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Stochastic thermodynamics of single enzymes and molecular motors

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Abstract.

For a single enzyme or molecular motor operating in an aqueous solution of non-equilibrated solute concentrations, a thermodynamic description is developed on the level of an individual trajectory of transitions between states. The concept of internal energy, intrinsic entropy and free energy for states follows from a microscopic description using one assumption on time scale separation. A first-law energy balance then allows the unique identification of the heat dissipated in one transition. Consistency with the second law on the ensemble level enforces both stochastic entropy as third contribution to the entropy change involved in one transition and the local detailed balance condition for the ratio between forward and backward rates for any transition. These results follow without assuming weak coupling between the enzyme and the solutes, ideal solution behavior or mass action law kinetics. The present approach highlights both the crucial role of the intrinsic entropy of each state and the physically questionable role of chemiostats for deriving the first law for molecular motors subject to an external force under realistic conditions.

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References

  1. P.R. Selvin, T. Ha, Single Molecule Techniques: A Laboratory Manual (Cold Spring Harbor Laboratory Press, New York, 2007)

  2. F. Ritort, J. Phys.: Condens. Matter 18, R531 (2006)

    Article  ADS  Google Scholar 

  3. J. Howard, Mechanics of Motor Proteins and the Cytoskeleton (Sinauer, New York, 2001)

  4. M. Schliwa, Molecular Motors (Wiley-VCH, Weinheim, 2003)

  5. K. Sekimoto, Stochastic Energetics (Springer-Verlag, Berlin, Heidelberg, 2010)

  6. C. Bustamante, J. Liphardt, F. Ritort, Phys. Today 58 (7), 43 (2005)

    Article  ADS  Google Scholar 

  7. U. Seifert, Eur. Phys. J. B 64, 423 (2008)

    Article  ADS  MATH  Google Scholar 

  8. K. Sekimoto, Prog. Theor. Phys. Suppl. 130, 17 (1998)

    Article  ADS  Google Scholar 

  9. U. Seifert, Phys. Rev. Lett. 95, 040602 (2005)

    Article  ADS  Google Scholar 

  10. G.M. Wang et al., Phys. Rev. Lett. 89, 050601 (2002)

    Article  ADS  Google Scholar 

  11. D.M. Carberry et al., Phys. Rev. Lett. 92, 140601 (2004)

    Article  ADS  Google Scholar 

  12. E.H. Trepagnier et al., Proc. Natl. Acad. Sci. U.S.A. 101, 15038 (2004)

    Article  ADS  Google Scholar 

  13. V. Blickle et al., Phys. Rev. Lett. 96, 070603 (2006)

    Article  ADS  Google Scholar 

  14. J.R. Gomez-Solano, A. Petrosyan, S. Ciliberto, R. Chetrite, Phys. Rev. Lett. 103, 040601 (2009)

    Article  ADS  Google Scholar 

  15. J. Mehl, V. Blickle, U. Seifert, C. Bechinger, Phys. Rev. E 82, 032401 (2010)

    Article  ADS  Google Scholar 

  16. C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)

    Article  ADS  Google Scholar 

  17. G.E. Crooks, Phys. Rev. E 60, 2721 (1999)

    Article  ADS  Google Scholar 

  18. G. Hummer, A. Szabo, Proc. Natl. Acad. Sci. U.S.A. 98, 3658 (2001)

    Article  ADS  Google Scholar 

  19. J. Liphardt et al., Science 296, 1832 (2002)

    Article  ADS  Google Scholar 

  20. D. Collin et al., Nature 437, 231 (2005)

    Article  ADS  Google Scholar 

  21. A. Imparato, S. Luccioli, A. Torcini, Phys. Rev. Lett. 99, 168101 (2007)

    Article  ADS  Google Scholar 

  22. F. Ritort, Adv. Chem. Phys. 137, 31 (2008)

    Article  Google Scholar 

  23. I. Junier, A. Mossa, M. Manosas, F. Ritort, Phys. Rev. Lett. 102, 070602 (2009)

    Article  ADS  Google Scholar 

  24. F. Jülicher, A. Ajdari, J. Prost, Rev. Mod. Phys. 69, 1269 (1997)

    Article  ADS  Google Scholar 

  25. R.D. Astumian, P. Hänggi, Phys. Today 55 (11), 33 (2002)

    Article  ADS  Google Scholar 

  26. P. Reimann, Phys. Rep. 361, 57 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. J.M.R. Parrondo, B.J.D. Cisneros, Appl. Phys. A 75, 179 (2002)

    Article  ADS  Google Scholar 

  28. M.E. Fisher, A.B. Kolomeisky, Proc. Natl. Acad. Sci. U.S.A. 96, 6597 (1999)

    Article  ADS  Google Scholar 

  29. R. Lipowsky, Phys. Rev. Lett. 85, 4401 (2000)

    Article  ADS  Google Scholar 

  30. M.E. Fisher, A.B. Kolomeisky, Proc. Natl. Acad. Sci. U.S.A. 98, 7748 (2001)

    Article  ADS  Google Scholar 

  31. C. Bustamante, D. Keller, G. Oster, Accounts Chem. Res. 34, 412 (2001)

    Article  Google Scholar 

  32. J.E. Baker, J. Theor. Biol. 228, 467 (2004)

    Article  Google Scholar 

  33. D. Andrieux, P. Gaspard, Phys. Rev. E 74, 011906 (2006)

    Article  ADS  Google Scholar 

  34. P. Gaspard, E. Gerritsma, J. Theor. Biol. 247, 672 (2007)

    Article  MathSciNet  Google Scholar 

  35. S. Liepelt, R. Lipowsky, EPL 77, 50002 (2007)

    Article  ADS  Google Scholar 

  36. S. Liepelt, R. Lipowsky, Phys. Rev. Lett. 98, 258102 (2007)

    Article  ADS  Google Scholar 

  37. R. Lipowsky, S. Liepelt, J. Stat. Phys. 130, 39 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  38. S. Liepelt, R. Lipowsky, Phys. Rev. E 79, 011917 (2009)

    Article  ADS  Google Scholar 

  39. R. Lipowsky, S. Liepelt, J. Stat. Phys. 135, 777 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  40. A.W.C. Lau, D. Lacoste, K. Mallick, Phys. Rev. Lett. 99, 158102 (2007)

    Article  ADS  Google Scholar 

  41. A.B. Kolomeisky, M.E. Fischer, Annu. Rev. Phys. Chem. 58, 675 (2007)

    Article  ADS  Google Scholar 

  42. R.D. Astumian, Biophys. J. 98, 2401 (2010)

    Article  ADS  Google Scholar 

  43. U. Seifert, Europhys. Lett. 70, 36 (2005)

    Article  ADS  Google Scholar 

  44. T. Schmiedl, T. Speck, U. Seifert, J. Stat. Phys. 128, 77 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  45. W. Min et al., NanoLett. 5, 2373 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  46. T. Shibata, cond-mat/0012404 (2000)

  47. P. Gaspard, J. Chem. Phys. 120, 8898 (2004)

    Article  ADS  Google Scholar 

  48. T. Schmiedl, U. Seifert, J. Chem. Phys. 126, 044101 (2007)

    Article  ADS  Google Scholar 

  49. H. Ge, H. Qian, Phys. Rev. E 81, 051133 (2010)

    Article  ADS  Google Scholar 

  50. K. Sekimoto, Phys. Rev. E 76, 060103(R) (2007)

    Article  ADS  Google Scholar 

  51. T.L. Hill, Free Energy Transduction and Biochemical Cycle Kinetics, 2nd ed. (Dover, Mineola, New York, 1989)

  52. K. Svoboda, C.F. Schmidt, B.J. Schnapp, S.M. Block, Nature 365, 721 (1993)

    Article  ADS  Google Scholar 

  53. J. Schnakenberg, Rev. Mod. Phys. 48, 571 (1976)

    Article  MathSciNet  ADS  Google Scholar 

  54. J.L. Luo, C. van den Broeck, G. Nicolis, Z. Phys. B Cond. Mat. 56, 165 (1984)

    Article  ADS  Google Scholar 

  55. C.Y. Mou, J.-L. Luo, G. Nicolis, J. Chem. Phys. 84, 7011 (1986)

    Article  ADS  Google Scholar 

  56. H. Qian, D.A. Beard, Biophys. Chem. 114, 213 (2005)

    Article  Google Scholar 

  57. S. Toyabe et al., Phys. Rev. Lett. 104, 198103 (2010)

    Article  ADS  Google Scholar 

  58. K. Hayashi, H. Ueno, R. Iino, H. Noji, Phys. Rev. Lett. 104, 218103 (2010)

    Article  ADS  Google Scholar 

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Seifert, U. Stochastic thermodynamics of single enzymes and molecular motors. Eur. Phys. J. E 34, 26 (2011). https://doi.org/10.1140/epje/i2011-11026-7

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