Approximating First Hitting Point Distribution in Milestoning for Rare Event Kinetics

Area of Science:

• Computational Chemistry
• Statistical Mechanics
• Chemical Kinetics

Background:

• Milestoning is a computational method for calculating rare event kinetics.
• Accuracy of Milestoning relies on the initial distribution of short trajectories.
• The true initial distribution, first hitting point distribution (FHPD), lacks a general analytical solution.

Purpose of the Study:

• To develop accurate and efficient algorithms for approximating FHPD in equilibrium systems.
• To improve the accuracy of mean first passage time (MFPT) calculations in Milestoning.
• To provide cost-effective alternatives to existing Milestoning methods.

Main Methods:

• Introduced Local Passage Time weighted Milestoning (LPT-M) and Bayesian Inference Milestoning (BI-M).
• Methods approximate FHPD by weighting trajectories sampled from the Boltzmann distribution.
• Developed an iterative correction algorithm for non-equilibrium stationary FHPD.

Main Results:

• Both LPT-M and BI-M significantly improve MFPT accuracy compared to classical Milestoning (CM).
• BI-M encompasses directional Milestoning for Hamiltonian dynamics.
• LPT-M offers advantages in computational cost and robustness with increasing milestones.

Conclusions:

• LPT-M and BI-M provide accurate and efficient approximations for FHPD.
• The developed methods enhance the reliability of rare event kinetics calculations.
• The iterative correction algorithm offers a cheaper path to exact MFPT than Exact Milestoning (ExM).