Guidelines for the analysis of free energy calculations

Abstract

Free energy calculations based on molecular dynamics (MD) simulations show considerable promise for applications ranging from drug discovery to prediction of physical properties and structure-function studies. But these calculations are still difficult and tedious to analyze, and best practices for analysis are not well defined or propagated. Essentially, each group analyzing these calculations needs to decide how to conduct the analysis and, usually, develop its own analysis tools. Here, we review and recommend best practices for analysis yielding reliable free energies from molecular simulations. Additionally, we provide a Python tool, , freely available on GitHub at https://github.com/choderalab/pymbar–examples, that implements the analysis practices reviewed here for several reference simulation packages, which can be adapted to handle data from other packages. Both this review and the tool covers analysis of alchemical calculations generally, including free energy estimates via both thermodynamic integration and free energy perturbation-based estimators. Our Python tool also handles output from multiple types of free energy calculations, including expanded ensemble and Hamiltonian replica exchange, as well as standard fixed ensemble calculations. We also survey a range of statistical and graphical ways of assessing the quality of the data and free energy estimates, and provide prototypes of these in our tool. We hope these tools and discussion will serve as a foundation for more standardization of and agreement on best practices for analysis of free energy calculations.

Molecular simulations and free-energy calculations suggest conformation-dependent anion binding to a cytoplasmic site as a mechanism for Na+/K+-ATPase ion selectivity

“…The Multi-state Bennett Acceptance Ratio (MBAR) method was used for free energy estimation, as implemented in the pymbar python package (49,50). Since our FEP calculations to determine the preferred protonation state show good energy overlap not only between adjacent, but also between more distant windows, we used the MBAR estimator, which integrates samples from all thermodynamic intermediates.…”

VR-SCOSMO: A smooth conductor-like screening model with charge-dependent radii for modeling chemical reactions

“…[9][10][11] The end goal of these studies is frequently to aid in the design of new drugs and therapeutic treatments. [12][13][14] Multiscale modeling approaches including long timescale molecular dynamics simulations to explore fluctuations and conformational changes of biomolecules, combined quantum mechanical/molecular mechanical (QM/MM) simulations to examine deeply embedded reactive chemical events, and implicit solvent calculations of small model reactions are used for this task.…”

Predicting Thermodynamic Properties over Combinatorially Large Chemical Spaces

“…The eigenvalues of the overlap matrix for our drawn samples have repeated 1's to machine precision [101,187], indicating that insufficient samples have been drawn to say we have global phase space overlap and better confidence in property estimations [56]. The simulations could be modified to bias away from sampling molecules with have unfavored free energy, depending on application.…”

“…[101,187] The individual elements of the overlap matrix, O ij , can be read as the probability of a sample generated in state j being observed in state i.…”

“…All other eigenvalues will be real and positive. [187] However, multiple eigenvalues of 1 in O indicate that there are discontinuous regions of sampled configuration space and O can be rearranged to a block diagonal matrix that illustrates which states are and are not connected.…”