Nonlinear signal analysis to understand the dynamics of the protein sequences

Abstract

Recurrence plots are a useful tool to identify structure in a data set in a time resolved way qualitatively. Recurrence plots and its quantification has become an important research tool in the analysis of nonlinear dynamical systems. In the present work, we utilize the recurrence property to study the protein sequences. The sequences that we analyze belong to two distinct classes, viz., soluble proteins and proteins that form inclusion bodies when over expressed in Escherichia coli. We use Kyte-Doolittle hydrophobicity scale in the analysis. We study the underlying dynamics and extract the information which codes the essential class of a protein using simple statistical and global characteristics based features as well as some advanced features based on recurrence quantification. The extracted features are used in probability estimation using Gaussian Process Classification technique. The results give meaningful insights to the level of understanding the protein sequence dynamics.

This is a preview of subscription content, access via your institution.

References

  1. S. Idicula-Thomas, P.V. Balaji, Curr. Sci. 92, 758 (2007)

    Google Scholar 

  2. S. Idicula-Thomas, P.V. Balaji, Prot. Eng. Des. Sel. 18, 175 (2005)

    Google Scholar 

  3. G. Georgiou, P. Valax, Meth. Enzymol. 309, 48 (1999)

    Google Scholar 

  4. S.C. Makrides, Microbiol. Rev. 60,512 (1996)

  5. S. Idicula-Thomas, A. Kulkarni, B.D. Kulkarni, V.K. Jayaraman, P.V. Balaji, Bioinformatics 22, 278 (2006)

  6. P. Smialowski, A.J. Martin-Galiano, A. Mikolajka, T. Girschick, T.A. Holak, D. Frishman, Bioinformatics (2006)

  7. J.P. Zbilut, A. Giuliani, C.L. Webber, A. Colosimo, Protein Eng. 11, 87 (1998)

  8. A. Giuliani, C. Manetti, Phys. Rev. E 53, 6336 (1996)

    Google Scholar 

  9. A. Giuliani, R. Benigni, P. Sirabella, J. Zbilut, A. Colosimo, Biophys. J. 78, 136 (1998)

    Google Scholar 

  10. J.P. Eckmann, D. Ruelle, Rev. Mod. Phys. 57, 617 (1985)

    Google Scholar 

  11. J.P. Eckmann, S. Kamphorst, D. Ruelle, Europhys. Lett. 4, 973 (1987)

    Google Scholar 

  12. M. Casdagli, Physica D 108, 12 (1997)

  13. J. Gao, H. Cai, Phys. Lett. A 270, 75 (2000)

    Google Scholar 

  14. J. Iwanski, E. Bradley, Chaos 8, 861 (1998)

    Google Scholar 

  15. M. Koebbe, G. Mayer-Kress, Nonlinear Modeling and Forecasting, edited by M. Casdagli, S. Eubank (Addison Wesley, New York, 1992)

  16. G. McGuire, N. Azar, M. Shelhammer, Phys. Lett. A 237, 43 (1997)

    Google Scholar 

  17. C. Webber, J. Zbilut, J. Appl. Phys. 76, 965 (1994)

    Google Scholar 

  18. J. Zbilut, A. Giuliani, C. Webber, Phys. Lett. A 246, 122 (1998)

    Google Scholar 

  19. J. Zbilut, C. Webber, Phys. Lett. A 171, 199 (1992)

    Google Scholar 

  20. A. Giuliani, G. Piccirillo, V. Marigliano, A. Colosimo, Am. J. Phys. 275, 1455 (1998)

    Google Scholar 

  21. L.L. Trulla, A. Giuliani, J.P. Zbilut, C.L. Webber, Phys. Lett. A 223, 255 (1996)

    Google Scholar 

  22. C.L. Webber, J.P. Zbilut, J. Appl. Phys. 76, 965 (1994)

    Google Scholar 

  23. J.P. Zbilut, C.L. Webber, Phys. Lett. A 171, 199 (1992)

    Google Scholar 

  24. J.P. Zbilut, A. Giuliani, C.L. Webber, Phys. Lett. A 237, 131 (1998)

    Google Scholar 

  25. N. Marwan, M.C. Romano, M. Thiel, J. Kurths, Phys. Rep. 438, 237 (2007)

    Google Scholar 

  26. https://expasy.org

  27. M.G. Bulmer, Principles of Statistics (Dover Press, 1979)

  28. X. Wang, K. Smith, R. Hyndman, Data. Min. Knowl. Disc. 13, 335 (2006)

    Google Scholar 

  29. T. Teraesvirta, C.F. Lin, C.W.J. Granger, J. Time Ser. Anal. 14, 209 (1993)

    Google Scholar 

  30. O. Rose, Research Report 137 (1996)

  31. M. Kuss, C.E. Rasmussen, J. Mach. Learn. Res. 6, 1679 (2005)

  32. C.E. Rasmussen, C.K.I. Williams, Gaussian Processes for Machine Learning (The MIT Press, Cambridge, MA, 2006)

  33. T.P. Minka, Ph.D. thesis, Department of Electrical Engineering and Computer Science, MIT, 2001

  34. R.E. Kass, A.E. Raftery, J. Amer. Statistical Assoc. 90, 773 (1995)

    Google Scholar 

  35. D.J.C. MacKay, Neural Comput. 11, 1035 (1999)

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to S. Angadi.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Angadi, S., Kulkarni, A. Nonlinear signal analysis to understand the dynamics of the protein sequences. Eur. Phys. J. Spec. Top. 164, 141–155 (2008). https://doi.org/10.1140/epjst/e2008-00840-6

Download citation

Keywords

  • Inclusion Body
  • European Physical Journal Special Topic
  • Recurrence Time
  • Recurrence Plot
  • Form Inclusion Body