CO binding to heme proteins: A model for barrier height distributions and slow conformational changes

A model for the dependence of the potential energy barrier on a ‘‘protein coordinate’’ is constructed. It is based on a two dimensional potential energy surface having as variables the CO–iron distance and a conceptual protein coordinate. The distribution of barrier heights observed in kinetics follows from an initial Boltzmann distribution for the protein coordinate. The experimental nonexponential rebinding kinetics at low temperatures or large viscosities (when the protein coordinates can be assumed ‘‘frozen’’) can be fit with a simply parametrized energy surface. Using the same energy surfaces and the theory of bounded diffusion perpendicular to the reaction coordinate, we generate (in qualitative agreement with experiment) the survival probability curves for larger diffusivity, when the constraint on the protein coordinate is relaxed. On the basis of our results, the outcomes of new experiments which examine the concepts underlying the theory can be predicted.