A coupled diffusion and barrier model for the recombination kinetics of myoglobin with carbon monoxide

The rebinding kinetics of myoglobin (Mb) with carbon monoxide (CO) after photodissociation have been analyzed using a single energy barrier coupled by a two-dimensional channel to the solvent. The total binding rate is written as the product of the barrier rate coefficient and the probability of the ligand being at the barrier. Assuming that the photodissociated ligands are initially localized near the barrier, the probability then decays as 1 t as the ligands migrate away toward the solvent. The time-dependent rate coefficient yields power-law kinetics as observed in the MbCO recombination kinetics. At a given temperature two parameters are sufficient to simulate power-law kinetics of arbitrary slope. Using a model of diffusion from a region of lower to higher diffusivity, four parameters can simulate an initial power law followed by a final slow exponential process. Estimates of the diffusion coefficients inside the protein are two to three orders of magnitude slower than the ligand diffusivity in the external solvent. A single Arrhenius rate coefficient for the barrier can be used for the entire range from 60 K to 320 K. The barrier diffusion model implies a certain shape of the kinetics which is in good agreement with the observed recombination kinetics of many heme protein ligand systems.