On the Relative Merits of Equilibrium and Non-Equilibrium Simulations for the Estimation of Free-Energy Differences

Xavier Daura, Roman Affentranger, Alan E. Mark

Research output: Contribution to journalArticleResearchpeer-review

9 Citations (Scopus)

Abstract

The possibility of estimating equilibrium free-energy profiles from multiple non-equilibrium simulations using the fluctuation-dissipation theory or the relation proposed by Jarzynski has attracted much attention. Although the Jarzynski estimator has poor convergence properties for simulations far from equilibrium, corrections have been derived for cases in which the work is Gaussian distributed. Here, we examine the utility of corrections proposed by Gore and collaborators using a simple dissipative system as a test case. The system consists of a single methane-like particle in explicit water. The Jarzynski equality is used to estimate the change in free energy associated with pulling the methane particle a distance of 3.9 nm at rates ranging from 0.1 to 100 m s-1. It is shown that although the corrections proposed by Gore and collaborators have excellent numerical performance, the profiles still converge slowly. Even when the corrections are applied in an ideal case where the work distribution is necessarily Gaussian, performing simulations under quasi-equilibrium conditions is still most efficient. Furthermore, it is shown that even for a single methane molecule in water, pulling rates as low as 1 m s-1 can be problematic. The implications of this finding for studies in which small molecules or even large biomolecules are pulled through inhomogeneous environments at similar pulling rates are discussed.Moving targets: A simple dissipative system is used to test the merits of performing equilibrium or non-equilibrium simulations to estimate free-energy differences. For moving a single methane molecule in water (see picture), where the work distribution is Gaussian, simulating under quasi-equilibrium conditions is most efficient. For non-equilibrium approaches, pulling rates as low as 1 nm ns-1 are problematic, casting doubt on the validity of many studies involving biomolecules. © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Original languageEnglish
Pages (from-to)3734-3743
JournalChemPhysChem
Volume11
DOIs
Publication statusPublished - 1 Dec 2010

Keywords

  • Computational chemistry
  • Equilibrium/nonequilibrium simulations
  • Free-energy difference
  • Molecular dynamics
  • Thermodynamics

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