Free Energy Landscapes, Diffusion Coefficients, and Kinetic Rates from Transition Paths

TL;DR

This paper introduces an efficient algorithm to accurately reconstruct free energy landscapes, diffusion coefficients, and kinetic rates from short molecular dynamics trajectories, improving modeling of complex system dynamics.

Contribution

The authors present a novel likelihood-based method for estimating Langevin and Fokker-Planck parameters from short trajectories, applicable to various evolution equations.

Findings

Algorithm is numerically efficient and robust on model systems.

Successfully applied to fullerene molecules in water.

Enables accurate thermodynamics and kinetics reconstruction from short trajectories.

Abstract

We address the problem of constructing accurate mathematical models of the dynamics of complex systems projected on a collective variable. To this aim we introduce a conceptually simple yet effective algorithm for estimating the parameters of Langevin and Fokker-Planck equations from a set of short, possibly out-of-equilibrium molecular dynamics trajectories, obtained for instance from transition path sampling or as relaxation from high free-energy configurations. The approach maximizes the model likelihood based on any explicit expression of the short-time propagator, hence it can be applied to different evolution equations. We demonstrate the numerical efficiency and robustness of the algorithm on model systems, and we apply it to reconstruct the projected dynamics of pairs of C60 and C240 fullerene molecules in explicit water. Our methodology allows reconstructing the accurate thermodynamics and kinetics of activated processes, namely free energy landscapes, diffusion coefficients, and kinetic rates. Compared to existing enhanced sampling methods, we directly exploit short unbiased trajectories at a competitive computational cost.