Conformational non-linear dynamical behavior of the peptide Boc-Gly-Leu-Gly-Gly-NMe

(Note: The full text of this document is currently only available in the PDF Version )

Vincenzo Villani, Luciano D’Alessio and Antonio M. Tamburro


Abstract

The conformational motion of a peptide has been investigated by means of molecular dynamics simulations and has been characterized in the time and the frequency domains. The tetrapeptide Boc-Gly-Leu-Gly-Gly-NMe has been considered as a model for some repetitive amino acid sequences of glycine-rich regions of elastin, which could play a key role in the entropic elasticity mechanism. The classical tools of dynamical analysis (time series, spectral density, time correlation functions, delay maps) have been used and new methods, introducing the idea of travelling trajectory packets and trajectories in the frequency space, have been developed. In vacuo, non-ergodic, essentially quasiperiodic motion has been revealed and solitons have been observed according to the non-linear dynamical behavior of systems with small anharmonic perturbation. This particularly concerns the dynamics of the end-to-end distance, a global variable very sensitive to the whole conformational flexibility of the model molecule. The dynamical picture has been joined with the experimentally observed conformational disorder and with the amplitude instability of KAM theory for non-linear systems: a transition is hypothesized from quasiperiodic (solitons) to ergodic motion (Hamiltonian chaos) for the peptide in solution and the entropic mechanism of elastin elasticity is interpreted from a new and unitary dynamical point of view.


References

  1. Molecular-Dynamics Simulation of Statistical-Mechanical Systems, ed. G. Ciccotti and W. G. Hoover, North-Holland, Amsterdam, 1986 Search PubMed.
  2. H. G. Schuster, Deterministic Chaos, VCH, Weinheim, 1995 Search PubMed.
  3. J. C. Maxwell, Philosophical Transactions of the Royal Society of London, 1867, CLVII, 49 Search PubMed.
  4. J.-P. Eckmann and D. Ruelle, Rev. Mod. Phys., 1985, 57, 617 CrossRef CAS.
  5. D. Ruelle, Chaotic evolution and strange attractors, Cambridge University Press, Cambridge, 1989 Search PubMed.
  6. D. Ruelle, Hasard et Chaos, Editions Odile Jacob, Paris, 1991 Search PubMed.
  7. F. A. L. Anet, J. Am. Chem. Soc., 1990, 112, 7172 CrossRef CAS.
  8. J. E. Straub, A. B. Rashkin and D. Thirumalai, J. Am. Chem. Soc., 1994, 116, 2049 CrossRef CAS.
  9. H. Zhou and L. Wang, J. Phys. Chem., 1996, 100, 8101 CrossRef CAS.
  10. J. M. Haile, Molecular dynamics simulation, Wiley, New York, 1992 Search PubMed.
  11. D. R. Cox and P. A. W. Lewis, The statistical analysis of series and events, Chapman and Hall, London, 1966 Search PubMed.
  12. A. M. Tamburro, in Elastin: Chemical and Biological aspects, ed. A. M. Tamburro and J. M. Davidson, Congedo, Italy, 1990, p. 126 Search PubMed.
  13. A. M. Tamburro, V. Guantieri, L. Pandolfo and A. Scopa, Biopolymers, 1990, 29, 855 CrossRef CAS.
  14. M. A. Castiglione Morelli, A. Scopa, A. M. Tamburro and V. Guantieri, Int. J. Biol. Macromol., 1990, 12, 363 CrossRef.
  15. M. A. Castiglione Morelli, M. De Biase, A. De Stradis and A. M. Tamburro, J. Biomol. Struct. Dyn., 1993, 11, 181 Search PubMed.
  16. V. Villani and A. M. Tamburro, J. Chem. Soc., Perkin Trans. 2, 1993, 1951 RSC.
  17. V. Villani and A. M. Tamburro, J. Mol. Struct. (THEOCHEM), 1994, 308, 141 CrossRef.
  18. V. Villani and A. M. Tamburro, J. Biomol. Struct. Dyn., 1995, 12, 1173 Search PubMed.
  19. V. Villani, J. Mol. Struct. (THEOCHEM), 1996, 363, 43 CrossRef CAS.
  20. D. A. Pearlman, D. A. Case, J. C. Caldwell, G. L. Seibel, U. Chandra Singh, P. Weiner and P. A. Kollman, AMBER 4.0, University of California, San Francisco, 1991.
  21. S. J. Weiner, P. A. Kollman, D. T. Nguyen and D. A. Case, J. Comput. Chem., 1986, 7, 230 CrossRef CAS.
  22. J. A. McCammon, B. R. Gelin and M. Karplus, Nature, 1977, 267, 585 CAS.
  23. M. Levitt, Nature, 1981, 294, 379 CrossRef CAS.
  24. W. F. van Gunsteren, H. J. C. Berendsen, J. Hermans, W. G. J. Hol and J. P. M. Postma, Proc. Natl. Acad. Sci. USA, 1983, 80, 4315 CAS.
  25. J. A. McCammon and S. C. Harvey, Dynamics of protein and nucleic acids, Cambridge University Press, Cambridge, 1988 Search PubMed.
  26. H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. Di Nola and J. R. Haak, J. Chem. Phys., 1984, 81, 3684 CrossRef CAS.
  27. L. Verlet, Phys. Rev., 1967, 159, 98 Search PubMed.
  28. J. P. Ryckaert, G. Ciccotti and H. J. C. Berendsen, J. Comput. Phys., 1977, 23, 327 CrossRef.
  29. Lord Rayleigh, F.R.S., Philos. Mag., 1883, 15, 229 Search PubMed.
  30. W. G. Hoover, Phys. Rev. A, 1985, 31, 3 CrossRef.
  31. J. M. T. Thompson and H. B. Stewart, Nonlinear Dynamics and Chaos, Wiley, Chichester, 1987 Search PubMed.
  32. J. K. Hale, Oscillations in nonlinear systems, Dover, New York, 1992 Search PubMed.
  33. P. J. Rossky and M. Karplus, J. Am. Chem. Soc., 1979, 101, 1913 CrossRef CAS.
  34. N. Packard, J. P. Crutchfield, J. D. Farmer and R. S. Shaw, Phys. Rev. Lett., 1980, 45, 712 CrossRef.
  35. L. Colace and A. R. Giona, in Chaos and fractals in chemical engineering, ed. G. Biardi, M. Giona and A. R. Giona, World Scientific, Singapore, 1995 Search PubMed.
  36. R. M. Levy, M. Karplus and J. A. McCammon, Chem. Phys. Lett., 1979, 65, 4 CrossRef CAS.
  37. F. Lelj, P. Grimaldi and P. L. Cristinziano, Biopolymers, 1991, 31, 6638 CrossRef.
  38. H. Goldstein, Classical Mechanics, Addison-Wesley, Reading, 1965 Search PubMed.
  39. F. C. Moon, Chaotic and Fractal Dynamics, Wiley, New York, 1992 Search PubMed.
  40. H. A. Davies and F. C. Moon, Chaos, 1993, 3, 93 CrossRef.
  41. J. Wright, Chaos, 1995, 5, 356 CrossRef.
  42. M. Schwartz and L. Shaw, Signal Processing, McGraw-Hill, New York, 1975 Search PubMed.
  43. M. Toda, Theory of nonlinear lattices, Springer-Verlag, Berlin, 1989 Search PubMed.
  44. E. Fermi, J. Pasta and S. Ulam, in Los Alamos Rpt. LA-1940 (1955) Collected Papers of Enrico Fermi, University of Chicago Press, Chicago, 1965, vol. 2, p. 968 Search PubMed.
  45. N. J. Zabusky and M. D. Kruskal, Phys. Rev. Lett., 1965, 15, 240 CrossRef.
  46. J. Waters and J. Ford, J. Math. Phys., 1966, 7, 399 CrossRef.
  47. Y. R. Shen, Science, 1997, 276, 1520 CrossRef CAS; A. W. Snyder and D. J. Mitchell, ibid., 1997, 276, 1538 Search PubMed.
  48. N. J. Zabusky and G. S. Deem, J. Comput. Phys., 1968, 2, 207 CrossRef.
  49. M. J. Feigenbaum, J. Stat. Phys., 1979, 21, 669.
  50. H. Bai-Lin, Chaos, World Scientific, Singapore, 1984 Search PubMed.
  51. G. H. Walker and J. Ford, Phys. Rev., 1969, 188, 416 Search PubMed.
  52. N. J. Zabusky and G. J. Deem, J. Comput. Phys., 1967, 2, 126 CrossRef.
  53. I. Prigogine, Non-equilibrium Statistical Mechanics, Wiley-Interscience, New York, 1962 Search PubMed.
  54. N. Saito and H. Hiraoka, J. Phys. Soc. Jpn., 1967, 23, 167 Search PubMed.
  55. Z. R. Wasserman and F. R. Salemme, Biopolymers, 1990, 29, 1613 CrossRef CAS.
  56. P. J. Flory, Principles of Polymer Chemistry, Cornell, Ithaca, NY, 1953 Search PubMed.
  57. W. R. Gray, L. B. Sandberg and J. A. Foster, Nature, 1973, 246, 461 CAS.
  58. J. M. Gosline, Biopolymers, 1978, 17, 677 CrossRef CAS.
  59. D. W. Urry, C. V. Venkatachalam, M. M. Long and K. U. Prasad, in Conformation in Biology, the Festschirft celebrating the sixtieth birthday of G. N. Ramachandran F.R.S., ed. R. Srinivasan and R. H. Sarna, Adenine Press, Guilderland, NY, 1982, p. 11 Search PubMed.
  60. V. Villani, L. D'Alessio and A. M. Tamburro, in Elastin and elastic tissue, ed. A. M. Tamburro, Procedings of an International Conference, Maratea (Italy), 17–20 October 1996, p. 31 Search PubMed.
  61. N. Nakagawa and Y. Kuramoto, Physica D, 1995, 80, 307 CrossRef.
  62. E. Thiele and D. J. Wilson, J. Chem. Phys., 1961, 35, 1256 CrossRef CAS.
  63. D. Bunker, J. Chem. Phys., 1962, 37, 393 CrossRef CAS.
  64. R. Fusco, L. Longo, L. Caccianotti, C. Aratari and G. Allegra, Makromol. Chem., Theory Simul., 1993, 2, 685 Search PubMed.
  65. Nonlinear Excitations in Biomolecules, ed. M. Peyrard, Les Editions de Physique, Springer Verlag, Paris, 1995 Search PubMed.
Click here to see how this site uses Cookies. View our privacy policy here.