Journal of Mathematical Chemistry

, Volume 51, Issue 2, pp 588–602

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

  • Biswajit Das
  • Kinshuk Banerjee
  • Gautam Gangopadhyay
Original Paper

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.

Keywords

Oligomeric enzyme kinetics Nonequilibrium steady state Single trajectory analysis Fluctuation theorem 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Collin D., Ritort F., Jarzynski C., Smith S.B., Tinoco I. Jr., Bustamante C.: Nature 437, 231 (2005)CrossRefGoogle Scholar
  2. 2.
    Jarzynski C.: Nat. Phys. 7, 591 (2011)CrossRefGoogle Scholar
  3. 3.
    Liphardt J., Dumont S., Smith S.B., Tinoco I. Jr., Bustamante C.: Science 296, 1832 (2002)CrossRefGoogle Scholar
  4. 4.
    Wang H., Oster G.: Nature 396, 279 (1998)CrossRefGoogle Scholar
  5. 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)CrossRefGoogle Scholar
  6. 6.
    Hummer G., Szabo A.: Proc. Natl. Acad. Sci. USA 98, 3658 (2001)CrossRefGoogle Scholar
  7. 7.
    Ritort F., Bustamante C., Tinoco I. Jr.: Proc. Natl. Acad. Sci. USA 99, 13544 (2002)CrossRefGoogle Scholar
  8. 8.
    Bustamante C., Liphardt J., Ritort F.: Phys. Today 58, 43 (2005)CrossRefGoogle Scholar
  9. 9.
    Mossa A., De Lorenzo S., Huguet J.M., Ritort F.: J. Chem. Phys. 130, 234116 (2009)CrossRefGoogle Scholar
  10. 10.
    M. Manosas, A. Mossa, N. Forns, J.M. Huguet, F. Ritort, J. Stat. Mech.: Theor. and Expt. 09, P02061 (2009)Google Scholar
  11. 11.
    Ritort F.: Adv. Chem. Phys. 137, 31 (2008)CrossRefGoogle Scholar
  12. 12.
    Tinoco I. Jr., Bustamante C.: Biophys. Chem. 101, 513 (2002)CrossRefGoogle Scholar
  13. 13.
    Bustamante C., Chemla Y.R., Forde N.R., Izhaky D.: Annu. Rev. Biochem. 73, 705 (2004)CrossRefGoogle Scholar
  14. 14.
    Jarzynski C.: Phys. Rev. Lett. 78, 2690 (1997)CrossRefGoogle Scholar
  15. 15.
    Jarzynski C.: Phys. Rev. E 56, 5018 (1997)CrossRefGoogle Scholar
  16. 16.
    Crooks G.E.: J. Stat. Phys. 90, 1481 (1998)CrossRefGoogle Scholar
  17. 17.
    Crooks G.E.: Phys. Rev. E 60, 2721 (1999)CrossRefGoogle Scholar
  18. 18.
    Seifert U.: Phys. Rev. Lett. 95, 040602 (2005)CrossRefGoogle Scholar
  19. 19.
    Hatano T., Sasa S.I.: Phys. Rev. Lett. 86, 3463 (2001)CrossRefGoogle Scholar
  20. 20.
    Esposito M., Vanden Broeck C.: Phys. Rev. Lett. 104, 090601 (2010)CrossRefGoogle Scholar
  21. 21.
    Evans D.J., Cohen E.G.D., Morriss G.P.: Phys. Rev. Lett. 71, 2401 (1993)CrossRefGoogle Scholar
  22. 22.
    Gallavotti G., Cohen E.G.D.: Phys. Rev. Lett. 74, 2694 (1995)CrossRefGoogle Scholar
  23. 23.
    Gallavotti G.: Phys. Rev. Lett. 77, 4334 (1996)CrossRefGoogle Scholar
  24. 24.
    Lebowitz J.L., Spohn H.: J. Stat. Phys. 95, 333 (1999)CrossRefGoogle Scholar
  25. 25.
    Lahiri S., Jayannavar A.M.: Eur. Phys. J. B69, 87 (2009)Google Scholar
  26. 26.
    Sevick E.M., Prabhakar R., Williams S.R., Searles D.J.: Annu. Rev. Phys. Chem. 59, 603 (2008)CrossRefGoogle Scholar
  27. 27.
    Schmiedl T., Seifert U.: J. Chem. Phys. 126, 044101 (2007)CrossRefGoogle Scholar
  28. 28.
    Blickle V., Speck T., Helden L., Seifert U., Bechinger C.: Phys. Rev. Lett. 96, 070603 (2006)CrossRefGoogle Scholar
  29. 29.
    Tietz C., Schuler S., Speck T., Seifert U., Wrachtrup J.: Phys. Rev. Lett. 97, 050602 (2006)CrossRefGoogle Scholar
  30. 30.
    Schmiedl T., Speck T., Seifert U.: J. Stat. Phys. 128, 77 (2007)CrossRefGoogle Scholar
  31. 31.
    Seifert U.: Europhys. Lett. 70(1), 36 (2005)CrossRefGoogle Scholar
  32. 32.
    Wiita A.P., Ainavarapu S.R.K., Huang H.H., Fernandez J.M.: Proc. Natl. Acad. Sci. USA 103, 7222 (2006)CrossRefGoogle Scholar
  33. 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)CrossRefGoogle Scholar
  34. 34.
    Gumpp H., Puchner E.M., Zimmermann J.L., Gerland U., Gaub H.E., Blank K.: Nano Lett. 9, 3290 (2009)CrossRefGoogle Scholar
  35. 35.
    Adhikari A.S., Chai J., Dunn A.R.: J. Am. Chem. Soc. 133, 1686 (2011)CrossRefGoogle Scholar
  36. 36.
    Lu H.P., Xun L., Xie X.S.: Science 282, 1877 (1998)CrossRefGoogle Scholar
  37. 37.
    Kou S.C., Cherayil B.J., Min W., English B.P., Xie X.S.: J. Phys. Chem. B 109, 19068 (2005)CrossRefGoogle Scholar
  38. 38.
    Yang S., Cao J.: J. Chem. Phys. 117, 10996 (2002)CrossRefGoogle Scholar
  39. 39.
    Das B., Gangopadhyay G.: J. Chem. Phys. 132, 135102 (2010)CrossRefGoogle Scholar
  40. 40.
    Andrieux D., Gaspard P.: J. Chem. Phys. 121, 6167 (2004)CrossRefGoogle Scholar
  41. 41.
    Migneault I., Dartiguenave C., Bertrand M.J., Waldron K.C.: BioTechniques 37, 790 (2004)Google Scholar
  42. 42.
    Bell G.: Science 200, 618 (1978)CrossRefGoogle Scholar
  43. 43.
    Gardiner C.W.: Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 2nd edn. Springer, New York (1985)Google Scholar
  44. 44.
    Vankampen N.G.: Stochastic Processes in Physics and Chemistry Amsterdam. Elsevier, The Netherlands (1992)Google Scholar
  45. 45.
    Gaspard P.: J. Chem. Phys. 120, 8898 (2004)CrossRefGoogle Scholar
  46. 46.
    Jiu-li L., Vanden Broeck C., Nicolis G.: Z. Phys. B 56, 165 (1984)CrossRefGoogle Scholar
  47. 47.
    Nicolis G., Prigogine I.: Self-Organization in Nonequilibrium Systems. Willey, New York (1977)Google Scholar
  48. 48.
    Vellela M., Qian H.: J.R. Soc. Interface 6, 925 (2009)CrossRefGoogle Scholar
  49. 49.
    Xiao T.J., Hou Z., Xin H.: J. Chem. Phys. 129, 114506 (2008)CrossRefGoogle Scholar
  50. 50.
    Gillespie D.T.: J. Comput. Phys. 22, 403 (1976)CrossRefGoogle Scholar
  51. 51.
    Gillespie D.T.: J. Phys. Chem. 81, 2340 (1977)CrossRefGoogle Scholar
  52. 52.
    Luo J., Zhao N., Hu B.: Phys. Chem. Chem. Phys. 4, 4149 (2002)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Biswajit Das
    • 1
  • Kinshuk Banerjee
    • 1
  • Gautam Gangopadhyay
    • 1
  1. 1.S. N. Bose National Centre for Basic SciencesKolkataIndia

Personalised recommendations