A temperature-dependent effective potential explains CO binding to myoglobin

Up to the onset of ligand escape from the heme pocket, CO binding to myoglobin can be explained by stochastic motion of the protein subject to an effective, temperature-dependent potential. Two temperature-models for the effective potential are investigated. The quantitative solution of the transient Smoluchowski equation for these models shows inhomogeneous kinetics at short times and protein relaxation at intermediate times. Additional two phases of ligand binding, ligand escape and bimolecular recombination, can be identified. Both models agree that the protein diffusion coefficient increases in an Arrhenius fashion through the solvent glass transition, indicating that protein relaxation occurs mainly in the interior of the protein. In contrast, the effective potential collapses above the glass transition temperature, indicating that it is determined also by interactions at the surface of the protein. In one of the models the parameters of the potential vary linearly with temperature, resembling the situation for rubber elasticity.