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J Chem Phys. 2008 Jul 14;129(2):024102. doi: 10.1063/1.2937892.

Bayesian estimates of free energies from nonequilibrium work data in the presence of instrument noise.

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1
Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA. paul.maragakis@deshaw.com

Abstract

The Jarzynski equality and the fluctuation theorem relate equilibrium free energy differences to nonequilibrium measurements of the work. These relations extend to single-molecule experiments that have probed the finite-time thermodynamics of proteins and nucleic acids. The effects of experimental error and instrument noise have not been considered previously. Here, we present a Bayesian formalism for estimating free energy changes from nonequilibrium work measurements that compensates for instrument noise and combines data from multiple driving protocols. We reanalyze a recent set of experiments in which a single RNA hairpin is unfolded and refolded using optical tweezers at three different rates. Interestingly, the fastest and farthest-from-equilibrium measurements contain the least instrumental noise and, therefore, provide a more accurate estimate of the free energies than a few slow, more noisy, near-equilibrium measurements. The methods we propose here will extend the scope of single-molecule experiments; they can be used in the analysis of data from measurements with atomic force microscopy, optical, and magnetic tweezers.

PMID:
18624511
PMCID:
PMC2669770
DOI:
10.1063/1.2937892
[Indexed for MEDLINE]
Free PMC Article
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