  To directly simulate rare events using atomistic molecular dynamics is a
significant challenge in computational biophysics. Well-established
enhanced-sampling techniques do exist to obtain the thermodynamic functions for
such systems. But developing methods for obtaining the kinetics of long
timescale processes from simulation at atomic detail is comparatively less
developed an area. Milestoning and the weighted ensemble (WE) method are two
different stratification strategies; both have shown promise for computing long
timescales of complex biomolecular processes. Nevertheless, both require a
significant investment of computational resources. We have combined WE and
milestoning to calculate observables in orders of magnitude less CPU and
wall-clock time. Our weighted ensemble milestoning method (WEM) uses WE
simulation to converge the transition probability and first passage times
between milestones, followed by the utilization of the theoretical framework of
milestoning to extract thermodynamic and kinetic properties of the entire
process. We tested our method for a simple one-dimensional double well
potential, an eleven-dimensional potential energy surface with energy barrier,
and on the biomolecular model system alanine dipeptide. We were able to recover
the free energy profiles, time correlation functions, and mean first passage
times for barrier crossing events at a significantly small computational cost.
WEM promises to extend the applicability of molecular dynamics simulation to
slow dynamics of large systems which are well beyond the scope of present day
brute-force computations.
