Thickness effects in the electromechanical stability of charged biological membranes

TL;DR

This paper develops a comprehensive theoretical framework to understand how finite thickness, surface charge, and electrohydrodynamics influence the stability of charged biological membranes under electric fields, unifying previous models and revealing new stabilization mechanisms.

Contribution

It introduces a unified, dimension-reduction theory that incorporates finite membrane thickness, surface charge, and electrohydrodynamics, providing new insights into membrane stability and electroporation thresholds.

Findings

Finite-thickness effects dominate electrostatic corrections at physiological conditions.

Surface charges can stabilize membranes and alter electroporation thresholds.

The theory generalizes and unifies previous models as limiting cases.

Abstract

Understanding how electric fields destabilize biological membranes is important for electroporation-based technologies and bioelectronic interfaces. However, theoretical descriptions of this phenomenon remain fragmented. Existing theories treat either electrostatics in membranes of finite thickness or electrohydrodynamic flows at idealized zero-thickness interfaces, leaving unresolved a unified description that simultaneously incorporates finite membrane thickness, surface charge, and bulk electrohydrodynamics. Here, we apply a recently-developed, dimension-reduction framework that captures the coupled electrohydrodynamic and mechanical effects governing height fluctuations of a charged lipid bilayer of thickness $\delta$ in an electrolyte characterized by Debye screening length $\lambda$. We derive voltage- and charge-dependent renormalizations of the effective surface tension and bending rigidity, along with a dispersion relation governing undulatory instabilities. A wide range of prior theoretical results arise as limiting cases of our more general theory when finite-thickness effects are neglected or screening is asymptotically strong. The key new contribution arises from traction moments generated across the finite membrane thickness, which are absent in zero-thickness descriptions. Under physiological screening ($\delta/\lambda\sim 4$), these contributions account for more than $>70\%$ of the total electrostatic correction to both surface tension and bending rigidity. The theory further reveals that surface charges can stabilize the membrane at physiological ionic strengths, increasing the effective tension and shifting electroporation thresholds in a manner that depends on charge asymmetry between the leaflets.