Models of Membrane Electrostatics

TL;DR

This paper derives formulas for electrostatic potentials near membranes modeled as dielectric slabs, enabling more accurate ion distribution calculations in biological systems compared to traditional Poisson-Boltzmann approaches.

Contribution

It introduces new analytical formulas for membrane electrostatics that improve the accuracy of ion distribution modeling in computational simulations.

Findings

Formulas for electrostatic potential near dielectric slabs

Analysis of ion distributions near charged membranes

Impact of phosphate head groups on membrane electrostatics

Abstract

I derive formulas for the electrostatic potential of a charge in or near a membrane modeled as one or more dielectric slabs lying between two semi-infinite dielectrics. One can use these formulas in Monte Carlo codes to compute the distribution of ions near cell membranes more accurately than by using Poisson-Boltzmann theory or its linearized version. Here I use them to discuss the electric field of a uniformly charged membrane, the image charges of an ion, the distribution of salt ions near a charged membrane, the energy of a zwitterion near a lipid slab, and the effect of including the phosphate head groups as thin layers of high electric permittivity.