Advances in milestoning. I. Enhanced sampling via wind-assisted reweighted milestoning (WARM)

The milestoning algorithm of Elber and co-workers creates a framework for computing the time scale of processes that are too long and too complex to be studied using simply brute force simulations. The fundamental objects involved in the milestoning algorithm are the first passage time distributions K_AB (τ) between adjacent conformational milestones A and B. The method proposed herein aims to further enhance milestoning (or other interface based sampling methods) by employing an artificially applied force, akin to a wind that blows the trajectories from their initial to their final states, and by subsequently applying corrective weights to the trajectories to yield the true first passage time distributions K_AB (τ) in a fraction of the computation time required for unassisted calculations. The re-weighting method is rooted in the formalism of stochastic path integrals. The theoretical basis for the technique and numerical examples are presented.