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.
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Collin D., Ritort F., Jarzynski C., Smith S.B., Tinoco I. Jr., Bustamante C.: Nature 437, 231 (2005)
Jarzynski C.: Nat. Phys. 7, 591 (2011)
Liphardt J., Dumont S., Smith S.B., Tinoco I. Jr., Bustamante C.: Science 296, 1832 (2002)
Wang H., Oster G.: Nature 396, 279 (1998)
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)
Hummer G., Szabo A.: Proc. Natl. Acad. Sci. USA 98, 3658 (2001)
Ritort F., Bustamante C., Tinoco I. Jr.: Proc. Natl. Acad. Sci. USA 99, 13544 (2002)
Bustamante C., Liphardt J., Ritort F.: Phys. Today 58, 43 (2005)
Mossa A., De Lorenzo S., Huguet J.M., Ritort F.: J. Chem. Phys. 130, 234116 (2009)
M. Manosas, A. Mossa, N. Forns, J.M. Huguet, F. Ritort, J. Stat. Mech.: Theor. and Expt. 09, P02061 (2009)
Ritort F.: Adv. Chem. Phys. 137, 31 (2008)
Tinoco I. Jr., Bustamante C.: Biophys. Chem. 101, 513 (2002)
Bustamante C., Chemla Y.R., Forde N.R., Izhaky D.: Annu. Rev. Biochem. 73, 705 (2004)
Jarzynski C.: Phys. Rev. Lett. 78, 2690 (1997)
Jarzynski C.: Phys. Rev. E 56, 5018 (1997)
Crooks G.E.: J. Stat. Phys. 90, 1481 (1998)
Crooks G.E.: Phys. Rev. E 60, 2721 (1999)
Seifert U.: Phys. Rev. Lett. 95, 040602 (2005)
Hatano T., Sasa S.I.: Phys. Rev. Lett. 86, 3463 (2001)
Esposito M., Vanden Broeck C.: Phys. Rev. Lett. 104, 090601 (2010)
Evans D.J., Cohen E.G.D., Morriss G.P.: Phys. Rev. Lett. 71, 2401 (1993)
Gallavotti G., Cohen E.G.D.: Phys. Rev. Lett. 74, 2694 (1995)
Gallavotti G.: Phys. Rev. Lett. 77, 4334 (1996)
Lebowitz J.L., Spohn H.: J. Stat. Phys. 95, 333 (1999)
Lahiri S., Jayannavar A.M.: Eur. Phys. J. B69, 87 (2009)
Sevick E.M., Prabhakar R., Williams S.R., Searles D.J.: Annu. Rev. Phys. Chem. 59, 603 (2008)
Schmiedl T., Seifert U.: J. Chem. Phys. 126, 044101 (2007)
Blickle V., Speck T., Helden L., Seifert U., Bechinger C.: Phys. Rev. Lett. 96, 070603 (2006)
Tietz C., Schuler S., Speck T., Seifert U., Wrachtrup J.: Phys. Rev. Lett. 97, 050602 (2006)
Schmiedl T., Speck T., Seifert U.: J. Stat. Phys. 128, 77 (2007)
Seifert U.: Europhys. Lett. 70(1), 36 (2005)
Wiita A.P., Ainavarapu S.R.K., Huang H.H., Fernandez J.M.: Proc. Natl. Acad. Sci. USA 103, 7222 (2006)
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)
Gumpp H., Puchner E.M., Zimmermann J.L., Gerland U., Gaub H.E., Blank K.: Nano Lett. 9, 3290 (2009)
Adhikari A.S., Chai J., Dunn A.R.: J. Am. Chem. Soc. 133, 1686 (2011)
Lu H.P., Xun L., Xie X.S.: Science 282, 1877 (1998)
Kou S.C., Cherayil B.J., Min W., English B.P., Xie X.S.: J. Phys. Chem. B 109, 19068 (2005)
Yang S., Cao J.: J. Chem. Phys. 117, 10996 (2002)
Das B., Gangopadhyay G.: J. Chem. Phys. 132, 135102 (2010)
Andrieux D., Gaspard P.: J. Chem. Phys. 121, 6167 (2004)
Migneault I., Dartiguenave C., Bertrand M.J., Waldron K.C.: BioTechniques 37, 790 (2004)
Bell G.: Science 200, 618 (1978)
Gardiner C.W.: Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 2nd edn. Springer, New York (1985)
Vankampen N.G.: Stochastic Processes in Physics and Chemistry Amsterdam. Elsevier, The Netherlands (1992)
Gaspard P.: J. Chem. Phys. 120, 8898 (2004)
Jiu-li L., Vanden Broeck C., Nicolis G.: Z. Phys. B 56, 165 (1984)
Nicolis G., Prigogine I.: Self-Organization in Nonequilibrium Systems. Willey, New York (1977)
Vellela M., Qian H.: J.R. Soc. Interface 6, 925 (2009)
Xiao T.J., Hou Z., Xin H.: J. Chem. Phys. 129, 114506 (2008)
Gillespie D.T.: J. Comput. Phys. 22, 403 (1976)
Gillespie D.T.: J. Phys. Chem. 81, 2340 (1977)
Luo J., Zhao N., Hu B.: Phys. Chem. Chem. Phys. 4, 4149 (2002)
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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
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DOI: https://doi.org/10.1007/s10910-012-0099-2