette aspiration results suggests that the observed phenomenology (Fig. 4) could be explained by a decrease in surface tension (by ∼50%) and/or bending rigidity (by ∼2 orders). Such changes are large but not entirely unrealistic, as a decrease in surface tension by ∼10% was demonstrated in lipid monolayer pulses (50), and during phase transitions in lipid bilayers, κ can be reduced by 1–2 orders of magnitude (56). For most state changes, however, σ and κ will change simultaneously. For example, when a fluid lipid membrane is compressed isothermally into the phase transition regime, the lateral pressure as well as κ increase. Finally, the permeability of a membrane depends on its thermodynamic state and thus any state change, whether induced isothermally or adiabatically, will lead to the realization of a different permeability (57). Thus, a propagating state change in the plasma membrane could entail transmembrane transport phenomena.

Conclusions

This work demonstrated that an AP is associated with a significant surface deformation (∼1–10 μm) in plasmolyzed Chara cells. This deformation copropagates with the electrical signal, is biphasic (72% of cases), and is reversible. Due to the magnitude of the displacements as well as the slow timescales of the pulse, this preparation is well suited to study cell mechanical changes during excitation. Falsifiable predictions were made concerning the surface property changes (p_out, σ, κ) that may be involved. Future work should aim at understanding the coupling between the electrical and the mechanical pulse in Charophytes and neurons. It will be of central interest if cellular deformations in myocytes, axons, excitable plant cells, and cortical tissue can be explained by a common mechanism.

Author Contributions

C.F., M.M., and M.F.S. designed research. C.F. and J.M. contributed experimental data. C.F., M.M., and J.M. analyzed data. C.F., M.M., and M.F.S. wrote the manuscript.

Editor: Valentin Nagerl.

Supporting Material

Movie S1. Cell Surface Deflection during an AP

A typical plasmolyzed 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 × 110 μm.

Movie S2. Closeup 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 × 35 μm.

Movie 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 × 90 μm.