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The Metropolis Monte Carlo (MC) method is used to extract reaction kineticsfrom a given equilibrium distribution of states of a complex system. Theapproach is illustrated by the folding/unfolding reaction for two proteins - amodel beta-hairpin and a-helical protein a3D. For beta-hairpin, the free energysurfaces (FESs) and free energy profiles (FEPs) are employed as the equilibriumdistributions of states, playing a role of the potentials of mean force todetermine the acceptance probabilities of new states in the MC simulations.Based on the FESs and PESs for a set of temperatures that were simulated withthe molecular dynamics (MD) method, the MC simulations are performed to extractfolding/ unfolding rates. It has been found that the rate constants andfirst-passage time (FPT) distributions obtained in the MC simulations changewith temperature in good agreement with those from the MD simulations. For a3Dprotein, whose equilibrium folding/unfoldingwas studied with thesingle-molecule FRET method (Chung et al., J. Phys. Chem. A, 115, 2011, 3642),the FRET-efficiency histograms at different denaturant concentrations were usedas the equilibrium distribution of protein states. It has been found that therate constants for folding and unfolding obtained in the MC simulations changewith denaturant concentration in reasonable agreement with the constants thatwere extracted from the photon trajectories on the basis of theoretical models.The simulated FPT distributions are single-exponential, which is consistentwith the assumption of two-state kinetics that was made in the theoreticalmodels. The promising feature of the present approach is that it is basedsolely on the equilibrium distributions of states, without introducing anyadditional parameters to perform simulations, which suggests its applicabilityto other complex systems.

Extraction of kinetics from equilibrium distributions of states using the Metropolis Monte Carlo method