P Systems, a New Computational Modelling Tool for Systems Biology

  • Mario Jesús Pérez-Jiménez
  • Francisco José Romero-Campero
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4220)


In this paper we present P systems as a reliable computational modelling tool for Systems Biology that takes into account the discrete character of the quantity of components of biological systems, the inherently randomness in biological phenomena and the key role played by membranes in the functioning of living cells. We will introduce two different strategies for the evolution of P systems, namely, Multi-compartmental Gillespie’s Algorithm based on the well known Gillespie’s Algorithm but running on more than one compartment; and Deterministic Waiting Times Algorithm, an exact deterministic method. In order to illustrate these two strategies we have modelled two biological systems: the EGFR Signalling Cascade and the Quorum Sensing System in the bacterium Vibrio Fischeri. Our simulations results show that for the former system a deterministic approach is valid whereas for the latter a stochastic approach like Multi-compartmental Gillespie’s Algorithm is necessary.


Epidermal Growth Factor System Biology Membrane Structure Quorum Sensing Venn Diagram 
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  1. 1.
    Aho, A.V., Sethi, R., Ulmann, J.D.: Compilers: Principles, Techniques, and Tools. Addison-Wesley, Reading (1986)Google Scholar
  2. 2.
    Ardelean, I., Cavaliere, M.: Playing with a Probabilistic P Simulator: Mathematical and Biological Problems. In: Cavaliere, M., Martin-Vide, C., Păun, G. (eds.) Brainstorming Week on Membrane Computing, Tarragona, February 5-11 (2003); Tech. Rep. 26/03, Universitat Rovira i Virgili, Tarragona, Spain, pp. 37–45Google Scholar
  3. 3.
    Bernardini, F., Gheorghe, M., Muniyandi, R.C., Krasnogor, N., Pérez-Jiménez, M.J., Romero-Campero, F.J.: On P Systems as a Modelling Tool for Biological Systems. In: Freund, R., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2005. LNCS, vol. 3850, pp. 114–133. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
    Bernardini, F., Manca, V.: P Systems with Boundary Rules. In: [20], pp. 107–118 (2003)Google Scholar
  5. 5.
    Besozzi, D.: Computational and Modelling Power of P systems, Ph.D. Thesis, Università degli Studi di Milano, Milan, Italy (2004)Google Scholar
  6. 6.
    Bianco, L., Fontana, F., Franco, G., Manca, V.: P Systems for Biological Dynamics. In: Ciobanu, G., Păun, G., Pérez-Jiménez, M.J. (eds.) Applications of Membrane Computing, pp. 81–126. Springer, Heidelberg (2005)Google Scholar
  7. 7.
    Bianco, L., Fontana, F., Manca, V.: P Systems and the Modelling of Biochemical Oscillation. In: Pre-Proceedings of WMC6 - Vienna 2005, pp. 214–225 (2005)Google Scholar
  8. 8.
    Gibson, M.A., Bruck, J.: Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels. Journal of Physical Chemistry 104(25), 1876–1889 (2000)Google Scholar
  9. 9.
    Gillespie, D.T.: A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions. J. Comput. Physics 22, 403–434 (1976)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Gillespie, D.T.: Exact Stochastic Simulation of Coupled Chemical Reactions. The Journal of Physical Chemistry 81(25), 2340–2361 (1977)CrossRefGoogle Scholar
  11. 11.
    Gillespie, D.T.: Approximate Accelerated Stochastic Simulation of Chemically Reacting Systems. Journal of Chemical Physics 115(4), 1716–1733 (2001)CrossRefGoogle Scholar
  12. 12.
    Gillespie, D.T.: Improved Leap-size Selection for Accelerated Stochastic Simulation. Journal of Chemical Physics 119(16), 8229–8234 (2003)CrossRefGoogle Scholar
  13. 13.
    Karwowski, R., Prusinkiewicz, P.: Design and Implementation of the L+C Modelling Language. Electronics Notes in Theoretical Computer Science 82(2), 1–19 (2003)Google Scholar
  14. 14.
    Meng, T.C., Somani, S., Dhar, P.: Modelling and Simulation of Biological Systems with Stochasticity. In: Silico Biology, vol. 4, p. 0024 (2004)Google Scholar
  15. 15.
    Milner, R.: Communicating and Mobile System: The π-Calculus. Cambridge University Press, Cambridge (1999)Google Scholar
  16. 16.
    Moehren, G., et al.: Temperature Dependence of the Epidermal Growth Factor Receptor Signaling Network Can Be Accounted for by a Kinetic Model. Biochemistry 41, 306–320 (2002)CrossRefGoogle Scholar
  17. 17.
    Păun, A., Păun, G.: The Power of Communication: P Systems with Symport/Antiport. New Generation Computing 20(3), 295–305 (2002)zbMATHCrossRefGoogle Scholar
  18. 18.
    Păun, G.: Computing with Membranes. Journal of Computer and System Sciences 61(1), 108–143 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Păun, G.: Membrane Computing. An Introduction. Springer, Heidelberg (2002)zbMATHGoogle Scholar
  20. 20.
    Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.): WMC 2002. LNCS, vol. 2597. Springer, Heidelberg (2003)zbMATHGoogle Scholar
  21. 21.
    Philips, A., Cardelli., L.: A Correct Abstract Machine for the Stochastic Pi-calculus. Electronical Notes in Theoretical Computer Science (to appear, 2004)Google Scholar
  22. 22.
    Priami, C., Regev, A., Shapiro, E., Silverman, W.: Application of a Stochastic Name-Passing Calculus to Representation and Simulation of Molecular Processes. Information Processing Letters 80, 25–31 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Schoeberl, B., et al.: Computational Modeling of the Dynamics of the MAP Kinase Cascade Activated by Surface and Internalized EGF Receptors. Nature Biotech. 20, 370–375 (2002)CrossRefGoogle Scholar
  24. 24.
    Stundzia, A.B., Lumsden, C.J.: Stochastic Simulation of Coupled Reaction-Diffusion Processes. Journal of Computational Physics 127, 196–207 (1996)zbMATHCrossRefGoogle Scholar
  25. 25.
    Nottingham Quorum Sensing Web Site,
  26. 26.
    ISI Web Site (2003) html,
  27. 27.
    Scilab Web Pages:
  28. 28.
    The P Systems Web Page:
  29. 29.
    The Stochastic Pi-Machine:
  30. 30.
    SciLab Web Site,

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Mario Jesús Pérez-Jiménez
    • 1
  • Francisco José Romero-Campero
    • 1
  1. 1.Research Group on Natural Computing, Department of Computer Science and Artificial IntelligenceUniversity of SevillaSevillaSpain

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