Electrostatic forces on charged surfaces of bilayer lipid membranes

TL;DR

This paper develops a continuum model to accurately compute electrostatic forces on charged bilayer lipid membranes, essential for understanding protein-membrane interactions in biological systems.

Contribution

It introduces a new electrostatic energy functional and applies shape calculus to derive forces, advancing the modeling of membrane electrostatics.

Findings

Electrostatic forces can be computed as shape derivatives of the energy functional.

The model accounts for continuous charge distributions on membrane surfaces.

The approach enables more accurate simulations of protein-membrane interactions.

Abstract

Simulating protein-membrane interactions is an important and dynamic area of research. A proper definition of electrostatic forces on membrane surfaces is necessary for developing electromechanical models of protein-membrane interactions. Here we modeled the bilayer membrane as a continuum with general continuous distributions of lipids charges on membrane surfaces. A new electrostatic potential energy functional was then defined for this solvated protein-membrane system. We investigated the geometrical transformation properties of the membrane surfaces under a smooth velocity field. These properties allows us to apply the Hadamard-Zolesio structure theorem, and the electrostatic forces on membrane surfaces can be computed as the shape derivative of the electrostatic energy functional.