Journal of Statistical Physics

, Volume 100, Issue 1–2, pp 405–422 | Cite as

Dissipative Dynamics and the Statistics of Energy States of a Hookean Model for Protein Folding

  • Erkan Tüzel
  • Ayşe Erzan


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.

protein folding dissipative dynamics 


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  1. 1.
    D. ben-Avraham, Phys. Rev. B 47:14559 (1993).Google Scholar
  2. 2.
    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).Google Scholar
  3. 3.
    M. M. Tirion, Phys. Rev. Lett. 77:1905 (1996).Google Scholar
  4. 4.
    T. Haliloglu, I. Bahar, and B. Erman, Phys. Rev. Lett. 79:3090 (1997).Google Scholar
  5. 5.
    B. Erman and K. Dill, J. Chem. Phys. 112:1050 (2000).Google Scholar
  6. 6.
    B. Erman, Hydrophobic collapse of proteins into their near-native configurations, unpublished.Google Scholar
  7. 7.
    E. Tüzel and A. Erzan, Phys. Rev. E 61:1040 (2000).Google Scholar
  8. 8.
    E. Wigner, Proc. Cambridge Phil. Soc. 47:790 (1951); Ann. Math. 62:548 (1955).Google Scholar
  9. 9.
    T. Brody, J. Flores, J. B. French, P. A. Mello, A. Pandey, and S. S. S. Wong, Rev. Mod. Phys. 53:385 (1981).Google Scholar
  10. 10.
    C. E. Porter, Statistical Theories of Spectra: Fluctuations (Academic Press, New York, 1965).Google Scholar
  11. 11.
    C. E. Porter, J. Math. Phys. 4:1039 (1963).Google Scholar
  12. 12.
    W. Feller, An Introduction to Probability Theory and its Applications, Vol. II (Wiley, New York, 1957), p. 332ff.Google Scholar
  13. 13.
    C. N. Chen, C. I. Chou, C. R. Hwang, J. Kang, T. K. Lee, and S. P. Li, Phys. Rev. E 60:2388 (1999).Google Scholar
  14. 14.
    H. Frauenfelder, S. G. Sligar, and P. G. Wolynes, Science 254:1598 (1991).Google Scholar
  15. 15.
    J. L. Green, J. Fan, and C. A. Angell, J. Phys. Chem. 98:13780 (1994).Google Scholar
  16. 16.
    B. Erman and I. Bahar, Macromol. Symp. 133:33 (1998).Google Scholar
  17. 17.
    J. Colmenero, A. Arbe, and A. Algera, Phys. Rev. Lett. 71:2603 (1993).Google Scholar
  18. 18.
    A. Yu. Grosberg, J. Stat. Phys. 38:149 (1985).Google Scholar
  19. 20.
    P. J. Flory, Statistical Mechanics of Chain Molecules (Interscience, New York, 1969).Google Scholar
  20. 21.
    T. Halpin Healy and Y. C. Zhang, Physics Reports 254:215-414 (1995).Google Scholar
  21. 22.
    J. Krug, P. Meakin, and T. Halpin-Healy, Phys. Rev. A 45:638 (1992).Google Scholar
  22. 23.
    A. Erzan, E. Veermans, R. Heijungs, and L. Pietronero, Phys. Rev. B 41:11522 (1990).Google Scholar
  23. 24.
    E. Veermans, A. Erzan, R. Heijungs, and L. Pietronero, Physica A 166:447 (1990).Google Scholar
  24. 25.
    G. Parisi and L. Pietronero, Physica A 179:16 (1991).Google Scholar
  25. 26.
    N. D. Socci and J. N. Onuchic, J. Chem. Phys. 103:4732 (1995).Google Scholar
  26. 27.
    H. Risken, The Fokker-Planck Equation (Springer, Berlin, 1984).Google Scholar
  27. 28.
    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.Google Scholar
  28. 29.
    We are indebted to Nazmi Postacíoğlu for this remark.Google Scholar
  29. 30.
    M. L. Mehta, Random Matricies and the Statistical Theory of Energy Levels (Academic Press, New York, 1967).Google Scholar
  30. 31.
    M. V. Berry and M. Robnik. J. Phys. A 17:2413 (1984).Google Scholar
  31. 32.
    E. Yurtsever and J. Brickman, Phys. Rev. A 38:1027 (1988).Google Scholar
  32. 33.
    E. Yurtsever and J. Brickman, Phys. Rev. A 41:6688 (1990).Google Scholar
  33. 34.
    D. Wales, private communication.Google Scholar
  34. 35.
    D. Bohigas, M. J. Giannoni, and C. Schmidt, Phys. Rev. Lett. 52:1 (1984).Google Scholar

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Erkan Tüzel
    • 1
  • Ayşe Erzan
    • 1
    • 2
  1. 1.Department of Physics, Faculty of Sciences and LettersIstanbul Technical University, MaslakIstanbulTurkey
  2. 2.Gürsey InstituteIstanbulTurkey

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