Theory and simulation on the kinetics of protein-ligand binding coupled to conformational change.

Conformational change during protein-ligand binding may significantly affect both the binding mechanism and the rate constant. Most earlier theories and simulations treated conformational change as stochastic gating with transition rates between reactive and nonreactive conformations uncoupled to ligand binding. Recently, we introduced a dual-transition-rates model in which the transition rates between reactive and nonreactive conformations depend on the protein-ligand distance [H.-X. Zhou, Biophys. J. 98, L15 (2010)]. Analytical results of that model showed that the apparent binding mechanism switches from conformational selection to induced fit, when the rates of conformational transitions increase from being much slower than the diffusional approach of the protein-ligand pair to being much faster. The conformational-selection limit (k(CS)) and the induced-fit limit (k(IF)) provide lower and upper bounds, respectively, for the binding rate constant. Here we introduce a general model in which the energy surface of the protein in conformational space is coupled to ligand binding, and present a method for calculating the binding rate constant from Brownian dynamics simulations. Analytical and simulation results show that, for an energy surface that switches from favoring the nonreactive conformation while the ligand is away to favoring the reactive conformation while the ligand is near, k(CS) and k(IF) become close and, thus, provide tight bounds to the binding rate constant. This finding has significant mechanistic implications and presents routes for obtaining good estimates of the rate constant at low cost.