摘要(英) |
We present a theoretical model that describes ligand-receptor cluster under external force. We modify the model of Bell [1] by considering the rebinding of broken bonds in a consistent way. The stability of the cluster is studied by the rate equation of Nb, the number of connected bonds. Our study reveals that for a cluster with N parallel bonds under external force F, the lifetime of the cluster depends only on the force acting on each bond f = F/N. There exists a critical force Fc = Nfc below which the cluster is stable and above which the cluster dissociates. When f = fc, the number of rupture events per unit time is equal to that of rebinding at Nb^* = Nnb^*. We find nb^*~1, i.e., the effect of rebinding is important when most of the bonds are connected. When f approaches fc from above, the cluster spends most of the time near nb^*, the true lifetime of the cluster is shorter than Bell’s prediction and has a power law behavior T ~(f − fc)^(−1/2). We also show that the true lifetime of the cluster is longer than Bell’s prediction when f is significantly greater than fc due to different number of connected bonds predicted by both theories in the absence of force. When f =fc, for a finite size cluster, the bond number fluctuation is important, the lifetime of the cluster is related to the cluster size by T ~N^(1/3). |
參考文獻 |
[1] G. I. Bell, Science 200, 618 (1978).
[2] E. Evans, Annu. Rev. Biophys. Biomol. Struct. 30, 105 (2001).
[3] R. Merkel, Phys. Rep. 346, 344 (2001).
[4] E.-L. Florin, V. T. Moy, and H.E. Gaub, Science 264, 415 (1994).
[5] R. Merkel, P. Nassoy, A. Leung, K. Ritchie, and E. Evans, Nature (London) 397, 50 (1999).
[6] K. Prechtel, A. R. Bausch, V. Marchi-Artzner, M. Kantlehner, H. Kessler, and R. Merkel, Phys. Rev. Lett. 89, 028101 (2002).
[7] U. Seifert, Phys. Rev. Lett. 84, 2750 (2000).
[8] T. Erdmann and U. S. Schwarz, Phys. Rev. Lett. 92, 108102 (2004).
[9] T. Erdmann and U. S. Schwarz, Europhys. Lett. 66, 603 (2004).
[10] E. Evans, and K. Ritchie, Biophys. J. 76, 2439 (1999).
[11] U. Seifert, Europhys. Lett. 58, 792 (2002).
[12] A. Garg, Phys. Rev. B 51, 15592 (1995).
[13] H.A. Kramers, Physica (Amsterdam) 7, 284 (1940).
[14] N. G. van Kampen, Stochastic Processes in Physics and Chemistry, revised edition. (North-Holland, Amsterdam, 1992).
[15] J. L. Barrat and J. P. Hansen, Basic Concepts for Simple and Complex Liquids. (Cambridge University Press, 2003).
[16] L. D. Landau and E.M. Lifshitz, Fluid Mechanics. (Prentice-Hall, Englewood CLiffs, NJ, 1962).
[17] M. Doi and S. F. Edwards, The Theory of Polymer Dynamics. (Clarendon, Oxford, 1986).
[18] A. Einstein, Ann. Physik 17, 549 (1905) and 19, 371 (1906).
[19] H. Risken, The Fokker-Planck equation. (Springer-Verlag, Berlin, 1989).
[20] H. Y. Chen and Y. P. Chu, Phys. Rev. E 71, 010901(R)(2005).
[21] E. Evans, A. Leung, V. Heinrich, and C. Zhu, Proc. Natl. Acad. Sci. U.S.A. 101,11281-11286 (2004).
[22] E. Evans and K. Ritchie, Biophys. J. 72, 1541 (1997).
[23] P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equation. (Springer-Verlag, Berlin, 1992). |