Skip to main content
Log in

Entropy production of a mechanically driven single oligomeric enzyme: a consequence of fluctuation theorem

  • Original Paper
  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

In this work we have shown how an applied mechanical force affects an oligomeric enzyme kinetics in a chemiostatic condition where the statistical characteristics of random walk of the substrate molecules over a finite number of active sites of the enzyme plays important contributing factors in governing the overall rate and nonequilibrium thermodynamic properties. The analytical results are supported by the simulation of single trajectory based approach of entropy production using Gillespie’s stochastic algorithm. This microscopic numerical approach not only gives the macroscopic entropy production from the mean of the distribution of entropy production which depends on the force but also a broadening of the distribution by the applied mechanical force, a kind of power broadening. In the nonequilibrium steady state (NESS), both the mean and the variance of the distribution increases and then saturates with the rise in applied force corresponding to the situation when the net rate of product formation reaches a limiting value with an activationless transition. The effect of the system-size and force on the entropy production distribution is shown to be constrained by the detailed fluctuation theorem.

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

Access this article

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

    Article  CAS  Google Scholar 

  2. Jarzynski C.: Nat. Phys. 7, 591 (2011)

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  4. Wang H., Oster G.: Nature 396, 279 (1998)

    Article  CAS  Google Scholar 

  5. Carberry D.M., Baker M.A.B., Wang G.M., Sevick E.M., Evans D.J.: J. Opt. A Pure Appl. Opt. 9, S204 (2007)

    Article  Google Scholar 

  6. Hummer G., Szabo A.: Proc. Natl. Acad. Sci. USA 98, 3658 (2001)

    Article  CAS  Google Scholar 

  7. Ritort F., Bustamante C., Tinoco I. Jr.: Proc. Natl. Acad. Sci. USA 99, 13544 (2002)

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  9. Mossa A., De Lorenzo S., Huguet J.M., Ritort F.: J. Chem. Phys. 130, 234116 (2009)

    Article  Google Scholar 

  10. M. Manosas, A. Mossa, N. Forns, J.M. Huguet, F. Ritort, J. Stat. Mech.: Theor. and Expt. 09, P02061 (2009)

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

    Article  CAS  Google Scholar 

  12. Tinoco I. Jr., Bustamante C.: Biophys. Chem. 101, 513 (2002)

    Article  Google Scholar 

  13. Bustamante C., Chemla Y.R., Forde N.R., Izhaky D.: Annu. Rev. Biochem. 73, 705 (2004)

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  16. Crooks G.E.: J. Stat. Phys. 90, 1481 (1998)

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  19. Hatano T., Sasa S.I.: Phys. Rev. Lett. 86, 3463 (2001)

    Article  CAS  Google Scholar 

  20. Esposito M., Vanden Broeck C.: Phys. Rev. Lett. 104, 090601 (2010)

    Article  Google Scholar 

  21. Evans D.J., Cohen E.G.D., Morriss G.P.: Phys. Rev. Lett. 71, 2401 (1993)

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  23. Gallavotti G.: Phys. Rev. Lett. 77, 4334 (1996)

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  25. Lahiri S., Jayannavar A.M.: Eur. Phys. J. B69, 87 (2009)

    Google Scholar 

  26. Sevick E.M., Prabhakar R., Williams S.R., Searles D.J.: Annu. Rev. Phys. Chem. 59, 603 (2008)

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  29. Tietz C., Schuler S., Speck T., Seifert U., Wrachtrup J.: Phys. Rev. Lett. 97, 050602 (2006)

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  31. Seifert U.: Europhys. Lett. 70(1), 36 (2005)

    Article  CAS  Google Scholar 

  32. Wiita A.P., Ainavarapu S.R.K., Huang H.H., Fernandez J.M.: Proc. Natl. Acad. Sci. USA 103, 7222 (2006)

    Article  CAS  Google Scholar 

  33. Wiita A.P., Perez-Jimenez R., Walther K.A., Grater F., Berne B.J., Holmgren A., Sanchez-Ruiz J.M., Fernandez J.M.: Nature 450, 124 (2007)

    Article  CAS  Google Scholar 

  34. Gumpp H., Puchner E.M., Zimmermann J.L., Gerland U., Gaub H.E., Blank K.: Nano Lett. 9, 3290 (2009)

    Article  CAS  Google Scholar 

  35. Adhikari A.S., Chai J., Dunn A.R.: J. Am. Chem. Soc. 133, 1686 (2011)

    Article  CAS  Google Scholar 

  36. Lu H.P., Xun L., Xie X.S.: Science 282, 1877 (1998)

    Article  CAS  Google Scholar 

  37. Kou S.C., Cherayil B.J., Min W., English B.P., Xie X.S.: J. Phys. Chem. B 109, 19068 (2005)

    Article  CAS  Google Scholar 

  38. Yang S., Cao J.: J. Chem. Phys. 117, 10996 (2002)

    Article  CAS  Google Scholar 

  39. Das B., Gangopadhyay G.: J. Chem. Phys. 132, 135102 (2010)

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  41. Migneault I., Dartiguenave C., Bertrand M.J., Waldron K.C.: BioTechniques 37, 790 (2004)

    CAS  Google Scholar 

  42. Bell G.: Science 200, 618 (1978)

    Article  CAS  Google Scholar 

  43. Gardiner C.W.: Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 2nd edn. Springer, New York (1985)

    Google Scholar 

  44. Vankampen N.G.: Stochastic Processes in Physics and Chemistry Amsterdam. Elsevier, The Netherlands (1992)

    Google Scholar 

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

    Article  CAS  Google Scholar 

  46. Jiu-li L., Vanden Broeck C., Nicolis G.: Z. Phys. B 56, 165 (1984)

    Article  Google Scholar 

  47. Nicolis G., Prigogine I.: Self-Organization in Nonequilibrium Systems. Willey, New York (1977)

    Google Scholar 

  48. Vellela M., Qian H.: J.R. Soc. Interface 6, 925 (2009)

    Article  CAS  Google Scholar 

  49. Xiao T.J., Hou Z., Xin H.: J. Chem. Phys. 129, 114506 (2008)

    Article  Google Scholar 

  50. Gillespie D.T.: J. Comput. Phys. 22, 403 (1976)

    Article  CAS  Google Scholar 

  51. Gillespie D.T.: J. Phys. Chem. 81, 2340 (1977)

    Article  CAS  Google Scholar 

  52. Luo J., Zhao N., Hu B.: Phys. Chem. Chem. Phys. 4, 4149 (2002)

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gautam Gangopadhyay.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Das, B., Banerjee, K. & Gangopadhyay, G. Entropy production of a mechanically driven single oligomeric enzyme: a consequence of fluctuation theorem. J Math Chem 51, 588–602 (2013). https://doi.org/10.1007/s10910-012-0099-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-012-0099-2

Keywords

Navigation