Skip to main content

Nonequilibrium Methods for Equilibrium Free Energy Calculations

  • Chapter

Part of the book series: Springer Series in CHEMICAL PHYSICS ((CHEMICAL,volume 86))

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   299.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   379.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   379.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Jarzynski, C., Nonequilibrium equality for free energy differences, Phys. Rev. Lett. 1997,78,2690-2693

    Article  CAS  Google Scholar 

  2. Jarzynski, C., Equilibrium free energy differences from nonequilibrium measurements. A master-equation approach, Phys. Rev. E 1997, 56, 5018-5035

    Article  CAS  Google Scholar 

  3. Hummer, G.; Szabo, A., Free energy reconstruction from nonequilibrium single-molecule pulling experiments, Proc. Natl Acad. Sci. USA 2001, 98, 3658-3661

    Article  CAS  Google Scholar 

  4. Liphardt, J.; Dumont, S.; Smith, S. B.; Tinoco, I.; Bustamante, C., Equilibrium information from nonequilibrium measurements in an experimental test of Jarzynski’s equality, Science 2002, 296, 1832-1835

    Article  CAS  Google Scholar 

  5. Noy, A., Direct determination of the equilibrium unbinding potential profile for a short DNA duplex from force spectroscopy data, Appl. Phys. Lett. 2004, 85, 4792-4794

    Article  CAS  Google Scholar 

  6. Trepagnier, E. H.; Jarzynski, C.; Ritort, F.; Crooks, G. E.; Bustamante, C. J.; Liphardt, J., Experimental test of Hatano and Sasa’s nonequilibrium steady-state equality, Proc. Natl Acad. Sci. USA 2004, 101, 15038-15041

    Article  CAS  Google Scholar 

  7. Born, M., Volumen und Hydratationsw ärme der Ionen, Z. Phys. 1920, 1, 45-48

    Article  CAS  Google Scholar 

  8. Postma, J. P. M.; Berendsen, H. J. C.; Haak, J. R., Thermodynamics of cavity formation in water. A molecular dynamics study, Faraday Symp. Chem. Soc. 1982, 17, 55

    Article  Google Scholar 

  9. Straatsma, T. P.; Berendsen, H. J. C.; Postma, J. P. M., Free energy of hydrophobic hydration. A molecular dynamics study of noble gases in water, J. Chem. Phys. 1986, 85,6720-6727

    Article  CAS  Google Scholar 

  10. Wood, R. H.; M ühlbauer, W. C. F.; Thompson, P. T., Systematic errors in free energy perturbation calculations due to a finite sample of configuration space. Sample-size hys-teresis, J. Phys. Chem. 1991, 95, 6670-6675

    Article  CAS  Google Scholar 

  11. Hermans, J., Simple analysis of noise and hysteresis in (slow-growth) free energy simulations, J. Phys. Chem. 1991, 95, 9029-9032

    Article  CAS  Google Scholar 

  12. Zwanzig, R. W., High-temperature equation of state by a perturbation method. I. Non-polar gases, J. Chem. Phys. 1954, 22, 1420-1426

    Article  CAS  Google Scholar 

  13. Oberhofer, H.; Dellago, C.; Geissler, P. L., Biased sampling of nonequilibrium trajectories. Can fast switching simulations outperform conventional free energy cal-culation methods, J. Phys. Chem. B 2005, 109, 6902-6915

    Article  CAS  Google Scholar 

  14. Roepstorff, G., Path Integral Approach to Quantum Physics, Springer: Berlin, Heidelberg, New York, 1994

    Google Scholar 

  15. Hummer, G.; Szabo, A., Free energy surfaces from single-molecule force spectroscopy, Acc. Chem. Res. 2005, 38, 504-513

    Article  CAS  Google Scholar 

  16. Crooks, G. E., Path-ensemble averages in systems driven far from equilibrium, Phys. Rev. E 2000, 61, 2361-2366

    Article  CAS  Google Scholar 

  17. Hatano, T.; Sasa, S., Steady-state thermodynamics of Langevin systems, Phys. Rev. Lett. 2001,86,3463-3466

    Article  CAS  Google Scholar 

  18. Crooks, G. E., Nonequilibrium measurements of free energy differences for microscopically reversible Markovian systems, J. Stat. Phys. 1998, 90, 1481-1487

    Article  Google Scholar 

  19. Crooks, G. E., Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences, Phys. Rev. E 1999, 60, 2721-2726

    Article  CAS  Google Scholar 

  20. Hummer, G., Fast-growth thermodynamic integration error and efficiency analysis, J. Chem. Phys. 2001, 114, 7330-7337

    Article  CAS  Google Scholar 

  21. Bennett, C. H., Efficient estimation of free energy differences from Monte Carlo data, J. Comput. Phys. 1976, 22, 245-268

    Article  Google Scholar 

  22. Shirts, M. R.; Bair, E.; Hooker, G.; Pande, V. S., Equilibrium free energies from non-equilibrium measurements using maximum-likelihood methods, Phys. Rev. Lett. 2003, 91,140601

    Article  Google Scholar 

  23. Shirts, M. R.; Pande, V. S., Comparison of efficiency and bias of free energies computed by exponential averaging. The Bennett acceptance ratio and thermodynamic integration, J. Chem. Phys. 2005, 122, 144107

    Article  Google Scholar 

  24. Allen, M. P.; Tildesley, D. J., Computer Simulation of Liquids, Clarendon: Oxford, UK, 1987

    Google Scholar 

  25. Lechner, W.; Oberhofer, H.; Dellago, C.; Geissler, P. L., Equilibrium free energies from fast-switching trajectories with large time steps, J. Chem. Phys. 2006, 124, 044113

    Article  Google Scholar 

  26. Reinhardt, W. P.; Hunter III, J. E., Variational path optimization and upper and lower bounds for the free energy via finite time minimization of the external work, J. Chem. Phys. 1992, 97, 1599-1601

    Article  Google Scholar 

  27. Miller, M. A.; Reinhardt, W. P., Efficient free energy calculations by variationally op-timized metric scaling concepts and applications to the volume dependence of cluster free energies and to solid-solid phase transitions, J. Chem. Phys. 2000, 113, 7035-7046

    Article  CAS  Google Scholar 

  28. Best, R. B.; Hummer, G., Reaction coordinates and rates from transition paths, Proc. Natl Acad. Sci. USA 2005, 102, 6732-6737

    Article  CAS  Google Scholar 

  29. Chandler, D., Statistical mechanics of isomerization dynamics in liquids and the transition state approximation, J. Chem. Phys. 1978, 68, 2959-2970

    Article  CAS  Google Scholar 

  30. Hummer, G., From transition paths to transition states and rate coefficients, J. Chem. Phys. 2004, 120, 516-523

    Article  CAS  Google Scholar 

  31. Jarzynski, C., Rare events and the convergence of exponentially averaged work values, Phys. Rev. E 2006, 73, 046105

    Article  Google Scholar 

  32. Frenkel, D., Free-energy computation and first-order phase transitions. In Molecular Dynamics Simulations of Statistical Mechanical Systems. Proceedings of the Enrico Fermi Summer School, Varenna, 1985 (Amsterdam, 1986), Ciccotti, G.; Hoover, W. G., Eds., North-Holland, pp. 151-188

    Google Scholar 

  33. Gore, J.; Ritort, F.; Bustamante, C., Bias and error in estimates of equilibrium free-energy differences from nonequilibrium measurements, Proc. Natl Acad. Sci. USA 2003,100,12564-12569

    Article  CAS  Google Scholar 

  34. Zuckerman, D. M.; Woolf, T. B., Theory of a systematic computational error in free energy differences, Phys. Rev. Lett. 2002, 89, 180602

    Article  Google Scholar 

  35. Wu, D.; Kofke, D. A., Asymmetric bias in free-energy perturbation measurements using two Hamiltonian-based models, Phys. Rev. E 2004, 70, 066702

    Article  Google Scholar 

  36. Zuckerman, D. M.; Woolf, T. B., Overcoming finite-sampling errors in fast-switching free-energy estimates. Extrapolative analysis of a molecular system, Chem. Phys. Lett. 2002,351,445-453

    Article  CAS  Google Scholar 

  37. Ytreberg, F. M.; Zuckerman, D. M., Efficient use of nonequilibrium measurement to estimate free energy differences for molecular systems, J. Comp. Chem. 2004, 25, 1749-1759

    Article  CAS  Google Scholar 

  38. Rodriguez-Gomez, D.; Darve, E.; Pohorille, A., Assessing the efficiency of free energy calculation methods, J. Chem. Phys. 2004, 120, 3563-3578

    Article  CAS  Google Scholar 

  39. Hummer, G.; Szabo, A., Calculation of free energy differences from computer simulations of initial and final states, J. Chem. Phys. 1996, 105, 2004-2010

    Article  CAS  Google Scholar 

  40. Grubm üller, H.; Heymann, B.; Tavan, P., Ligand binding molecular mechanics calcula-tion of the streptavidin biotin rupture force, Science 1996, 271, 997-999

    Article  Google Scholar 

  41. Izrailev, S.; Stepaniants, S.; Balsera, M.; Oono, Y.; Schulten, K., Molecular dynamics study of unbinding of the avidin-biotin complex, Biophys. J. 1997, 72, 1568-1581

    Article  CAS  Google Scholar 

  42. Paci, E.; Karplus, M., Forced unfolding of fibronectin type 3 modules. An analysis by biased molecular dynamics simulations, J. Mol. Biol. 1999, 288, 441-459

    Article  CAS  Google Scholar 

  43. Park, S.; Schulten, K., Calculating potentials of mean force from steered molecular dynamics simulations, J. Chem. Phys. 2004, 120, 5946-5961

    Article  CAS  Google Scholar 

  44. Ferrenberg, A. M.; Swendsen, R. H., Optimized Monte Carlo data analysis, Phys. Rev. Lett. 1989, 63, 1195-1198

    Article  CAS  Google Scholar 

  45. Park, S.; Khalili-Araghi, F.; Tajkhorshid, E.; Schulten, K., Free energy calculation from steered molecular dynamics simulations using Jarzynski’s equality, J. Chem. Phys. 2003,119,3559-3566

    Article  CAS  Google Scholar 

  46. Sun, S. X., Equilibrium free energies from path sampling of nonequilibrium trajectories, J. Chem. Phys. 2003, 118, 5769-5775

    Article  CAS  Google Scholar 

  47. Ytreberg, F. M.; Zuckerman, D. M., Single-ensemble nonequilibrium path-sampling estimates of free energy differences, J. Chem. Phys. 2004, 120, 10876-10879

    Article  CAS  Google Scholar 

  48. Hendrix, D. A.; Jarzynski, C., A fast growth method of computing free energy differences, J. Chem. Phys. 2001, 114, 5974-5981

    Article  CAS  Google Scholar 

  49. Hummer, G., Fast-growth thermodynamic integration results for sodium ion hydration, Mol. Simul. 2002, 28, 81-90

    Article  CAS  Google Scholar 

  50. Hu, H.; Yun, R. H.; Hermans, J., Reversibility of free energy simulations slow growth may have a unique advantage with a note on use of Ewald summation, Mol. Simul. 2002, 28,67-80

    Article  CAS  Google Scholar 

  51. Darve, E.; Pohorille, A., Calculating free energies using average force, J. Chem. Phys. 2001,115,9169-9183

    Article  CAS  Google Scholar 

  52. Marszalek, P. E.; Lu, H.; Li, H. B.; Carrion-Vazquez, M.; Oberhauser, A. F.; Schulten, K.; Fernandez, J. M., Mechanical unfolding intermediates in titin modules, Nature 1999, 402, 100-103

    Article  CAS  Google Scholar 

  53. Jensen, M. O.; Park, S.; Tajkhorshid, E.; Schulten, K., Energetics of glycerol conduction through aquaglyceroporin glpf, Proc. Natl Acad. Sci. USA 2002, 99, 6731-6736

    Article  CAS  Google Scholar 

  54. Amaro, R.; Luthey-Schulten, Z., Molecular dynamics simulations of substrate channeling through an alpha-beta barrel protein, Chem. Phys. 2004, 307, 147-155

    Article  CAS  Google Scholar 

  55. Mukamel, S., Quantum extension of the Jarzynski relation analogy with stochastic de-phasing, Phys. Rev. Lett. 2003, 90, 170604

    Article  Google Scholar 

  56. Jarzynski, C.; Wojcik, D. K., Classical and quantum fluctuation theorems for heat exchange, Phys. Rev. Lett. 2004, 92, 230602

    Article  Google Scholar 

  57. De Roeck, W.; Maes, C., Quantum version of free-energy-irreversible-work relations, Phys. Rev. E 2004, 69, 026115

    Article  Google Scholar 

  58. Atilgan, E.; Sun, S. X., Equilibrium free energy estimates based on nonequilibrium work relations and extended dynamics, J. Chem. Phys. 2004, 121, 10392-10400

    Article  CAS  Google Scholar 

  59. Ytreberg, F. M.; Zuckerman, D. M., Peptide conformational equilibria computed via a single-stage shifting protocol, J. Phys. Chem. B 2005, 109, 9096-9103

    Article  CAS  Google Scholar 

  60. Chernyak, V.; Chertkov, M.; Jarzynski, C., Dynamical generalization of nonequilibrium work relation, Phys. Rev. E 2005, 71, 025102

    Article  CAS  Google Scholar 

  61. Rodinger, T.; Pom ès, R., Enhancing the accuracy the efficiency and the scope of free energy simulations, Curr. Opin. Struct. Biol. 2005, 15, 164-170

    Article  CAS  Google Scholar 

  62. De Koning, M., Optimizing the driving function for nonequilibrium free-energy calculations in the linear regime. A variational approach, J. Chem. Phys. 2005, 122, 104106

    Article  Google Scholar 

  63. Lua, R. C.; Grosberg, A. Y., Practical applicability of the Jarzynski relation in statistical mechanics. A pedagogical example, J. Phys. Chem. B 2005, 109, 6805-6811

    Article  CAS  Google Scholar 

  64. Adib, A. B., Entropy and density of states from isoenergetic nonequilibrium processes, Phys. Rev. E 2005, 71, 056128

    Article  Google Scholar 

  65. Collin, D.; Ritort, F.; Jarzynski, C.; Smith, S.B.; Tinoco, I.; Bustamante, C. Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies. Nature 2005,437,231-234

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Hummer, G. (2007). Nonequilibrium Methods for Equilibrium Free Energy Calculations. In: Chipot, C., Pohorille, A. (eds) Free Energy Calculations. Springer Series in CHEMICAL PHYSICS, vol 86. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-38448-9_5

Download citation

Publish with us

Policies and ethics