Brownian dynamics study of the influences of electrostatic interaction and diffusion on protein-protein association kinetics.

A unified model is presented for protein-protein association processes that are under the influences of electrostatic interaction and diffusion (e.g., protein oligomerization, enzyme catalysis, electron and energy transfer). The proteins are modeled as spheres that bear point charges and undergo translational and rotational Brownian motion. Before association can occur the two spheres have to be aligned properly to form a reaction complex via diffusion. The reaction complex can either go on to form the product or it can dissociate into the separate reactants through diffusion. The electrostatic interaction, like diffusion, influences every step except the one that brings the reaction complex into the product. The interaction potential is obtained by extending the Kirkwood-Tanford protein model (Tanford, C., and J. G. Kirkwood. 1957. J. Am. Chem. Soc. 79:5333-5339) to two charge-embedded spheres and solving the consequent equations under a particular basis set. The time-dependent association rate coefficient is then obtained through Brownian dynamics simulations according an algorithm developed earlier (Zhou, H.-X. 1990. J. Phys. Chem. 94:8794-8800). This method is applied to a model system of the cytochrome c and cytochrome c peroxidase association process and the results confirm the experimental dependence of the association rate constant on the solution ionic strength. An important conclusion drawn from this study is that when the product is formed by very specific alignment of the reactants, as is often the case, the effect of the interaction potential is simply to scale the association rate constant by a Boltzmann factor. This explains why mutations in the interface of the reaction complex have strong influences on the association rate constant whereas those away from the interface have minimal effects. It comes about because the former mutations change the interaction potential of the reaction complex significantly and the latter ones do not.