Efficient Estimation of Rare-Event Kinetics

Abstract

The efficient calculation of rare-event kinetics in complex dynamical systems, such as the rate and pathways of ligand dissociation from a protein, is a generally unsolved problem. Markov state models can systematically integrate ensembles of short simulations and thus effectively parallelize the computational effort, but the rare events of interest still need to be spontaneously sampled in the data. Enhanced sampling approaches, such as parallel tempering or umbrella sampling, can accelerate the computation of equilibrium expectations massively, but sacrifice the ability to compute dynamical expectations. In this work we establish a principle to combine knowledge of the equilibrium distribution with kinetics from fast “downhill” relaxation trajectories using reversible Markov models. This approach is general, as it does not invoke any specific dynamical model and can provide accurate estimates of the rare-event kinetics. Large gains in sampling efficiency can be achieved whenever one direction of the process occurs more rapidly than its reverse, making the approach especially attractive for downhill processes such as folding and binding in biomolecules. Our method is implemented in the PyEMMA software.