Dielectric permittivity of a lipid bilayer: Theory and simulations

Lipid bilayer membranes are an essential component of biological cells: they are barriers regulating the passage of ions and molecules, and platforms for biochemical reactions. Lipid molecules have large dipole moments, such that external electric fields (1) affect the energetics of lipid–lipid and lipid–water interactions and (2) cause out-of-plane membrane shape displacements. Moreover, the dipole moment in a lipid molecule predominantly lies parallel to the membrane surface—for which the dielectric permittivity is an anisotropic tensor. In this work, we present a theory relating the microscopic fluctuations in lipid dipole moments to the macroscopic dielectric constant, all in the context of a polarizable microscopic system. We then run polarizable molecular dynamics simulations, and apply our theory to extract the tensorial dielectric constant. Our framework addresses the limitations of existing theories, which primarily describe non-polarizable systems, and can be extended to determine electromechanical coefficients from simulations.