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Force field optimization by imposing kinetic constraints with path reweighting

Empirical force fields employed in molecular dynamics simulations of complex systems can be optimised to reproduce experimentally determined structural and thermodynamic properties. In contrast, experimental knowledge about the rates of interconversion between metastable states in such systems, is hardly ever incorporated in a force field, due to a lack of an efficient approach. Here, we introduce such a framework, based on the relationship between dynamical observables such as rate constants, and the underlying force field parameters, using the statistical mechanics of trajectories. Given a prior ensemble of molecular trajectories produced with imperfect force field parameters, the approach allows the optimal adaption of these parameters, such that the imposed constraint of equal predicted and experimental rate constant is obeyed. To do so, the method combines the continuum path ensemble Maximum Caliber approach with path reweighting methods for stochastic dynamics. When multiple solutions are found, the method selects automatically the combination that corresponds to the smallest perturbation of the entire path ensemble, as required by the Maximum Entropy principle. To show the validity of the approach we illustrate the method on simple test systems undergoing rare event dynamics. Next to simple 2D potentials we explore particle models representing molecular isomerisation reactions as well as protein-ligand unbinding. Besides optimal interaction parameters the methodology gives physical insight into what parts of the model are most sensitive to the kinetics. We discuss the generality and broad implications of the methodology.