Stochastic Approximation to MBAR and TRAM: Batchwise Free Energy Estimation

Abstract

The dynamics of molecules are governed by rare event transitions between long-lived (metastable) states. To explore these transitions efficiently, many enhanced sampling protocols have been introduced that involve using simulations with biases or changed temperatures. Two established statistically optimal estimators for obtaining unbiased equilibrium properties from such simulations are the multistate Bennett acceptance ratio (MBAR) and the transition-based reweighting analysis method (TRAM). Both MBAR and TRAM are solved iteratively and can suffer from long convergence times. Here, we introduce stochastic approximators (SA) for both estimators, resulting in SAMBAR and SATRAM, which are shown to converge faster than their deterministic counterparts, without significant accuracy loss. Both methods are demonstrated on different molecular systems.

Characterization of binding kinetics and intracellular signaling of new psychoactive substances targeting cannabinoid receptor using transition-based reweighting method

“…For ligand with low off rates, the use of reversible transition matrix would yield incorrect estimates of unbinding kinetics. Therefore, we use The Transition-based reweighting analysis (TRAM) 48,108 method to accurately estimate the unbinding kinetics of new psychoactive substances. TRAM is a thermodynamics and kinetics estimator method, which, unlike MSM, can combine unbiased and biased simulation data to estimate thermodynamics and kinetics.…”

“…70 Second, it is challenging to model these large numbers of residues accurately with template-free ab initio modeling because of the combinatorial expansions of conformational space. Therefore, the closest 20 residues (89)(90)(91)(92)(93)(94)(95)(96)(97)(98)(99)(100)(101)(102)(103)(104)(105)(106)(107)(108) were modeled as membrane proximal regions of the N-terminus were shown to be important for CB 1 signaling by allosterically modulating ligand affinity. 71 Furthermore, ∆89CB 1 (CB 1 with first 88 residues truncated in N-terminus) have similar ligand binding affinity compared to CB 1 with full sequence.…”

Implementation of Girsanov Reweighting in OpenMM and Deeptime

“…Girsanov reweighting − is a dynamical reweighting technique to recover the unbiased dynamics of a molecular system from simulations that were conducted with a biased potential. It differs from other dynamical reweighting techniques − in that it does not assume an effective model of the molecular dynamics but reweights the dynamics directly on the level of the stochastic MD integrator. In this sense, Girsanov reweighting is an exact reweighting technique.…”

Vendi Sampling For Molecular Simulations: Diversity As A Force For Faster Convergence And Better Exploration

“…These enhanced sampling or extended ensemble methods rely on two broad strategies: finding a surrogate of the Boltzmann ensemble that rapidly mixes between metastable states or exchanging the state variable with one or multiple ensembles that mix faster Camilloni et al (2013); Abrams and Bussi (2013); Grubmüller (1995); Sugita and Okamoto (1999); Swendsen and Wang (1986); Laio and Parrinello (2002); Kříž et al (2017); Šućur and Spiwok (2016). To ensure that the modified ensembles sufficiently overlap with the true Boltzmann ensemble, statistical reweighing techniques such as importance sampling, the weighted histogram analysis method Ferrenberg and Swendsen (1989), the multistate Bennett acceptance ratio Shirts and Chodera (2008), or transition-based methods Wu et al (2016); Stelzl and Hummer (2017); Galama et al (2023) are used. These techniques allow for an effective reweighting of the equilibrium statistics but are disadvantaged by the intrinsic need to identify collective variables, perturb macroscopic thermodynamic variables, or alter Hamiltonians, which often rely on manual trial-and-error of numerous potential candidates Henin et al (2022).…”