Electrostatic Forces on Charged Surfaces of Bilayer Lipid Membranes

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 model the bilayer membrane as a continuum with general continuous distributions of lipids charges on membrane surfaces. A new electrostatic potential energy functional is then defined for this solvated protein-membrane system. Key geometrical transformation properties of the membrane surfaces under a smooth velocity field allow us to apply the Hadamard-Zolésio structure theorem, and the electrostatic forces on membrane surfaces can be computed as the shape derivative of the electrostatic energy functional.