Measurement of work in single-molecule pulling experiments.

A main goal of single-molecule experiments is to evaluate equilibrium free energy differences by applying fluctuation relations to repeated work measurements along irreversible processes. We quantify the error that is made in a free energy estimate by means of the Jarzynski equality when the accumulated work expended on the whole system (including the instrument) is erroneously replaced by the work transferred to the subsystem consisting of the sole molecular construct. We find that the error may be as large as 100%, depending on the number of experiments and on the bandwidth of the data acquisition apparatus. Our theoretical estimate is validated by numerical simulations and pulling experiments on DNA hairpins using optical tweezers.

[1]  G. Crooks.  Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  G. Hummer,et al.  Free energy reconstruction from nonequilibrium single-molecule pulling experiments , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[3]  Martin Karplus,et al.  Bayesian estimates of free energies from nonequilibrium work data in the presence of instrument noise. , 2007, The Journal of chemical physics.

[4]  R. Astumian.  Equilibrium theory for a particle pulled by a moving optical trap. , 2006, The Journal of chemical physics.

[5]  U. Seifert,et al.  Probing molecular free energy landscapes by periodic loading. , 2004, Physical review letters.

[6]  F. Sbrana,et al.  Reconstructing the free-energy landscape of a polyprotein by single-molecule experiments , 2008, 0804.2980.

[7]  E. Bertin,et al.  Generalized extreme value statistics and sum of correlated variables , 2006, cond-mat/0601189.

[8]  F. Ritort,et al.  Dynamic force spectroscopy of DNA hairpins: I. Force kinetics and free energy landscapes , 2009, 0902.3632.

[9]  F. Ritort,et al.  Thermodynamic and kinetic aspects of RNA pulling experiments. , 2004, Biophysical journal.

[10]  I. Tinoco,et al.  Equilibrium Information from Nonequilibrium Measurements in an Experimental Test of Jarzynski's Equality , 2002, Science.

[11]  Michael R. Shirts,et al.  Equilibrium free energies from nonequilibrium measurements using maximum-likelihood methods. , 2003, Physical review letters.

[12]  Ignacio Tinoco,et al.  Force as a useful variable in reactions: unfolding RNA. , 2004, Annual review of biophysics and biomolecular structure.

[13]  Christopher Jarzynski,et al.  Fluctuation relations and coarse-graining , 2007, 0708.2437.

[14]  F. Ritort,et al.  Nonequilibrium fluctuations in small systems: From physics to biology , 2007, 0705.0455.

[15]  Carlos Bustamante,et al.  Optical-trap force transducer that operates by direct measurement of light momentum. , 2003, Methods in enzymology.

[16]  Estimate of the free energy difference in mechanical systems from work fluctuations: experiments and models , 2005, cond-mat/0504465.

[17]  Eric Bertin,et al.  Global fluctuations and Gumbel statistics. , 2005, Physical review letters.

[18]  L. Peliti,et al.  Evaluation of free energy landscapes from manipulation experiments , 2006 .

[19]  C. Kiang,et al.  Experimental free energy surface reconstruction from single-molecule force spectroscopy using Jarzynski's equality. , 2007, Physical review letters.

[20]  C. Jarzynski.  Nonequilibrium Equality for Free Energy Differences , 1996, cond-mat/9610209.

[21]  The nonequilibrium thermodynamics of small systems , 2007 .

[22]  A. Vulpiani,et al.  Fluctuation-dissipation: Response theory in statistical physics , 2008, 0803.0719.

[23]  F. Ritort,et al.  Force-dependent fragility in RNA hairpins. , 2006, Physical review letters.

[24]  David D L Minh,et al.  Optimized free energies from bidirectional single-molecule force spectroscopy. , 2008, Physical review letters.

[25]  F. Ritort,et al.  A two-state kinetic model for the unfolding of single molecules by mechanical force , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[26]  F. Ritort,et al.  Dynamic force spectroscopy of DNA hairpins: II. Irreversibility and dissipation , 2009, 0902.3634.

[27]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[28]  D. Herschlag,et al.  Nanomechanical measurements of the sequence-dependent folding landscapes of single nucleic acid hairpins. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[29]  F. Ritort,et al.  Methods and Applications , 2006 .

[30]  宁北芳,et al.  疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A , 2005 .

[31]  Bryant S. Fujimoto,et al.  Equalities for the Nonequilibrium Work Transferred from an External Potential to a Molecular System. Analysis of Single-Molecule Extension Experiments , 2003 .

[32]  F. Douarche,et al.  An experimental test of the Jarzynski equality in a mechanical experiment , 2005 .

[33]  Changbong Hyeon,et al.  Force-dependent hopping rates of RNA hairpins can be estimated from accurate measurement of the folding landscapes , 2008, Proceedings of the National Academy of Sciences.

[34]  F. Ritort,et al.  Bias and error in estimates of equilibrium free-energy differences from nonequilibrium measurements , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[35]  D. Herschlag,et al.  Direct Measurement of the Full, Sequence-Dependent Folding Landscape of a Nucleic Acid , 2006, Science.

[36]  Gerhard Hummer,et al.  Free energy surfaces from single-molecule force spectroscopy. , 2005, Accounts of chemical research.

[37]  C. Jarzynski,et al.  Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies , 2005, Nature.

[38]  D. Thirumalai,et al.  Measuring the energy landscape roughness and the transition state location of biomolecules using single molecule mechanical unfolding experiments , 2006, Journal of Physics: Condensed Matter.

[39]  Asymmetry of the work probability distribution , 2006, cond-mat/0612423.