Applying a potential across a biomembrane: electrostatic contribution to the bending rigidity and membrane instability

TL;DR

This paper explores how an external electric potential influences the mechanical properties of biomembranes, revealing that it can alter tension and rigidity, potentially causing instabilities depending on the electrostatic screening and dielectric conditions.

Contribution

It provides explicit formulas for electrostatic effects on membrane tension and bending rigidity, considering different electrostatic regimes and dielectric contrasts, which advances understanding of membrane electro-mechanics.

Findings

Electrostatic potential decreases membrane tension and increases bending rigidity in the short-range screening limit.

Large voltages can induce membrane stretching instability due to negative tension contributions.

Dielectric contrasts can lead to membrane undulation instability through long-range electrostatic interactions.

Abstract

We investigate the effect on biomembrane mechanical properties due to the presence an external potential for a non-conductive non-compressible membrane surrounded by different electrolytes. By solving the Debye-Huckel and Laplace equations for the electrostatic potential and using the relevant stress-tensor we find: in (1.) the small screening length limit, where the Debye screening length is smaller than the distance between the electrodes, the screening certifies that all electrostatic interactions are short-range and the major effect of the applied potential is to decrease the membrane tension and increase the bending rigidity; explicit expressions for electrostatic contribution to the tension and bending rigidity are derived as a function of the applied potential, the Debye screening lengths and the dielectric constants of the membrane and the solvents. For sufficiently large voltages the negative contribution to the tension is expected to cause a membrane stretching instability. For (2.) the dielectric limit, i.e. no salt (and small wavevectors compared to the distance between the electrodes), when the dielectric constant on the two sides are different the applied potential induces an effective (unscreened) membrane charge density, whose long-range interaction is expected to lead to a membrane undulation instability.