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To directly simulate rare events using atomistic molecular dynamics is asignificant challenge in computational biophysics. Well-establishedenhanced-sampling techniques do exist to obtain the thermodynamic functions forsuch systems. But developing methods for obtaining the kinetics of longtimescale processes from simulation at atomic detail is comparatively lessdeveloped an area. Milestoning and the weighted ensemble (WE) method are twodifferent stratification strategies; both have shown promise for computing longtimescales of complex biomolecular processes. Nevertheless, both require asignificant investment of computational resources. We have combined WE andmilestoning to calculate observables in orders of magnitude less CPU andwall-clock time. Our weighted ensemble milestoning method (WEM) uses WEsimulation to converge the transition probability and first passage timesbetween milestones, followed by the utilization of the theoretical framework ofmilestoning to extract thermodynamic and kinetic properties of the entireprocess. We tested our method for a simple one-dimensional double wellpotential, an eleven-dimensional potential energy surface with energy barrier,and on the biomolecular model system alanine dipeptide. We were able to recoverthe free energy profiles, time correlation functions, and mean first passagetimes for barrier crossing events at a significantly small computational cost.WEM promises to extend the applicability of molecular dynamics simulation toslow dynamics of large systems which are well beyond the scope of present daybrute-force computations.

Weighted Ensemble Milestoning (WEM): A Combined Approach for Rare Event Simulations