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Journal of Chemical Physics / Volume 129 / Issue 12 / ARTICLES / Theoretical Methods and Algorithms

J. Chem. Phys. 129, 124105 (2008); http://dx.doi.org/10.1063/1.2978177 (10 pages)

Statistically optimal analysis of samples from multiple equilibrium states

Michael R. Shirts1 and John D. Chodera2

1Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22904, USA
2Department of Chemistry, Stanford University, Stanford, California 94305, USA

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(Received 17 June 2008; accepted 15 August 2008; published online 23 September 2008)

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.

© 2008 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. EXTENDED BRIDGE SAMPLING ESTIMATORS
  3. FREE ENERGIES
  4. EQUILIBRIUM EXPECTATIONS
  5. APPLICATION TO LABORATORY EXPERIMENTS
  6. DISCUSSION

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KEYWORDS and PACS

Keywords

DNA, free energy, statistical analysis, thermodynamics

PACS

  • 31.15.bt

    Statistical model calculations (including Thomas-Fermi and Thomas-Fermi-Dirac models)

  • 05.70.Ce

    Thermodynamic functions and equations of state

  • 02.50.-r

    Probability theory, stochastic processes, and statistics

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.2978177

PUBLICATION DATA

ISSN

0021-9606 (print)  
1089-7690 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
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