A Poisson-Boltzmann approach for a lipid membrane in an electric field

TL;DR

This paper presents a theoretical analysis of lipid membrane behavior in an electrolyte under a static electric field using the nonlinear Poisson-Boltzmann framework, revealing voltage-dependent electrostatic effects on membrane elasticity.

Contribution

It introduces a nonlinear Poisson-Boltzmann model to analyze electrostatic effects on membrane elastic moduli under high voltage conditions.

Findings

Electrostatic surface tension crosses over from quadratic to linear voltage dependence at low salt.

Membrane bending modulus saturates at high voltages due to Debye layer effects.

Membrane instability persists at high voltages despite nonlinear electrostatic corrections.

Abstract

The behavior of a non-conductive quasi-planar lipid membrane in an electrolyte and in a static (DC) electric field is investigated theoretically in the nonlinear (Poisson-Boltzmann) regime. Electrostatic effects due to charges in the membrane lipids and in the double layers lead to corrections to the membrane elastic moduli which are analyzed here. We show that, especially in the low salt limit, i) the electrostatic contribution to the membrane's surface tension due to the Debye layers crosses over from a quadratic behavior in the externally applied voltage to a linear voltage regime. ii) the contribution to the membrane's bending modulus due to the Debye layers saturates for high voltages. Nevertheless, the membrane undulation instability due to an effectively negative surface tension as predicted by linear Debye-H\"uckel theory is shown to persist in the nonlinear, high voltage regime.