The dynamics of single enzyme reactions: A reconsideration of Kramers' model for colored noise processes

The utility of an approximate heuristic version of Kramers' theory of reaction rates that was earlier used [Chaudhury and Cherayil, J. Chem. Phys. 125, 024904 (2006)] to successfully describe the nonexponential waiting time distributions of the enzyme beta-galactosidase is reassessed. The original model, based on the Smoluchowski equation, is reformulated in terms of the phase space variables of the reaction coordinate, without neglecting inertial contributions. A new derivation of the Fokker-Planck equation (FPE) that describes the dynamics of this coordinate is presented. This derivation, based on functional methods, provides a more direct alternative to the existing distribution function approach used by Hanggi and Mojtabai [Phys. Rev. A 26, 1168 (1982)]. The time-dependent coefficients in the FPE, when incorporated into the exact expression for the transmission coefficient obtained from a reactive-flux formalism [Kohen and Tannor, J. Chem. Phys. 103, 6013 (1995)], are found to yield virtually the same results as the earlier heuristic model.