Statistically optimal analysis of samples from multiple equilibrium states.

By Michael R. Shirts, John D. Chodera. Journal of Chemical Physics, 2008

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We present a new estimator for computing free energy differences and thermodynamic expectations as well as their uncertainties from samples obtained from multiple equilibrium states via either simulation or experiment. The estimator, which we call the multistate Bennett acceptance ratio estimator (MBAR) because it reduces to the Bennett acceptance ratio estimator (BAR) when only two states are considered, has significant advantages over multiple histogram reweighting methods for combining data from multiple states. It does not require the sampled energy range to be discretized to produce histograms, eliminating bias due to energy binning and significantly reducing the time complexity of computing a solution to the estimating equations in many cases. Additionally, an estimate of the statistical uncertainty is provided for all estimated quantities. In the large sample limit, MBAR is unbiased and has the lowest variance of any known estimator for making use of equilibrium data collected from multiple states. We illustrate this method by producing a highly precise estimate of the potential of mean force for a DNA hairpin system, combining data from multiple optical tweezer measurements under constant force bias.

Subfields: Atomic and Molecular Physics, and Optics, Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/fe8f026619dd5550f1ac23a3698b1e00e959b4cd

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Citations in the corpus

Predicting binding free energies: Frontiers and benchmarks (2016, positive): “Test calculations should typically agree with reference results to within 95% confidence intervals, from established methods [51, 158], For this purpose, the correctly computed values need not agree with experiment; indeed, experimental results are unnecessary.”
Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning (2019, background): “Other ensembles can be modeled by incorporating the choice of ensemble into the reduced potential ( 41 ).”
Discrete Variational Autoencoders (2016, methodology): “For this purpose, we estimate the log partition function using bridge sampling, a variant of Bennett’s acceptance ratio method (Bennett, 1976; Shirts & Chodera, 2008), which produces unbiased estimates of the partition function.”
From Proteins to Perturbed Hamiltonians: A Suite of Tutorials for the GROMACS-2018 Molecular Simulation Package [Article v1.0] (2019, methodology): “Interested readers may wish to refer to the Multistate BAR (MBAR) method [82], in which free energy differences are computed from all states.”
Standard binding free energies from computer simulations: What is the best strategy? (2012, methodology): “62 In all alchemical transformations, p41 was restrained to its native confirmation by means of a root mean-square deviation (RMSD) collective variable.”
Guidelines for the analysis of free energy calculations (2015, methodology): “Some of them, like BAR [1] and MBAR [35], are in common use and are deeply”
Adversarial Message Passing For Graphical Models (2016, methodology): “This procedure yields two Markov chains transitioning from evidence to prior and from prior to evidence in a setting similar to that used for the Bennet acceptance ratio estimator [16] and related newer work [17, 18, 19, 20, 21].”
Enhanced Sampling Methods for Molecular Dynamics Simulations [Article v1.0] (2022, methodology): “Similarly to BAR, there are a standardways to solve this set of equations implemented in a number of different codes [70, 72, 73].”
Computer-Aided Drug Design Methods (2017, methodology): “Calculate the free energy difference, ΔG, in the presence of the protein and in aqueous solution based on the free energy perturbation formula (105) or the Bennett acceptance ratio (BAR) as described elsewhere (106).”