Free Energy Reconstruction from Logarithmic Mean-Force Dynamics Using Multiple Nonequilibrium Trajectories

Abstract

Efficient and reliable estimation of the mean force (MF), the derivatives of the free energy with respect to a set of collective variables (CVs), has been a challenging problem because free energy differences are often computed by integrating the MF. Among various methods for computing free energy differences, logarithmic mean-force dynamics (LogMFD) [ Morishita et al., Phys. Rev. E 2012 , 85 , 066702 ] invokes the conservation law in classical mechanics to integrate the MF, which allows us to estimate the free energy profile along the CVs on-the-fly. Here, we present a method called parallel dynamics, which improves the estimation of the MF by employing multiple replicas of the system and is straightforwardly incorporated in LogMFD or a related method. In the parallel dynamics, the MF is evaluated by a nonequilibrium path-ensemble using the multiple replicas based on the Crooks-Jarzynski nonequilibrium work relation. Thanks to the Crooks relation, realizing full-equilibrium states is no longer mandatory for estimating the MF. Additionally, sampling in the hidden subspace orthogonal to the CV space is highly improved with appropriate weights for each metastable state (if any), which is hardly achievable by typical free energy computational methods. We illustrate how to implement parallel dynamics by combining it with LogMFD, which we call logarithmic parallel dynamics (LogPD). Biosystems of alanine dipeptide and adenylate kinase in explicit water are employed as benchmark systems to which LogPD is applied to demonstrate the effect of multiple replicas on the accuracy and efficiency in estimating the free energy profiles using parallel dynamics.

Promoting transparency and reproducibility in enhanced molecular simulations

“…The EDS module implements the Experiment Directed Simulation approach to adaptively construct linear restraints that ensure that the biased CVs sample a new target mean value 26 . The logmfd module can be used to perform enhanced-sampling using logarithmic meanforce dynamics 27 . The piv module contains an implementation of the permutation invariant vector 28 , which is a general purpose representation of the structure of materials that can be used to analyze and simulate the transitions between ordered and disordered forms that take place in processes such as crystal nucleation.…”

Effect of Surface Coverage of Water Molecules on Methane Adsorption on Muscovite and Pyrophyllite: Molecular Dynamics Study

“…In the free energy calculation, the logarithmic mean force dynamics (LogMFD) method , was used. The PLUMED plug-in module in conjunction with GROMACS was used to perform the LogMFD calculations.…”

Mean force based temperature accelerated sliced sampling: Efficient reconstruction of high dimensional free energy landscapes

“…Mean force based computation of free energies is core to several techniques 10,39–43 . Mean force based reconstruction of free energy surfaces in the frame work of extended Lagrangian has been reported earlier for adaptive bias sampling (ABF), 10,44–48 logarithmic mean‐force dynamics 24 TAMD/d‐AFED, UFED and metadynamics 42,49 .…”

“…Mean force based computation of free energies is core to several techniques. 10,[39][40][41][42][43] Mean force based reconstruction of free energy surfaces in the frame work of extended Lagrangian has been reported earlier for adaptive bias sampling (ABF) 10,[44][45][46][47][48] , logarithmic mean-force dynamics 24 TAMD/d-AFED, UFED and metadynamics. 42,49 Such techniques use the gradient of the underlying free energy to compute free energy surfaces using thermodynamic integration as…”