Surface deformation during an action potential in pearled cells

Electric pulses in biological cells (action potentials) have been reported to be accompanied by a propagating cell-surface deformation with a nanoscale amplitude. Typically, this cell surface is covered by external layers of polymer material (extracellular matrix, cell wall material, etc.). It was recently demonstrated in excitable plant cells (Chara braunii) that the rigid external layer (cell wall) hinders the underlying deformation. When the cell membrane was separated from the cell wall by osmosis, a mechanical deformation, in the micrometer range, was observed upon excitation of the cell. The underlying mechanism of this mechanical pulse has, to date, remained elusive. Herein we report that Chara cells can undergo a pearling instability, and when the pearled fragments were excited even larger and more regular cell shape changes were observed ($\sim 10–100\mu \mathrm{m}$ in amplitude). These transient cellular deformations were captured by a curvature model that is based on three parameters: surface tension, bending rigidity, and pressure difference across the surface. In this paper these parameters are extracted by curve-fitting to the experimental cellular shapes at rest and during excitation. This is a necessary step to identify the mechanical parameters that change during an action potential.

Figure 1

Illustration of (a) fully turgid, (b) slightly plasmolyzed, and (c) pearled internodal Chara cell. Dashed line represents the cell wall. Solid line represents the cell membrane. (d) Image of pearled Chara fragment. Arrow indicates location of tether. (e) Membrane potential pulse (upper) and out-of-plane displacement of a point on the cell surface close to the tether (lower). Arrow marks time point of stimulation. A close-up of the tether region (f) before stimulation, and (g) at the peak of the surface deformation.

Figure 2

(a) Traces of the cell surface before ($t=0$) and during various stages of an AP. Inset demonstrates an inward displacement near the cell wall. Cell radius is $r_{\max }=330\mu \mathrm{m}$. (b) Illustration of the fixed circle (collection of points on the surface that do not move during a deformation) that separates the hemispherical cap into two parts: one which moves outward (frontal) and one which moves inward (rear). Four small arrows indicate the respective direction of deformation.

Figure 3

Total (a) volume and (b) area of the hemispherical cap as a function of time (solid line), upon excitation of an AP at $t=0$. Values were normalized by the resting state value ($t=0$). Volume and area were also calculated separately for the frontal (dashed line) and rear (dashed-dotted line) parts of the hemispherical cap [see Fig. 2].

Figure 4

Parametrization of the surface curve.

Figure 5

(a) Experimental traces of the hemispherical cap, before stimulation (solid black line) and at the peak of the deformation during an AP (dashed black line). These are compared with solutions of the Zhong-Can–Helfrich equation (solid and dashed gray lines, respectively). Parameters of the curved solutions are given in Ref. [32]. (b) Multiple parameter combinations which led to a good fit of the experimental shapes are plotted in phase space. The four areas correspond to successful fits to the four contours shown in Fig. 2 [error function $<1.5\times {10}^{-4}$, Eq. (9)].