Abstract
We study the conformations of polymer chains in a poor solvent, with and without bending rigidity, by means of a simple statistical mechanics model. This model can be exactly solved for chains of length up to N = 55 using exact enumeration techniques. We analyze in detail the differences between the constant force and constant distance ensembles for large but finite N. At low temperatures, and in the constant force ensemble, the force–extension curve shows multiple plateaus (intermediate states), in contrast with the abrupt transition to an extended state prevailing in the N → ∞ limit. In the constant distance ensemble, the same curve provides a unified response to pulling and compressing forces, and agrees qualitatively with recent experimental results. We identify a cross-over length, proportional to N, below which the critical force of unfolding decreases with temperature, while above, it increases with temperature. Finally, the force–extension curve for stiff chains exhibits “saw-tooth” like behavior, as observed in protein unfolding experiments.
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References
Rief M. et al.: Science 276, 1109 (1997)
M.S.Z. Kellermayer et al., Science 276, 1112 (1997); L. Tskhovrebova et al., Nature 387, 308 (1997)
Bustamante C. et al.: Annu. Rev. Biochem. 73, 705 (2004)
Itzhaki L.S., Evans P.A.: Protein Sci. 5, 140 (1996)
I. Rouzina, V.A. Bloomfield, Biophys. J. 80, 882 (2001); Biophys. J. 80, 894 (2001)
E. Evans, K. Ritchie, Biophys. J. 72, 1541 (1997); Biophys. J. 76, 2439 (1999)
Bhattacharjee S.M.: J. Phys. A 33, L423 (2000)
Bustamante C., Bryant Z., Smith S.B.: Nature 421, 423 (2003)
Haupt B.J., Senden T.J., Sevick E.M.: Langmuir 18, 2174 (2002)
de Gennes P.G.: Scaling Concepts in Polymer Physics. Cornell University Press, Ithaca (1979)
Mao H. et al.: Biophys. J. 89, 1308 (2005)
A.S. Lemak, J.R. Lepock, J.Z.Y. Chen, Phys. Rev. E 67, 031910 (2003); Proteins: Struct. Funct. Genet. 51 224 (2003)
Bustamante C., Liphardt J., Ritort F.: Phys. Today 58, 43 (2005)
Zemanova M., Bleha T.: Macromol. Theory Simul. 14, 596 (2005)
Fixman M.: J. Chem. Phys. 58, 1559 (1973)
Doi M., Edwards S.F.: Theory of Polymer Dynamics. Oxford University Press, Oxford (1988)
Bastolla U., Grassberger P.: J. Stat. Phys. 89, 1061 (1997)
Doniach S., Garel T., Orland H.: J. Chem. Phys. 105, 1601 (1996)
Kumar S. et al.: Phys. Rev. Lett. 98, 128101 (2007)
Vanderzande C.: Lattice Models of Polymers. Cambridge University Press, Cambridge (1998)
A.J. Guttmann, in Phase Transitions and Critical Phenomena, vol. 13, ed. by C. Domb, J.L. Lebowitz (Academic Press, New York, 1989)
Singh Y., Giri D., Kumar S.: J. Phys. A 34, L67 (2001)
Marenduzzo D. et al.: Phys. Rev. Lett. 90, 088301 (2003)
S. Kumar, D. Giri, Phys. Rev. E 72, 052901 (2005); Phys. Rev. Lett. 98, 048101 (2007)
Jensen I.: J. Phys. A 37, 5503 (2004)
E. Orlandini et al., J. Phys. A 34, L751 (2001); D. Marenduzzo et al., Phys. Rev. Lett. 88, 028102 (2002)
Dietz H., Rief M.: PNAS 101, 16192 (2004)
Guffond M.C., Williams D.R.M., Sevick E.M.: Langmuir 13, 5691 (1997)
Jimenez J., Rajagopalan R.: Langmuir 14, 2598 (1998)
Rief M. et al.: Science 275, 1295 (1997)
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Guttmann, A.J., Jacobsen, J.L., Jensen, I. et al. Modeling force-induced bio-polymer unfolding. J Math Chem 45, 223–237 (2009). https://doi.org/10.1007/s10910-008-9377-4
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DOI: https://doi.org/10.1007/s10910-008-9377-4