Efficient, Correct Simulation of Biological Processes in the Stochastic Pi-calculus

  • Andrew Phillips
  • Luca Cardelli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4695)

Abstract

This paper presents a simulation algorithm for the stochastic π-calculus, designed for the efficient simulation of biological systems with large numbers of molecules. The cost of a simulation depends on the number of species, rather than the number of molecules, resulting in a significant gain in efficiency. The algorithm is proved correct with respect to the calculus, and then used as a basis for implementing the latest version of the SPiM stochastic simulator. The algorithm is also suitable for generating graphical animations of simulations, in order to visualise system dynamics.

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References

  1. 1.
    Bloch, A., Haagensen, B., Hoyer, M.K., Knudsen, S.U.: The StoPi-calculus and Simulator, http://www.cs.aau.dk/bh/education.html
  2. 2.
    Blossey, R., Cardelli, L., Phillips, A.: A compositional approach to the stochastic dynamics of gene networks. Transactions in Computational Systems Biology 3939, 99–122 (2006)MathSciNetGoogle Scholar
  3. 3.
    Gansner, E.R., North, S.C.: An open graph visualization system and its applications to software engineering. Software-Practice and Experience, 1–5 (1999)Google Scholar
  4. 4.
    Gibson, M.A., Bruck, J.: Efficient exact stochastic simulation of chemical systems with many species and many channels. J. Phys. Chem. 104, 1876–1889 (2000)Google Scholar
  5. 5.
    Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81(25), 2340–2361 (1977)CrossRefGoogle Scholar
  6. 6.
    Gillespie, D.T.: Approximate accelerated stochastic simulation of chemically reacting systems. J. Chem. Phys. 115, 1716–1733 (2001)CrossRefGoogle Scholar
  7. 7.
    Lecca, P., Priami, C.: Cell cycle control in eukaryotes: a biospi model. In: BioConcur 2003. ENTCS (2003)Google Scholar
  8. 8.
    Milner, R.: Communicating and Mobile Systems: the π-Calculus. Cambridge University Press, Cambridge (1999)Google Scholar
  9. 9.
    Phillips, A.: The Stochastic Pi-Machine (2006), Available from http://research.microsoft.com/~aphillip/spim/
  10. 10.
    Phillips, A., Cardelli, L.: A correct abstract machine for the stochastic pi-calculus. In: Bioconcur 2004, ENTCS (August 2004)Google Scholar
  11. 11.
    Phillips, A., Cardelli, L., Castagna, G.: A graphical representation for biological processes in the stochastic pi-calculus. In: Priami, C., Ingólfsdóttir, A., Mishra, B., Nielson, H.R. (eds.) Transactions on Computational Systems Biology VII. LNCS (LNBI), vol. 4230, pp. 123–152. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
    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)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Regev, A., Silverman, W., Shapiro, E.: Representation and simulation of biochemical processes using the pi- calculus process algebra. In: Pacific Symposium on Biocomputing, vol. 6, pp. 459–470 (2001)Google Scholar
  14. 14.
    Romanel, A., Dematte, L., Priami, C.: The Beta Workbench. Available from http://www.cosbi.eu/Rpty_Soft_BetaWB.php
  15. 15.
    Tian, T., Burrage, K.: Binomial leap methods for simulating stochastic chemical kinetics. J. Chem. Phys. 121, 10356–10364 (2004)CrossRefGoogle Scholar
  16. 16.
    Turner, D.N.: The Polymorphic Pi-Calculus: Theory and Implementation. PhD thesis CST-126-96 (June 1996) (also published as ECS-LFCS-96-345)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Andrew Phillips
    • 1
  • Luca Cardelli
    • 1
  1. 1.Microsoft Research, 7 JJ Thomson Avenue, CB3 0FB CambridgeUK

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