Electromechanical modeling of the transmembrane potential-dependent cell membrane capacitance

Abstract

The cell membrane experiences deformation and poration due to electrical stress. In this Letter, we develop continuum simulations of the capacitance-transmembrane potential (TMP) characteristics of the cell membrane. The electromechanical properties of biological cells are gaining increasing visibility so that the utility of numerical models should not be underestimated as a means to check and vet experimental analysis. While several early experiments with solvent-containing bilayers have demonstrated a nonlinear electric field dependence of the capacitance of artificial bilayer membranes, it is noteworthy that the TMP dependence of the membrane capacitance and resistance is not commonly reported in the computational literature. We consider both nonuniform tension and compression of the membrane to determine the anisotropic variation of its thickness, which depends on TMP and Young modulus. The membrane capacitance per unit area of the order of 10−2 Fm−2 and the areal membrane resistance of the order of 10−2 Ω m2 can be explained by the core (cytoplasm)-shell (membrane) structure of the cell. Our results show that a quadratic dependence of membrane capacitance and conductance captures the impact of the strain state under electric field excitation. We, furthermore, discuss the different degrees of influence on membrane capacitance and resistance that different structural parameters (cell aspect ratio, membrane thickness, and surface area) have. The method presented here provides a path forward toward exploring different core-shell models of biological cells in order to optimize cell electrodeformation and electroporation.