Energy landscape and transition state of protein-protein association

Formation of a stereospecific protein complex is favored by specific interactions between two proteins but disfavored by the loss of translational and rotational freedom. Echoing the protein folding process, we have previously proposed a transition state for protein-protein association. Here we clarify the specification of the transition state by working with two types of toy models for protein association. A hemisphere model consists of two matching hemispheres as associating proteins, and a crater model consists of a spherical protein with a crater to which another spherical protein fits snugly. Short-range pairwise interactions between sites across the interface hold together the bound complex. Small relative translation and rotation between the subunits quickly destroy the interactions, leading to a sharp transition between the bound state with numerous short-range interactions but restricted translation and rotational freedom and the unbound state with, at most, a small number of interactions but expanded configurational freedom. This transition sets the outer boundary of the bound state as well as the transition state for association. The energy landscape is funnel-like, with the deep well of the bound state surrounded by a broad shallow basin. Calculations with the toy models suggest that mutational change in the interaction energy in the x-ray structure of a protein-protein complex, commonly used to approximate the effect on the association constant, overestimates the effect of mutation by 10-20%. With an eye toward specifying the transition states of actual protein complexes, we find that the total number of contacts between the subunits serves as a good surrogate of the interaction energy. This formalism of protein-protein association is applied to the barnase-barstar complex, reproducing the experimental results for the association rate over a wide range of ionic strength.