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.
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14 July 2008
Research Article|
July 08 2008
Bayesian estimates of free energies from nonequilibrium work data in the presence of instrument noise
Paul Maragakis;
1Department of Chemistry and Chemical Biology,
Harvard University
, Cambridge, Massachusetts 02138, USA
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Felix Ritort;
Felix Ritort
2Departament de Física Fonamental, Facultat de Física and CIBER-BBN, Networking Centre on Bioengineering, Biomaterials and Nanomedicine,
Universitat de Barcelona
, 08028 Barcelona, Spain
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Carlos Bustamante;
Carlos Bustamante
3Howard Hughes Medical Institute and Departments of Physics and Molecular and Cell Biology,
University of California
, Berkeley, California 94720, USA
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Martin Karplus;
Martin Karplus
1Department of Chemistry and Chemical Biology,
Harvard University
, Cambridge, Massachusetts 02138, USA
4Laboratoire de Chimie Biophysique, Institut de Science et d’Ingénierie Supramoléculaires,
Université Louis Pasteur
, F-67083 Strasbourg Cedex, France
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Gavin E. Crooks
5Physical Biosciences Division,
Lawrence Berkeley National Laboratory
, Berkeley, California 94720, USA
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Paul Maragakis
1
Felix Ritort
2
Carlos Bustamante
3
Martin Karplus
1,4
Gavin E. Crooks
5
1Department of Chemistry and Chemical Biology,
Harvard University
, Cambridge, Massachusetts 02138, USA
2Departament de Física Fonamental, Facultat de Física and CIBER-BBN, Networking Centre on Bioengineering, Biomaterials and Nanomedicine,
Universitat de Barcelona
, 08028 Barcelona, Spain
3Howard Hughes Medical Institute and Departments of Physics and Molecular and Cell Biology,
University of California
, Berkeley, California 94720, USA
4Laboratoire de Chimie Biophysique, Institut de Science et d’Ingénierie Supramoléculaires,
Université Louis Pasteur
, F-67083 Strasbourg Cedex, France
5Physical Biosciences Division,
Lawrence Berkeley National Laboratory
, Berkeley, California 94720, USA
a)
Present address: D. E. Shaw Research, New York, New York 10036, USA. Electronic mail: [email protected].
b)
Electronic mail: [email protected].
J. Chem. Phys. 129, 024102 (2008)
Article history
Received:
June 14 2007
Accepted:
May 09 2008
Citation
Paul Maragakis, Felix Ritort, Carlos Bustamante, Martin Karplus, Gavin E. Crooks; Bayesian estimates of free energies from nonequilibrium work data in the presence of instrument noise. J. Chem. Phys. 14 July 2008; 129 (2): 024102. https://doi.org/10.1063/1.2937892
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