Correlated energy landscape model for finite, random heteropolymers

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 53, Issue 6 SUPPL. B, 1996, Pages 6271-6296

  Plotkin, Steven S ^a   Wang, Jin ^a   Wolynes, Peter G ^a  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONFORMATIONS; CORRELATION METHODS; ELECTRON ENERGY LEVELS; ENTROPY; FREE ENERGY; GLASS TRANSITION; MATHEMATICAL MODELS; PROBABILITY; TEMPERATURE; THERMODYNAMICS;

ENERGY LANDSCAPE; FINITE RANDOM HETEROPOLYMERS; GENERALIZED RANDOM ENERGY MODEL; GROUND STATE ENERGY; PACKING DENSITY; SPIN GLASSES;

POLYMERS;

EID: 0030165480     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/physreve.53.6271     Document Type: Article

References (59)

1. J. Bryngelson, J.O. Onuchic, N.D. Socci, and P.G, Wolynes, PROTEINS 21, 167 (1995).
2. P.G. Wolynes, J.N. Onuchic, and D. Thirumalai, Science 267, 1619 (1995).
3. J.N. Onuchic, P.G. Wolynes, Z. Luthey-Schulten, and N.D. Socci, Proc. Natl. Acad. Sci. USA, 92, 3626 (1995).
4. H. Frauenfelder and P.G. Wolynes, Phys. Today 47, (2) 58 (1994).
5. K.A. Dill, S. Bromberg, K. Yue, K.M. Fiebig, D.P. Yee, P.D. Thomas, and H.S. Chan, Protein Sci. 4, 561 (1995).
6. P.E. Leopold, M. Montai, and J.N. Onuchic, Proc. Natl. Acad. Sci. USA 89, 8721 (1992).
7. N. Go, Annu. Rev. Biophys. Bioeng. 12, 183 (1983).
8. J. Bryngelson and P.G. Wolynes, Proc. Natl. Acad. Sci. USA 84, 7524 (1987).
9. R.A. Goldstein, Z.A. Luthey-Schulten, and P.G. Wolynes, Proc. Natl. Acad. Sci. USA 89, 4918 (1992).
10. E.I. Shakhnovich, Phys. Rev. Lett. 72, 3907 (1994).
11. B. Derrida, Phys. Rev. B 24, 2613 (1981).
12. D.J. Gross and M. Mezard, Nucl. Phys. B 240, 431 (1984).
13. D.J. Gross, I. Kantor, and H. Sompolinsky, Phys. Rev. Lett. 55, 304 (1985); T.R. Kirkpatrick and P.G. Wolynes, Phys. Rev. B 36, 8552 (1987).
14. D.J. Gross, I. Kantor, and H. Sompolinsky, Phys. Rev. Lett. 55, 304 (1985); T.R. Kirkpatrick and P.G. Wolynes, Phys. Rev. B 36, 8552 (1987).
15. T. Garel and H. Orland, Europhys. Lett. 6, 307 (1988); E.I. Shakhnovich and A.M. Gutin, ibid. 8, 327 (1989); Biophys. Chem. 34, 187 (1989).
16. T. Garel and H. Orland, Europhys. Lett. 6, 307 (1988); E.I. Shakhnovich and A.M. Gutin, ibid. 8, 327 (1989); Biophys. Chem. 34, 187 (1989).
17. T. Garel and H. Orland, Europhys. Lett. 6, 307 (1988); E.I. Shakhnovich and A.M. Gutin, ibid. 8, 327 (1989); Biophys. Chem. 34, 187 (1989).
18. Z. Luthey-Schulten, B.E. Ramirez, and P.G. Wolynes, J. Phys. Chem. 99, 2177 (1995).
19. J.G. Saven and P.G. Wolynes, J. Mol. Biol. 257, 199 (1996).
20. B. Derrida and E. Gardner, J. Phys C 19, 2253 (1986).
21. P.J. Flory, J. Am. Chem. Soc. 78, 5222 (1956).
22. S.F. Edwards, in Proceedings of the Third International Conference on Amorphous Materials, edited by R.W. Douglass and B. Ellis (Wiley, New York, 1972), p. 279.
23. P. Goldbart and N. Goldenfeld, Phys. Rev. Lett. 58, 2676 (1987).
24. C. Levinthal, in Mossbauer Spectroscopy in Biological Systems (University of Illinois Press, Urbana, IL, 1969), p. 22.
25. J. Bryngelson and P.G. Wolynes, Biopolymers 30, 177 (1990).
26. J.F. Douglas and T. Ishinabe, Phys. Rev. E 51, 1791 (1995).
27. A.M. Nemirovsky, J. Dudowicz, and K.F. Freed, J. Stat. Phys. 67, 395 (1992).
28. The packing fraction for real proteins (without cavities) on an atomistic basis is about that of an fcc crystal (0.74), while the packing fraction for molten globules is somewhat less [P.M. Richards and W.A. Lim, Qt. Rev. Biophys. 26, 423 (1993)]. However, the packing fraction η used here should not be understood as the atomistic packing fraction: each monomer + side chain unit is crudely approximated as a lattice site, e.g., η=1 corresponds to the highest density of cubes on a cubic lattice.
29. B. Derrida, J. Phys. Lett. (Paris), 46, 401 (1993).
30. J.G. Kirkwood, J. Chem. Phys. 3, 300 (1935).
31. We have not assumed any dependence of the collapse parameter η on the overlap q with the given state, as would be the case if we had picked a particularly high or low energy state. This further complication will be dealt with in a later paper.
32. A.M. Gutin and E.I. Shakhnovich, J. Chem. Phys. 100, 5290 (1994).
33. Note confinement effects as determined by the scaling law (3.5) are not important in two-dimensional systems.
34. J. Bryngelson and D. Thirumalai, Phys. Rev. Lett. 76, 542 (1995).
35. N. Socci and J. Onuchic (private communication).
36. v obtained without the mixing term in the entropy is not significantly lower, so that the range in q where the mixing entropy is used invalidly is not too large.
37. P.J. Flory and R.R. Matheson, J. Phys. Chem. 88, 6606 (1984).
38. 1/2) to account for the antibond effect gives almost the same result.
39. A. Silberberg, J. Phys. Chem. 66, 1872 (1962).
40. C.A.J. Hoeve, E.A. DiMarzio, and P. Peyser, J. Chem. Phys. 42, 2558 (1965).
41. E.I. Shakhnovich and A.M. Gutin, J. Phys. A 22, 1647 (1989).
42. 2.
43. max<1 can be considered because of collective melting described in Sec. IV. The main important feature is two discretely different values of q.
44. max at T=0 .
45. B. Derrida and E. Gardner, J. Phys. C 19, 5783 (1986).
46. min(N)] to obtain an analogous de Almeida-Thouless line in the (μ,T) plane.
47. J.M. Flanagan, M. Kataoka, T. Fujisawa, and D.M. Engelman, Biochemistry 32, 10 359 (1993).
48. T.H. LaBean, S.A. Kauffman, and T.R. Butt (unpublished).
49. A.R. Davidson and R.T. Sauer, Proc. Natl. Acad. Sci. USA 91, 2146 (1994).
50. Y. Bal, T.R. Sosnick, L. Mayne, and S.W. Englander, Science 269, 192 (1995).
51. J. Wang, S.S. Plotkin, and P.O. Wolynes (unpublished).
52. K.A. Dill and D. Stigter, Adv. Protein Chem. 46, 59 (1995).
53. The ansatz of ultrametricity in the GREM and the resulting restriction on the allowable overlaps between states, for example, two states having overlap q with a third must have an overlap ≥q with each other, is certainly an approximation here, and one can conceive of triplets of polymeric states which do not satisfy this ultrametric requirement.
54. For the collapsed 27-mer there are 28 levels, for the 64-mer there are 82 levels. However, in analyzing small sequence fragments, we would wish to keep the possible overlaps discreet.
55. We will use the terms monomers and statistical segments interchangeably here. A polymer of length N is really understood to have N statistical segments.
56. The limits of the product II in this formula are modified when effects due to confinement of the polymer within its collapsed globule size are taken into account. This slightly modifies the bond-formation entropy formula (C16); see formulas (E15) and (E16).
57. S.F. Edwards and K.F. Freed, J. Phys. A 2, 145 (1969).
58. S. Chandrasakhar, Rev. Mod. Phys. 15, 1 (1943).
59. H.S. Chan and K.A. Dill, J. Chem. Phys. 99, 2116 (1993).