Girsanov reweighting for path ensembles and Markov state models

Abstract

The sensitivity of molecular dynamics on changes in the potential energy function plays an important role in understanding the dynamics and function of complex molecules.We present a method to obtain path ensemble averages of a perturbed dynamics from a set of paths generated by a reference dynamics. It is based on the concept of path probability measure and the Girsanov theorem, a result from stochastic analysis to estimate a change of measure of a path ensemble. Since Markov state models (MSM) of the molecular dynamics can be formulated as a combined phase-space and path ensemble average, the method can be extended toreweight MSMs by combining it with a reweighting of the Boltzmann distribution. We demonstrate how to efficiently implement the Girsanov reweighting in a molecular dynamics simulation program by calculating parts of the reweighting factor "on the fly" during the simulation, and we benchmark the method on test systems ranging from a two-dimensional diffusion process to an artificial many-body system and alanine dipeptide and valine dipeptide in implicit and explicit water. The method can be used to study the sensitivity of molecular dynamics on external perturbations as well as to reweight trajectories generated by enhanced sampling schemes to the original dynamics.

References in corpus (5)

• Canonical sampling through velocity-rescaling
• Combining simulations and solution experiments as a paradigm for RNA force field refinement
• Statistically optimal analysis of state-discretized trajectory data from multiple thermodynamic states
• xTRAM: Estimating equilibrium expectations from time-correlated simulation data at multiple thermodynamic states
• Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics

Cited by in corpus (13)

• Machine learning force fields and coarse-grained variables in molecular dynamics: application to materials and biological systems
• Enhanced Sampling in the Age of Machine Learning: Algorithms and Applications
• Particle-based membrane model for mesoscopic simulation of cellular dynamics
• Dynamical reweighting methods for Markov models
• Metadynamics of paths
• Estimation of the infinitesimal generator by square-root approximation
• A review of Girsanov Reweighting and of Square Root Approximation for building molecular Markov State Models
• Path probability ratios for Langevin dynamics -- exact and approximate
• Spectral Map for Slow Collective Variables, Markovian Dynamics, and Transition State Ensembles
• Microscopic reweighting for non-equilibrium steady states dynamics
• Reweighting non-equilibrium steady-state dynamics along collective variables
• Backward Simulation of Stochastic Process using a Time Reverse Monte Carlo method
• GROMACS Stochastic Dynamics and BAOAB are equivalent configurational sampling algorithms