Goldbeter’s Mitotic Oscillator Entirely Modeled by MP Systems

  • Vincenzo Manca
  • Luca Marchetti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6501)

Abstract

MP systems are a class of P systems introduced for modeling metabolic processes. Here we apply an algorithm, we call Log-Gain Stoichiometric Stepwise Regression (LGSS), to Golbeter’s oscillator. In general, LGSS derives MP models from the time series of observed dynamics. In the case of Golbeter’s oscillator, we found that by considering different values of the resolution time τ, different analytical forms of regulation maps were appropriate. By means of a suitable MATLAB implementation of LGSS, we automatically generated 700 MP models (τ varying from 10− 3 min to 700 ·10− 3 min with increments of 10− 3 min). Many of these models exhibit a good approximation, and have second degree polynomials as regulation maps. These results provide an experimental evidence of LGSS adequacy.

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References

  1. 1.
    von Bertalanffy, L.: General Systems Theory: Foundations, Developments, Applications. George Braziller Inc., New York (1967)Google Scholar
  2. 2.
    Draper, N., Smith, H.: Applied Regression Analysis, 2nd edn. John Wiley & Sons, New York (1981)MATHGoogle Scholar
  3. 3.
    Goldbeter, A.: A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. PNAS 88(20), 9107–9111 (1991)CrossRefGoogle Scholar
  4. 4.
    Goldbeter, A.: Biochemical Oscillations and Cellular Rhythms: The molecular bases of periodic and chaotic behaviour. Cambridge University Press, Cambridge (1996)CrossRefMATHGoogle Scholar
  5. 5.
    Goldbeter, A.: Computational approaches to cellular rhythms. Nature 420, 238–245 (2002)CrossRefGoogle Scholar
  6. 6.
    Hocking, R.R.: The Analysis and Selection of Variables in Linear Regression. Biometrics, 32 (1976)Google Scholar
  7. 7.
    Luenberger, D.G.: Optimization by Vector Space Methods. John Wiley & Sons, Chichester (1969)MATHGoogle Scholar
  8. 8.
    Manca, V.: Log-Gain Principles for Metabolic P Systems. In: Condon, A., et al. (eds.) Algorithmic Bioprocesses. Natural Computing Series, ch. 28, pp. 585–605. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  9. 9.
    Manca, V.: Fundamentals of Metabolic P Systems. In: [15], ch. 19.Oxford University Press, Oxford (2010)Google Scholar
  10. 10.
    Manca, V.: Metabolic P systems. Scholarpedia 5(3), 9273 (2010)CrossRefGoogle Scholar
  11. 11.
    Manca, V., Bianco, L., Fontana, F.: Evolutions and Oscillations of P systems: Theoretical Considerations and Application to biological phenomena. In: Mauri, G., Păun, G., Jesús Pérez-Jímenez, M., Rozenberg, G., Salomaa, A. (eds.) WMC 2004. LNCS, vol. 3365, pp. 63–84. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    Manca, V., Marchetti, L.: Metabolic approximation of real periodical functions. Journal of Logic and Algebraic Programming (2010), doi:10.1016/j.jlap.2010.03.005Google Scholar
  13. 13.
    Manca, V., Marchetti, L.: Log-Gain Stoichiometic Stepwise regression for MP systems. IJFCS (to appear, 2010)Google Scholar
  14. 14.
    Păun, G.: Membrane Computing. An Introduction. Springer, Heidelberg (2002)CrossRefMATHGoogle Scholar
  15. 15.
    Păun, G., Rozenberg, G., Salomaa, A. (eds.): Oxford Handbook of Membrane Computing. Oxford University Press, Oxford (2010)MATHGoogle Scholar
  16. 16.
    Pearson, K.: Notes on the History of Correlation. Biometrika 13(1), 25–45 (1920)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Vincenzo Manca
    • 1
  • Luca Marchetti
    • 1
  1. 1.Department of Computer ScienceUniversity of VeronaVeronaItaly

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