Computation of Rate Constants for Diffusion of Small Ligands to and from Buried Protein Active Sites

The diffusion of ligands to actives sites of proteins is essential to enzyme catalysis and many cellular signaling processes. In this contribution we review our recently developed methodology for calculation of rate constants for diffusion and binding of small molecules to buried protein active sites. The diffusive dynamics of the ligand obtained from molecular dynamics simulation is coarse grained and described by a Markov state model. Diffusion and binding rate constants are then obtained either from the reactive flux formalism or by fitting the time-dependent population of the Markov state model to a phenomenological rate law. The method is illustrated by applications to diffusion of substrate and inhibitors in [NiFe] hydrogenase, CO-dehydrogenase, and myoglobin. We also discuss a recently developed sensitivity analysis that allows one to identify hot spots in proteins, where mutations are expected to have the strongest effects on ligand diffusion rates.