Influence of molecular rebindings on the reaction rate of complex formation
T. Kalwarczyk, K. Bielec, K. Burdzy and R. Holyst
Phys. Chem. Chem. Phys., 2021
We simulated the Brownian diffusion and reaction-diffusion processes to study molecular rebinding’s influence on the reaction rates of bimolecular reactions. We found that the number of rebindings, Nreb , is proportional to the target’s size and inversely proportional to the diffusion coefficient D and simulation time-step ∆t. We found the proportionality constant close to π−1/2 . We confirmed that the number of rebinding is defined as a ratio of the activation-limited rate constant ka to the diffusion-limited rate constant, kD. We provide the formula describing the reactivity coefficient κ, modelling the transient-native complex transition for the activation-controlled reaction rates. We show that κ is proportional to (D/∆t)1/2 . Finally, we apply our rebinding-including reaction rate model to the real reactions of photoacid dissociation and protein association. Based on literature data for both types of reactions, we found the ∆t time-scale. We show that for the photodissociation of proton, the ∆t is equal to 171±18 fs and the average number of rebindings is approximately equal to 40. For proteins, ∆t is of the order of 100 ps with around 20 rebindings. In both cases the timescale is similar to the timescale of fluctuation of the solvent molecules surrounding the reactants; vibrations and bending in case of photoacid dissociation and diffusional motion for proteins.