Abstract
A generic model of a random polypeptide chain, with discrete torsional degrees of freedom and Hookean spring connecting pairs of hydrophobic residues, reproduces the energy probability distribution of real proteins over a very large range of energies. We show that this system with harmonic interactions, under dissipative dynamics driven by random noise, leads to a distribution of energy states obeying a modified one-dimensional Ornstein–Uhlenbeck process and giving rise to the so-called Wigner distribution. A tunably fine- or coarse-grained sampling of the energy landscape yields a family of distributions for the energies and energy spacings.
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REFERENCES
D. ben-Avraham, Phys. Rev. B 47:14559 (1993).
K. A. Dill, S. Bromberg, K. Yue, K. M. Feibig, D. P. Yee, P. D. Thomas, and H. S. Chan, Protein Science 4:561 (1995).
M. M. Tirion, Phys. Rev. Lett. 77:1905 (1996).
T. Haliloglu, I. Bahar, and B. Erman, Phys. Rev. Lett. 79:3090 (1997).
B. Erman and K. Dill, J. Chem. Phys. 112:1050 (2000).
B. Erman, Hydrophobic collapse of proteins into their near-native configurations, unpublished.
E. Tüzel and A. Erzan, Phys. Rev. E 61:1040 (2000).
E. Wigner, Proc. Cambridge Phil. Soc. 47:790 (1951); Ann. Math. 62:548 (1955).
T. Brody, J. Flores, J. B. French, P. A. Mello, A. Pandey, and S. S. S. Wong, Rev. Mod. Phys. 53:385 (1981).
C. E. Porter, Statistical Theories of Spectra: Fluctuations (Academic Press, New York, 1965).
C. E. Porter, J. Math. Phys. 4:1039 (1963).
W. Feller, An Introduction to Probability Theory and its Applications, Vol. II (Wiley, New York, 1957), p. 332ff.
C. N. Chen, C. I. Chou, C. R. Hwang, J. Kang, T. K. Lee, and S. P. Li, Phys. Rev. E 60:2388 (1999).
H. Frauenfelder, S. G. Sligar, and P. G. Wolynes, Science 254:1598 (1991).
J. L. Green, J. Fan, and C. A. Angell, J. Phys. Chem. 98:13780 (1994).
B. Erman and I. Bahar, Macromol. Symp. 133:33 (1998).
J. Colmenero, A. Arbe, and A. Algera, Phys. Rev. Lett. 71:2603 (1993).
A. Yu. Grosberg, J. Stat. Phys. 38:149 (1985).
P. J. Flory, Statistical Mechanics of Chain Molecules (Interscience, New York, 1969).
T. Halpin Healy and Y. C. Zhang, Physics Reports 254:215-414 (1995).
J. Krug, P. Meakin, and T. Halpin-Healy, Phys. Rev. A 45:638 (1992).
A. Erzan, E. Veermans, R. Heijungs, and L. Pietronero, Phys. Rev. B 41:11522 (1990).
E. Veermans, A. Erzan, R. Heijungs, and L. Pietronero, Physica A 166:447 (1990).
G. Parisi and L. Pietronero, Physica A 179:16 (1991).
N. D. Socci and J. N. Onuchic, J. Chem. Phys. 103:4732 (1995).
H. Risken, The Fokker-Planck Equation (Springer, Berlin, 1984).
H. Mach, D. B. Volkin, C. J. Burke, and C. R. Middaugh, Ultraviolet absorption spec troscopy, B. A. Shirley, ed., Methods in Molecular Biology, Vol. 40: Protein Stability and Folding (Humana Press, Totowa, New Jersey, 1995), pp. 91-114.
We are indebted to Nazmi Postacíoğlu for this remark.
M. L. Mehta, Random Matricies and the Statistical Theory of Energy Levels (Academic Press, New York, 1967).
M. V. Berry and M. Robnik. J. Phys. A 17:2413 (1984).
E. Yurtsever and J. Brickman, Phys. Rev. A 38:1027 (1988).
E. Yurtsever and J. Brickman, Phys. Rev. A 41:6688 (1990).
D. Wales, private communication.
D. Bohigas, M. J. Giannoni, and C. Schmidt, Phys. Rev. Lett. 52:1 (1984).
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Tüzel, E., Erzan, A. Dissipative Dynamics and the Statistics of Energy States of a Hookean Model for Protein Folding. Journal of Statistical Physics 100, 405–422 (2000). https://doi.org/10.1023/A:1018616417953
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DOI: https://doi.org/10.1023/A:1018616417953