Simple dielectric image charge models for electrostatic interactions in metalloproteins

Abstract

An investigation has been made of the electrostatic potential from an excess point charge near dielectric interfaces by the method of image charges. Two configurations were considered: one is a planar slab of low constant dielectric permittivity enclosed between two infinite regions of larger constant dielectric permittivity, and the other is a dielectric sphere of low constant dielectric permittivity embedded in an infinite region of larger constant dielectric permittivity. The systems are representative of charges near bilayer membranes and globular proteins, respectively. The potentials reduce to simple analytical forms in these configurations. The notion of an ‘effective dielectric permittivity’ εeff is useful, with characteristic distance and orientation dependence caused by the image charge distributions. εeff extends from values between the two constant intrinsic dielectric permittivities, but always larger than the lower of the two, to values which exceed significantly the value in the embedding regions. The spherical model has been compared with observed electrostatic effects in cytochrome c 551, azurin and plastocyanin. The effects refer to reduction potential changes caused by deprotonation, pK a in different oxidation states, charged residue replacement, and the effects of charged inhibitor molecules. Conformational changes are insignificant in these cases. The observable quantities mostly are reproduced well by the simple analytical potential form, pointing to the ready applicability of such models, supplementary to detailed numerical procedures.