Factorization of the association rate coefficient in ligand rebinding to heme proteins

Abstract

A stochastic theory of ligand migration in biomolecules is used to analyze the recombination of small ligands to heme proteins after flash photolysis. The stochastic theory is based on a generalized sequential barrier model in which a ligand binds by overcoming a series of barriers formed by the solvent protein interface, the protein matrix, and the heme distal histidine system. The stochastic theory shows that the association rate coefficient λon factorizes into three terms λon =γ12〈x2(0)〉Nout, where γ12 is the rate coefficient from the heme pocket to the heme binding site, 〈x2(0)〉 is the equilibrium pocket occupation factor, and Nout is the fraction of heme proteins which do not undergo geminate recombination of a flashed-off ligand. The factorization of λon holds for any number of barriers and with no assumptions regarding the various rate coefficients so long as the exponential solvent process occurs. Transitions of a single ligand are allowed between any two sites with two crucial exceptions: (i) the heme binding site acts as a trap so that thermal dissociation of a bound ligand does not occur within the time of the measurement; (ii) the final step in the rebinding process always has a ligand in the heme pocket from where the ligand binds to the heme iron.