Gibbs Sampler-Based λ-Dynamics and Rao-Blackwell Estimator for Alchemical Free Energy Calculation

Journal of Chemical Theory and Computation
Xinqiang DingCharles L Brooks

Abstract

λ-dynamics is a generalized ensemble method for alchemical free energy calculations. In traditional λ-dynamics, the alchemical switch variable λ is treated as a continuous variable ranging from 0 to 1 and an empirical estimator is utilized to approximate the free energy. In the present article, we describe an alternative formulation of λ-dynamics that utilizes the Gibbs sampler framework, which we call Gibbs sampler-based λ-dynamics (GSLD). GSLD, like traditional λ-dynamics, can be readily extended to calculate free energy differences between multiple ligands in one simulation. We also introduce a new free energy estimator, the Rao-Blackwell estimator (RBE), for use in conjunction with GSLD. Compared with the current empirical estimator, the advantage of RBE is that RBE is an unbiased estimator and its variance is usually smaller than the current empirical estimator. We also show that the multistate Bennett acceptance ratio equation or the unbinned weighted histogram analysis method equation can be derived using the RBE. We illustrate the use and performance of this new free energy computational framework by application to a simple harmonic system as well as relevant calculations of small molecule relative free energies of solv...Continue Reading

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Citations

Sep 4, 2018·Protein Science : a Publication of the Protein Society·Ryan L HayesCharles L Brooks
Aug 8, 2019·Proceedings of the National Academy of Sciences of the United States of America·Camrin D BraunSimon R Thorrold
Sep 9, 2017·Journal of Computer-aided Molecular Design·Xinqiang DingCharles L Brooks
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Jun 9, 2021·Journal of Chemical Theory and Computation·Jonah Z VilseckCharles L Brooks
Jan 29, 2019·Journal of Chemical Theory and Computation·Xinqiang DingCharles L Brooks
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Oct 29, 2021·Journal of Chemical Theory and Computation·Ryan L HayesCharles L Brooks

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