Three-slab model for the dielectric permittivity of a lipid bilayer

Abstract

A model for the tensorial dielectric permittivity of phospholipid membranes is presented here. The four-nanometer-thick membrane is treated as a composite made up of three dielectric slabs: one for each of the two phospholipid head-group regions, and one for the entire domain spanned by the lipid tails. Equal and opposite bound surface charge densities surround each head-group slab, and account for the membrane dipole potential. Three-slab model parameters are obtained from molecular dynamics simulations, and capture both the zero-field electric potential and the membrane response to applied electric fields. The tail region is well-approximated as having vacuum permittivity, while the head-group region is highly anisotropic due to the configurations of molecular dipoles. For the bilayers studied, the out-of-plane permittivity of the head-group region is 10--15 times that of the vacuum, while the in-plane permittivity is an order of magnitude larger. Membrane responses to applied electric fields up to 30 millivolts per nanometer are found to be in the linear regime. The model overcomes a fundamental limitation of microscopic theories---where the out-of-plane permittivity lacks a meaningful continuum interpretation in the head-group region due to large gradients in the local electric field---by averaging over slab widths, thereby introducing new length scales. Our approach can be extended to characterize general interfacial systems with similar microscopic permittivities.