Intramolecular dielectric screening in proteins.

This paper investigates the microscopic mechanisms of charge screening by proteins. For this purpose, we introduce the generalized susceptibility of a protein in response to a point charge, which is a scalar quantity dependent on position within the protein. The contribution to the susceptibility from atomic polarizabilities, associated with electronic degrees of freedom, is found to be highly uniform. By contrast, that from dynamic dipolar relaxation, associated with nuclear degrees of freedom, varies greatly between different regions of the protein. We investigate the possible rôle of this variation in the activity of proteins that interact functionally with charged species, and we formulate and test the hypothesis that this variation is correlated to functional activity. Model calculations give encouraging support to this hypothesis. The protein's dielectric properties are represented by a standard model in which electronic relaxation is described by a set of atomic polarizabilities, and dipolar relaxation is treated as a perturbation to normal mode dynamics. The model yields the desired susceptibility in closed form. Its obvious limitations are discussed. It is applied to several test systems, and is compared to various continuum models. Four model alpha-helices are considered, three of which play a rôle in vivo in the binding of charged ligands. We show that the intramolecular screening, and its spatial variation, can indeed play a part in this binding. The electron transfer between ferri- and ferrocytochrome c is considered. The dielectric relaxation of each molecule, associated respectively with its oxidation or its reduction, is known to be directly related to the activation free energy for the electron transfer reaction. Our analysis of the dielectric susceptibility will thus permit an estimate of this activation free energy. We show that the relaxation of the atomic positions ("dipolar relaxation") contributes 1 kcal/mol to this activation free energy, and that the molecule achieves this low value by providing a low dipolar susceptibility throughout its central part. In this case, the spatial variation of the susceptibility has a clear functional rôle.