A Benchmark Test Set for Alchemical Free Energy Transformations and Its Use to Quantify Error in Common Free Energy Methods

Abstract

There is a significant need for improved tools to validate thermophysical quantities computed via molecular simulation. In this paper we present the initial version of a benchmark set of testing methods for calculating free energies of molecular transformation in solution. This set is based on molecular changes common to many molecular design problems, such as insertion and deletion of atomic sites and changing atomic partial charges. We use this benchmark set to compare the statistical efficiency, reliability, and quality of uncertainty estimates for a number of published free energy methods, including thermodynamic integration, free energy perturbation, the Bennett acceptance ratio (BAR) and its multistate equivalent MBAR. We identify MBAR as the consistently best performing method, though other methods are frequently comparable in reliability and accuracy in many cases. We demonstrate that assumptions of Gaussian distributed errors in free energies are usually valid for most methods studied. We demonstrate that bootstrap error estimation is a robust and useful technique for estimating statistical variance for all free energy methods studied. This benchmark set is provided in a number of different file formats with the hope of becoming a useful and general tool for method comparisons.

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“…These are some of the most widely used throughput-focused molecular simulation methods, and aim to calculate a free energy difference ∆F between two systems with Hamiltonians H 0 and H 1 . The free energy difference between the two states is calculated using an average exponential quantities such as ligand-protein binding affinity in drug design, 28 solubility, 29 and phase stability. 30 In practice, this cannot be done in a single step without significant sampling error, so instead we introduce a Hamiltonian coupled to a parameter λ:…”

Capturing the Role of Temperature and Entropy in Crystal Polymorphs Through Molecular Simulations

“…Multistate reweighting techniques generally outperform Zwanzig approaches [257,304] because information from two or more sampled states is used to probe the configuration space of the unsampled state.…”

“…MBAR leads to free energy estimates identical to those from the weighted histogram analysis method in the limit of zero width bins [305], and also includes accurate asymptotic error estimates [304]. With both MBAR and NBB, an estimate of the free energy difference between two states in the expensive potential is calculated by evaluating the energy in the expensive potential of all configurations from some set of cheap sampled states.…”

“…The configurations were decorrelated before bootstrapping using the method of Chodera et al [213]. Uncertainties in the uncertainties for the SAMPL4 dataset were estimated assuming a normal distribution using Var σ 2 = 2σ 4 n−1 where σ 2 is the variance in the free energy estimate and n represents the number of bootstrap iterations [304].…”

“…This assumes we are in the limit that the squared uncertainties are inversely proportional to the number of reweighted configurations, which we generally do arrive at for most reweighting methods in the first few hundred samples [304]. Under this relatively mild assumption, then, the NBB-direct method would require 16x more QM/MM energy evaluations in order to produce the same magnitude of uncertainties as the full implementation of MBAR.…”