A model of a local dielectric constant in proteins

Abstract

A model for the calculation of the scalar, position-dependent static dielectric function of an ensemble consisting of polarizable sites and of free relaxing point dipoles at fixed positions is proposed. It is based on classical electrostatics and leads to an iteration equation or nonlinear partial differential equation for the local dielectric constant. The expressions contain the equations of Debye, Onsager, and Neumann as special cases and thus might be considered as an extension to inhomogeneous matter. The model may have applications in the case of biological macromolecules in particular proteins where the polar side chains can be identified with the model’s dipoles. The algorithm leads to a position dependent dielectric constant in the protein interior in contrast to the assumption of a homogeneous permittivity throughout the protein. By taking into account the dielectric fine structure inside the macromolecules we hope that our approach may help to improve continuum electrostatic models of these molecules. The relevant polarizabilities and dipole moments of the amino acids are given and their corresponding local dielectric constants are estimated as a first approximation based on the Onsager and Kirkwood equations.