A "parallel plate" electrostatic model for bimolecular rate constants applied to electron transfer proteins

Abstract

A "parallel plate" model describing the electrostatic potential energy of protein-protein interactions is presented that provides an analytical representation of the effect of ionic strength on a biomolecular rate constant. The model takes into account the asymmetric distribution of charge on the surface of the protein and localized charges at the site of electron transfer that are modeled as elements of a parallel plate condenser. Both monopolar and dipolar interactions are included. Examples of simple (monophasic) and complex (biphasic) ionic strength dependencies obtained from experiments with several electron transfer protein systems are presented, all of which can be accommodated by the model. The simple cases do not require the use of both monopolar and dipolar terms (i.e., they can be fit well by either alone). The biphasic dependencies can be fit only by using dipolar and monopolar terms of opposite sign, which is physically unreasonable for the molecules considered. Alternatively, the high ionic strength portion of the complex dependencies can be fit using either the monopolar term alone or the complete equation; this assumes a model in which such behavior is a consequence of electron transfer mechanisms involving changes in orientation or site of reaction as the ionic strength is varied. Based on these analyses, we conclude that the principal applications of the model presented here are to provide information about the structural properties of intermediate electron transfer complexes and to quantify comparisons between related proteins or site-specific mutants. We also conclude that the relative contributions of monopolar and dipolar effects to protein electron transfer kinetics cannot be evaluated from experimental data by present approximations.