Advertisement

Nonlinear Dynamics in the Binary DNA/RNA Coding Problem

  • Mladen Martinis

Abstract

The concepts of chaos, nonlinearity and fractal can be applied to a number of properties of proteins. Recently, there has been a rapid accumulation of new information in this area (Elber, 1990, Weigend and Gershenfeld, 1993). However, since proteins are finite systems, although highly inhomogeneous in their structure, their fractal description can only be true in an average or statistical sense. Even if a fractal description is applicable, the question, What new insight does it provide? is sometimes necessary to answer. For proteins this answer is not always clear and straightforward. Nevertheless, deterministic chaos if detected offers a striking explanation for irregular behaviour and anomalies in the protein structure which can not be attributed to the randomness alone.

Keywords

Fractal Dimension Lyapunov Exponent Chaotic System Strange Attractor Hurst Exponent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Casdagli, M., and Weigend, A.S., 1993, Exploring Continuum between Deterministic and Stochastic Modeling. In Proc. of Santa Fe Institute Studies in the Sciences of Complexity, Addison-Wesley, Reading, MA, Vol. XV.Google Scholar
  2. Elber, R., 1990, Fractal Analysis of Proteins. In The Fractal Approach to Heterogeneous Chemistry, (D. Anvir, ed.) John Willey & Sons, NY.Google Scholar
  3. Farmer, J.D., 1982, Chaotic attractors of an infinite-dimensional chaotic system. Physica 4D:366–393.Google Scholar
  4. Feder, J., 1989, Fractals, Plenum Press, NY.Google Scholar
  5. Grassberger, P., and Procaccia, I., 1983, Measuring the strangenes of strange attractor.Physica 9D: 189–208.Google Scholar
  6. Grassberger, P., 1983, Generalized dimension of strange attractors. Phys. Lett. A97: 227–230.Google Scholar
  7. Grassberger, P., Schreiber, T., and Schaffrath, C, 1991, Nonlinear time sequence analysis.Intl. J. Bif. & Chaos 1:512–520.Google Scholar
  8. Katz, H., and Schreiber, T., 1997, Nonlinear Time Series Analysis, Cambridge University Press, Cambridge, UK.Google Scholar
  9. Martinis, M., Štambuk, N., and Črnugelj, J., Fractal dimensions of α-helices and β-sheets, in preparation.Google Scholar
  10. Packard, N.H., Crutchfeld, J.P., Farmer, J.D., and Show, R.S., 1980, Geometry from a time series. Phys. Rev. Lett. 45: 712–716.CrossRefGoogle Scholar
  11. Peng, C.K., Havlin, S., Stanley, H.E., and Goldberger, A.L., 1995, Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos 5: 82.PubMedCrossRefGoogle Scholar
  12. Peng. C.K., Buldyrev, S.V., Goldberger, A.L., Havlin, S., Simon, M., and Stanley, H.E.,1992, Long-range correlations in nucleotide sequences. Nature 356: 168–170.PubMedCrossRefGoogle Scholar
  13. Proceedings of Santa Fe Institute Studies in the Sciences of Complexity, 1993, (A. S. Weigend and N. A. Gershenfeld, eds.) Addison-Wesley, Reading, MA, Vol. XV.Google Scholar
  14. Ruelle, D., 1990, Deterministic chaos: The Science and the Fiction. Proc. Roy. Soc. London Ser. A427: 241–248.CrossRefGoogle Scholar
  15. Sauer, T., Yorke, J.A., and Casdagli, M., 1991, Embedology. J. Stat. Phys. 65: 579–616.CrossRefGoogle Scholar
  16. Takens, F., 1981, Detecting Strange Attractors in Turbulence. In Dynamical Systems and Turbulence, (D. Rand and L.-S. Young, eds.), Springer-Verlag, Berlin.Google Scholar
  17. Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A., 1985, Determining Lyapunov Exponents from a Time Series. Physica 16D: 285–317.Google Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Mladen Martinis
    • 1
  1. 1.Department of Physics, Theory DivisionRuđer Bošković InstituteZagrebCroatia

Personalised recommendations