Improved Kinetics of Molecular Simulations using Biased Markov State Models

Molecular simulations can provide microscopic insight into the physical and chemical driving forces of complex molecular processes. Despite tremendous advances in the accuracy of models as well as in the sophistication of simulation methodology, force-field errors can always potentially cause inconsistencies between simulated and experimentally-measured observables. The present work presents a robust and systematic framework to reweight the ensemble of dynamical paths sampled in a molecular simulation in order to be consistent with a set of kinetic observables. The method employs the well-developed Markov state modeling framework in order to efficiently treat simulated dynamical paths. By biasing the Markov state model to reproduce a small number of kinetic constraints, we not only improve the kinetic description of the system, but also the equilibrium distributions. The method is illustrated on two distinct coarse-grained peptide models, for which we observe clear improvements of the equilibrium distributions as well as the largest eigenvalues and corresponding eigenvectors. The latter quantities describe the time scales and associated flux between microstates for the slowest kinetic processes sampled in the underlying simulation trajectory. Biasing a Markov state model with coarse dynamical information provides a robust, generic, and simple way to systematically refine the microscopic description of a simulation model.