The Milestoning algorithm, developed by Ron Elber et al., is an enhanced sampling method for determining the kinetics of complex molecular motions. Milestoning involves dividing the space describing the motions into subspaces, using molecular dynamics to determine the distributions of transition times between subspaces, and then solving a matrix of transition probabilities between the interfaces, called milestones, to obtain the equilibrium flux values through the set of milestones. This work aims to build on the success of Milestoning in two distinct areas: computational speedup for the calculation of transition time distributions via artificially accelerated and re-weighted trajectories, and extending the reach of Milestoning into non-equilibrium regimes with a coarse-grained random walk methodology, which we applied to calculating both time-dependent fluxes and time correlation functions.<br/><br/>We call the first method "Wind Assisted Re-weighted Milestoning", or WARM. The reason for this is that the method works by including an extra force term in the Langevin equation describing the dynamics that biases the trajectories to move toward the target milestone, similar to the way a strong steady wind at the backs of a soccer team could assist them in advancing the ball toward their opponent’s goal. Although the bias causes the trajectories to arrive at the target milestone artificially fast, the distribution of transition times is re-weighted using a formalism rooted in Ito's stochastic calculus to yield the true distribution of transition times. We were able to demonstrate computational speedup by factors of around 4 up to 40, depending on the system.<br/><br/>Central to our second method is the construction of random walks between milestones by drawing from two data sets available in any Milestoning simulation: the set of transition probabilities between milestones and the set of probability density functions of transition times for all possible transitions. These random walks can be processed to obtain the set of time-dependent fluxes through the milestones, given an initial configuration. The process is reminiscent of obtaining the manifold solutions to Fokker-Planck diffusion equations by applying stochastic path integration to Langevin trajectories. We show that time correlation functions can be calculated from these discrete manifolds, which in turn demonstrates that this method can be used to calculate experimental observables from Milestoning simulations.

Advancements in milestoning: Computational speedup by re-weighting artificially accelerated trajectories and venturing into the non-equilibrium with coarse-grained random walks in milestone space

251st National Meeting (2016)

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