Milestoning with wind: Exploring the impact of a biasing potential in exact calculation of kinetics

We consider the algorithm wind-assisted reweighted Milestoning of Grazioli and Andricioaei [J. Chem. Phys 149(8), 084103 (2018)], expand it, and assess its performance. We derive exact expressions for underdamped and overdamped Langevin dynamics and examine its efficiency for a simple model system (Mueller's potential) and for bond breaking in solution. The use of a biasing force (wind) significantly enhances the sampling of otherwise rare trajectories but also introduces an exponential weight to the trajectories that significantly impact the value of the statistics. In our examples, computing averages and standard deviations are not better using wind compared to straightforward Milestoning. However, the biasing force is useful for highly steep energy landscapes. On these landscapes, the probability of sampling straightforward Milestoning trajectories, which overcome the barrier, is low and the biasing force enables the observations of these rare events.