Rule-Based Modelling, Symmetries, Refinements

  • Vincent Danos
  • Jérôme Feret
  • Walter Fontana
  • Russell Harmer
  • Jean Krivine
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5054)

Abstract

Rule-based modelling is particularly effective for handling the highly combinatorial aspects of cellular signalling. The dynamics is described in terms of interactions between partial complexes, and the ability to write rules with such partial complexes -i.e., not to have to specify all the traits of the entitities partaking in a reaction but just those that matter- is the key to obtaining compact descriptions of what otherwise could be nearly infinite dimensional dynamical systems. This also makes these descriptions easier to read, write and modify.

In the course of modelling a particular signalling system it will often happen that more traits matter in a given interaction than previously thought, and one will need to strengthen the conditions under which that interaction may happen. This is a process that we call rule refinement and which we set out in this paper to study. Specifically we present a method to refine rule sets in a way that preserves the implied stochastic semantics.

This stochastic semantics is dictated by the number of different ways in which a given rule can be applied to a system (obeying the mass action principle). The refinement formula we obtain explains how to refine rules and which choice of refined rates will lead to a neutral refinement, i.e., one that has the same global activity as the original rule had (and therefore leaves the dynamics unchanged). It has a pleasing mathematical simplicity, and is reusable with little modification across many variants of stochastic graph rewriting. A particular case of the above is the derivation of a maximal refinement which is equivalent to a (possibly infinite) Petri net and can be useful to get a quick approximation of the dynamics and to calibrate models. As we show with examples, refinement is also useful to understand how different subpopulations contribute to the activity of a rule, and to modulate differentially their impact on that activity.

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References

  1. 1.
    Orton, R.J., Sturm, O.E., Vyshemirsky, V., Calder, M., Gilbert, D.R., Kolch, W.: Computational modelling of the receptor tyrosine kinase activated MAPK pathway. Biochemical Journal 392(2), 249–261 (2005)CrossRefGoogle Scholar
  2. 2.
    Söderberg, B.: General formalism for inhomogeneous random graphs. Physical Review E 66(6), 66121 (2002)CrossRefGoogle Scholar
  3. 3.
    Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81, 2340–2361 (1977)CrossRefGoogle Scholar
  4. 4.
    Danos, V., Feret, J., Fontana, W., Krivine, J.: Abstract interpretation of cellular signalling networks. In: Logozzo, F., et al. (eds.) VMCAI 2008. LNCS, vol. 4905, pp. 83–97. Springer, Heidelberg (2008)Google Scholar
  5. 5.
    Danos, V., Feret, J., Fontana, W., Krivine, J.: Scalable simulation of cellular signaling networks. In: Shao, Z. (ed.) APLAS 2007. LNCS, vol. 4807, pp. 139–157. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  6. 6.
    Danos, V., Feret, J., Fontana, W., Harmer, R., Krivine, J.: Rule-based modelling of cellular signalling. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR. LNCS, vol. 4703. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Danos, V.: Agile modelling of cellular signalling. In: Proceedings of ICCMSE (2007)Google Scholar
  8. 8.
    Blinov, M.L., Faeder, J.R., Goldstein, B., Hlavacek, W.S.: A network model of early events in epidermal growth factor receptor signaling that accounts for combinatorial complexity. BioSystems 83, 136–151 (2006)CrossRefGoogle Scholar
  9. 9.
    Hlavacek, W.S., Faeder, J.R., Blinov, M.L., Posner, R.G., Hucka, M., Fontana, W.: Rules for Modeling Signal-Transduction Systems. Science’s STKE 2006(344) (2006)Google Scholar
  10. 10.
    Blinov, M.L., Yang, J., Faeder, J.R., Hlavacek, W.S.: Graph theory for rule-based modeling of biochemical networks. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653. Springer, Heidelberg (2005)Google Scholar
  11. 11.
    Faeder, J.R., Blinov, M.L., Goldstein, B., Hlavacek, W.S.: Combinatorial complexity and dynamical restriction of network flows in signal transduction. Systems Biology 2(1), 5–15 (2005)CrossRefGoogle Scholar
  12. 12.
    Regev, A., Silverman, W., Shapiro, E.: Representation and simulation of biochemical processes using the π-calculus process algebra. In: Altman, R.B., Dunker, A.K., Hunter, L., Klein, T.E. (eds.) Pacific Symposium on Biocomputing, vol. 6, pp. 459–470. World Scientific Press, Singapore (2001)Google Scholar
  13. 13.
    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 (2001)Google Scholar
  14. 14.
    Regev, A., Shapiro, E.: Cells as computation. Nature 419 (September 2002)Google Scholar
  15. 15.
    Priami, C., Quaglia, P.: Beta binders for biological interactions. In: Danos, V., Schachter, V. (eds.) CMSB 2004. LNCS (LNBI), vol. 3082, pp. 20–33. Springer, Heidelberg (2005)Google Scholar
  16. 16.
    Danos, V., Krivine, J.: Formal molecular biology done in CCS. In: Proceedings of BIO-CONCUR 2003, Marseille, France. Electronic Notes in Theoretical Computer Science, vol. 180, pp. 31–49. Elsevier, Amsterdam (2003)Google Scholar
  17. 17.
    Regev, A., Panina, E.M., Silverman, W., Cardelli, L., Shapiro, E.: BioAmbients: an abstraction for biological compartments. Theoretical Computer Science 325(1), 141–167 (2004)CrossRefMathSciNetMATHGoogle Scholar
  18. 18.
    Cardelli, L.: Brane calculi. In: Proceedings of BIO-CONCUR 2003. Electronic Notes in Theoretical Computer Science, vol. 180. Elsevier, Amsterdam (2003)Google Scholar
  19. 19.
    Calder, M., Gilmore, S., Hillston, J.: Modelling the influence of RKIP on the ERK signalling pathway using the stochastic process algebra PEPA. In: Priami, C., Ingólfsdóttir, A., Mishra, B., Riis Nielson, H. (eds.) Transactions on Computational Systems Biology VII. LNCS (LNBI), vol. 4230, pp. 1–23. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  20. 20.
    Gillespie, D.T.: A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comp. Phys. 22, 403–434 (1976)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Lack, S., Sobocinski, P.: Adhesive and quasiadhesive categories. Theoretical Informatics and Applications 39(3), 511–546 (2005)CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Vincent Danos
    • 1
    • 3
  • Jérôme Feret
    • 2
  • Walter Fontana
    • 2
  • Russell Harmer
    • 3
  • Jean Krivine
    • 2
  1. 1.University of Edinburgh 
  2. 2.Harvard Medical School 
  3. 3.CNRSUniversité Paris Diderot 

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