Calculation of the dielectric permittivity profile for a nonuniform system: Application to a lipid bilayer simulation

We derive an expression relating the static dielectric permittivity profile for a system nonuniform in one dimension to correlations between the net system dipole moment and the local polarization density. The permittivity profile of a dipalmitoylphosphatidylcholine (DPPC) lipid bilayer in water is calculated from an all-atom 20-ns molecular dynamics simulation. The component of the permittivity parallel to the bilayer shows a nonmonotonic decrease from the value in bulk water to the value in the membrane interior; the interfacial region itself has a very large permittivity, greater than that of bulk water. In high-dielectric regions, obtaining a quantitative estimate of the component normal to the bilayer is not possible because of large numerical uncertainty. However, the calculated correlation function is consistent with a value for the interface at least as large as that of bulk water. In general, the transition to a low-dielectric environment is sharp and is located on the inner border of the region where there is significant probability of finding the polar head groups.