Nonexponential ligand rebinding of CO and O2 in myoglobin controlled by fluctuations of the protein

The kinetics of first-order processes which depend on a fluctuating coordinate are studied analytically. The fluctuations are described as uncorrelated jumps with an arbitrary time distribution between jumps. As an example, the nonexponential ligand rebinding kinetics in proteins is analyzed in the adiabatic limit where the reaction is controlled by the motion along the reaction coordinate. A new powertime law is deduced for the rebinding at low temperatures.