THEORY AND SIMULATION OF STOCHASTICALLY-GATED DIFFUSION-INFLUENCED REACTIONS

The kinetics of the irreversible diffusion-influenced reaction between a protein (P) and a ligand (L) is studied when [L] much greater than [P] and the reactivity is stochastically gated due to conformational f luctuations of one of the species. If gating is due to the ligand, we show that the Smoluchowski rate equation, d[P(t)]/dt = -k(t)[L][P(t)], can be generalized by simply using a stochastically-gated time-depend ent rate coefficient, k(sg)(t). However, if gating is due to the prote in, this is no longer true, except when the gating dynamics is suffici ently fast or the Ligand concentration is very low. The dynamics of ai l the ligands around a protein become correlated even when they diffus e independently. An approximate theory for the kinetics of protein-gat ed reactions that is exact in both the fast and slow gating limits is developed. In order to test this theory, a Brownian dynamics simulatio n algorithm based on a path-integral formulation is introduced to calc ulate both k(sg)(t) and the time dependence of the protein concentrati on. Illustrative simulations using a simple model are carried out for a variety of gating rates. The results are in good agreement with the approximate theory.