Incorporating rate constants as kinetic constraints in molecular dynamics simulations

From the point of view of statistical mechanics, a full characterization of a molecular system requires an accurate determination of its possible states, their populations and the respective interconversion rates. Towards this goal, well-established methods increase the accuracy of molecular dynamics simulations by incorporating experimental information about states using structural restraints, and about populations using thermodynamics restraints. However, until so far it remains unclear how to include experimental knowledge about interconversion rates. Here we introduce a novel method of imposing known rate constants as constraints in molecular dynamics simulations, which is based on a combination of the maximum entropy and maximum caliber principles. Starting from an existing ensemble of trajectories, obtained from either molecular dynamics or enhanced trajectory sampling, such as transition path sampling, this method provides a minimally perturbed path distribution by reweighting trajectories, consistent with the kinetic constraints. In addition, the approach yields a modified free energy and committor landscape. We illustrate the application of the method to model systems, including all atom molecular simulations of protein folding. Our results show that by combining experimental rate constants and molecular dynamics simulations this approach enables improved determination of transition states, reaction mechanisms and free energies. We anticipate that this method will extend the applicability of molecular simulations to kinetic studies in structural biology, and that it will assist the development of force fields to reproduce kinetic and thermodynamic observables. Furthermore, this approach is generally applicable to a wide range of systems in biology, physics, chemistry, and material science.