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)


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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

Personalised recommendations