Experiment-Guided Refinement of Milestoning Network

Milestoning is an efficient method for calculating rare event kinetics by constructing a continuous-time kinetic network that connects the reactant and product states. Its accuracy depends on both the quality of the underlying force fields and the trajectory sampling. The sampling error can be effectively controlled through various methods. However, the force fields are often not accurate enough, leading to quantitative discrepancies between simulations and experimental data. To address this challenge, we present a refinement approach for Milestoning network based on the maximum caliber (MaxCal), a general variational principle for dynamical systems, to combine simulations and experimental data. The Kullback-Leibler divergence rate between two Milestoning networks is analytically evaluated and minimized as the loss function. Meanwhile, experimental thermodynamic (equilibrium constants) and kinetic (rate constants) data are incorporated as constraints. The use of MaxCal implies that the refined kinetic network is minimally perturbed from the original one while satisfying the experimental constraints. The refined network is expected to align better with available experimental data. The refinement approach is demonstrated using the binding and unbinding dynamics of a series of six small molecule ligands for the model host system, β-cyclodextrin.