Assessing transition rates as functions of environmental variables

TL;DR

This paper introduces a method to estimate molecular transition rates influenced by environmental variables using reweighted MD simulations, discretization of the Fokker-Planck operator, and coarse-graining techniques, applicable to drug design.

Contribution

It formalizes a novel framework combining reweighting, SqRA, and PCCA+ to efficiently estimate environment-dependent transition rates in molecular systems.

Findings

The method accurately estimates transition rates as functions of environmental variables.

Numerical experiments validate the approach against non-equilibrium MD Monte Carlo results.

The framework is applicable to modeling biochemical processes in varying cellular conditions.

Abstract

We present a method to estimate the transition rates of molecular systems under different environmental conditions which cause the formation or the breaking of bonds and require the sampling of the Grand Canonical Ensemble. For this purpose, we model the molecular system in terms of probable "scenarios", governed by different potential energy functions, which are separately sampled by classical MD simulations. Reweighting the canonical distribution of each scenario according to specific environmental variables, we estimate the grand canonical distribution, then we use the Square Root Approximation (SqRA) method to discretize the Fokker-Planck operator into a rate matrix and the robust Perron Cluster Cluster Analysis (PCCA+) method to coarse-grain the kinetic model. This permits to efficiently estimate the transition rates of conformational states as functions of environmental variables, for example, the local pH at a cell membrane. In this work we formalize the theoretical framework of the procedure and we present a numerical experiment comparing the results with those provided by a constant-pH method based on non-equilibrium Molecular Dynamics Monte Carlo simulations. The method is relevant for the development of new drug design strategies which take into account how the cellular environment influences biochemical processes.