Skip to main content
SpringerLink
Log in

Entropy Production for Mechanically or Chemically Driven Biomolecules

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

Entropy production along a single stochastic trajectory of a biomolecule is discussed for two different sources of non-equilibrium. For a molecule manipulated mechanically by an AFM or an optical tweezer, entropy production (or annihilation) occurs in the molecular conformation proper or in the surrounding medium. Within a Langevin dynamics, a unique identification of these two contributions is possible. The total entropy change obeys an integral fluctuation theorem and a class of further exact relations, which we prove for arbitrarily coupled slow degrees of freedom including hydrodynamic interactions. These theoretical results can therefore also be applied to driven colloidal systems. For transitions between different internal conformations of a biomolecule involving unbalanced chemical reactions, we provide a thermodynamically consistent formulation and identify again the two sources of entropy production, which obey similar exact relations. We clarify the particular role degenerate states have in such a description.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. C. Bustamante, J. Liphardt and F. Ritort, Phys. Today 58:43 (2005).

    Article  Google Scholar 

  2. F. Ritort, Sém. Poincaré 2:63 (2003).

    Google Scholar 

  3. K. Sekimoto, Prog. Theor. Phys. Supp. 130: 17 (1998).

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  5. C. Jarzynski, Phys. Rev. E 56: 5018 (1997).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  7. G. E. Crooks, Phys. Rev. E 61: 2361 (2000).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. J. Liphardt, S. Dumont, S. B. Smith, I. Tinoco Jr. and C. Bustamante, Science 296:1832 (2002).

    Article  ADS  Google Scholar 

  10. O. Braun, A. Hanke and U. Seifert, Phys. Rev. Lett. 93: 158105 (2004).

    Article  ADS  Google Scholar 

  11. S. Park and K. Schulten, J. Chem. Phys. 120:5946 (2004).

    Article  ADS  Google Scholar 

  12. D. Collin, F. Ritort, C. Jarzynski, S. Smith, I. Tinoco and C. Bustamante, Nature 437:231 (2005).

    Article  ADS  Google Scholar 

  13. T. Speck and U. Seifert, Eur. Phys. J. B 43:543 (2005).

    Article  Google Scholar 

  14. T. Speck and U. Seifert, Phys. Rev. E 70:066112 (2004).

    Article  ADS  Google Scholar 

  15. A. Imparato and L.Peliti, Europhys. Lett. 69:643 (2005).

    Article  ADS  Google Scholar 

  16. A. Imparato and L. Peliti, Europhys. Lett. 70:740 (2005).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  18. G. Oster, A. Perelson and A. Katchalsky, Nature 234: 393 (1971).

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  20. T. L. Hill, Free Energy Transduction and Biochemical Cycle Kinetics, 2nd ed. (Dover, 1989).

  21. G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems:From Dissipative Structures to Order through Fluctuations (Wiley, 1977).

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

    Article  ADS  Google Scholar 

  23. D. Andrieux and P. Gaspard, J. Chem. Phys. 121:6167 (2004).

    Article  ADS  Google Scholar 

  24. H.Qian and D. A. Beard, Biophys. Chem. 114:213 (2005).

    Article  Google Scholar 

  25. H. Qian, J. Phys.: Condens. Matter 17:S3783 (2005).

    Article  Google Scholar 

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

  27. U. Seifert, Europhys. Lett. 70:36, (2005).

    Article  ADS  Google Scholar 

  28. P. Schwille, Cell Biochem. Biophys. 34:383 (2001).

    Article  Google Scholar 

  29. X. S. Xie, J. Chem. Phys. 117:11024 (2002).

    Article  ADS  Google Scholar 

  30. H. Qian, Biophys. Chem. 67:263 (1997).

    Article  Google Scholar 

  31. F. Jülicher, A. Adjari and J. Prost, Rev. Mod. Phys. 69:1269 (1997).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  34. H. Qian, Phys. Rev. E 64:022101 (2001).

    Article  ADS  Google Scholar 

  35. P. Reimann, Phys. Rep. 361:57 (2002).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  36. C. Maes and M. H. van Wieren, J. Stat. Phys. 112:329 (2003).

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  38. T. Hatano and S. Sasa, Phys. Rev. Lett. 86:3463 (2001).

    Article  ADS  Google Scholar 

  39. G. M. Wang, E. M. Sevick, E. Mittag, D. J. Searles and D. J. Evans, Phys. Rev. Lett. 89:050601 (2002).

    Article  ADS  Google Scholar 

  40. D. M. Carberry, J. C. Reid, G. M. Wang, E. M. Sevick, D. J. Searles and D. J. Evans, Phys. Rev. Lett. 92:140601 (2004).

    Article  ADS  Google Scholar 

  41. R. van Zon and E. G. D. Cohen, Phys. Rev. Lett. 91:110601 (2003).

    Article  ADS  Google Scholar 

  42. R. van Zon and E. G. D. Cohen, Phys. Rev. E 67:46102 (2003).

    Article  ADS  Google Scholar 

  43. E. H. Trepagnier, C. Jarzynski, F. Ritort, G. E. Crooks, C. J. Bustamante and J. Liphardt, Proc. Natl. Acad. Sci. U.S.A. 101:15038 (2004).

    Article  ADS  Google Scholar 

  44. V. Blickle, T. Speck, L. Helden, U. Seifert and C. Bechinger, Phys. Rev. Lett. 96:070603 (2006).

    Article  ADS  Google Scholar 

  45. M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, Oxford, 1986).

    Google Scholar 

  46. C. Jarzynski, J. Stat. Phys. 96:415 (1999).

    Article  MATH  Google Scholar 

  47. D. A. McQuarrie, Statistical Mechanics, (University Science Books, Sausalito, 2000).

    Google Scholar 

  48. D. J. Evans and D. J. Searles, Phys. Rev. E 50:1645 (1994).

    Article  ADS  Google Scholar 

  49. G. Gallavotti and E. G. D. Cohen, Phys. Rev. Lett. 74:2694 (1995).

    Article  ADS  Google Scholar 

  50. J. Kurchan, J. Phys. A: Math. Gen. 31:3719 (1998).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  51. J. L. Lebowitz and H. Spohn, J. Stat. Phys. 95:333 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  52. C. Maes, Sém. Poincaré 2:29 (2003).

    Google Scholar 

  53. H. Qian, J. Phys. Chem. B 106:2065 (2002).

    Article  Google Scholar 

  54. O. Braun and U. Seifert, Eur. Phys. J. E 18:1 (2005).

    Article  Google Scholar 

  55. T. Schmiedl and U. Seifert, in preparation.

  56. S. Schuler, T. Speck, C. Tietz, J. Wrachtrup and U. Seifert, Phys. Rev. Lett. 94:180602 (2005).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. II. Institut für Theoretische Physik, Universität Stuttgart, 70550, Stuttgart, Germany

    Tim Schmiedl, Thomas Speck & Udo Seifert

Authors
  1. Tim Schmiedl
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Thomas Speck
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Udo Seifert
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

PACS numbers: 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion, 05.70.-a Thermodynamics, 82.39.-k Chemical kinetics in biological systems, 87.15.-v Biomolecules: structure and physical properties

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schmiedl, T., Speck, T. & Seifert, U. Entropy Production for Mechanically or Chemically Driven Biomolecules. J Stat Phys 128, 77–93 (2007). https://doi.org/10.1007/s10955-006-9148-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-006-9148-1

Keywords

Search

Navigation