Advancements in Milestoning I: Accelerated Milestoning via "Wind" Assisted Re-weighted Milestoning (WARM)

TL;DR

This paper introduces WARM, an accelerated Milestoning method that uses an artificial wind force and re-weighting to efficiently compute first passage times in complex molecular systems.

Contribution

It develops a novel re-weighting approach based on Ito's calculus to enhance Milestoning with wind-assisted trajectory acceleration.

Findings

WARM significantly reduces computation time for first passage time estimation.

Theoretical validation confirms the accuracy of re-weighted distributions.

Numerical examples demonstrate improved efficiency over traditional Milestoning.

Abstract

The Milestoning algorithm created by Ron Elber et al. is a method for determining the time scale of processes too complex to be studied using brute force simulation methods. The fundamental objects implemented in the Milestoning algorithm are the first passage time distributions between adjacent protein configuration milestones. The method proposed herein aims to further enhance Milestoning by employing an artificial applied force, akin to wind, which pushes the trajectories from their initial states to their final states, and subsequently re-weights the trajectories to yield the true first passage time distributions in a fraction of the computation time required for unassisted calculations. The re-weighting method, rooted in Ito's stochastic calculus, was adapted from previous work by Andricioaei et al. The theoretical basis for this technique and numerical examples are presented.