Kramers model with a power-law friction kernel: Dispersed kinetics and dynamic disorder of biochemical reactions

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Abstract
Kramers’ model for the rate of chemical reaction is generalized to explain the phenomena of dispersed kinetics and dynamic disorder in biochemical reactions, by incorporating the newly observed power-law friction kernel into the generalized Langevin equation for a one-dimensional reaction ordinate. This new model accounts for time scale overlap between conformational and chemical dynamics, and quantitatively describes the multi-exponential kinetics and memory effects of fluctuating rate constants, which have been revealed by recent single-molecule experiments.