Advertisement

Probabilistic Model Checking of Complex Biological Pathways

  • J. Heath
  • M. Kwiatkowska
  • G. Norman
  • D. Parker
  • O. Tymchyshyn
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4210)

Abstract

Probabilistic model checking is a formal verification technique that has been successfully applied to the analysis of systems from a broad range of domains, including security and communication protocols, distributed algorithms and power management. In this paper we illustrate its applicability to a complex biological system: the FGF (Fibroblast Growth Factor) signalling pathway. We give a detailed description of how this case study can be modelled in the probabilistic model checker PRISM, discussing some of the issues that arise in doing so, and show how we can thus examine a rich selection of quantitative properties of this model. We present experimental results for the case study under several different scenarios and provide a detailed analysis, illustrating how this approach can be used to yield a better understanding of the dynamics of the pathway.

Keywords

Fibroblast Growth Factor Model Check Fibroblast Growth Factor Receptor Continuous Time Markov Chain Probabilistic Model Check 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aziz, A., Sanwal, K., Singhal, V., Brayton, R.: Verifying continuous time Markov chains. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 269–276. Springer, Heidelberg (1996)Google Scholar
  2. 2.
    Baier, C., Haverkort, B., Hermanns, H., Katoen, J.-P.: Model checking continuous-time Markov chains by transient analysis. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 358–372. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  3. 3.
    Calder, M., Gilmore, S., Hillston, J.: Modelling the influence of RKIP on the ERK signalling pathway using the stochastic process algebra PEPA. Transactions on Computational Systems Biology (to appear, 2006)Google Scholar
  4. 4.
    Calder, M., Vyshemirsky, V., Gilbert, D., Orton, R.: Analysis of signalling pathways using continuous time Markov chains. Transactions on Computational Systems Biology (to appear, 2006)Google Scholar
  5. 5.
    Dikic, I., Giordano, S.: Negative receptor signalling. Curr. Opin. Cell Biol. 15, 128–135 (2003)CrossRefGoogle Scholar
  6. 6.
    Eswarakumar, V., Lax, I., Schlessinger, J.: Cellular signaling by fibroblast growth factor receptors. Cytokine Growth Factor Rev. 16(2), 139–149 (2005)CrossRefGoogle Scholar
  7. 7.
    Gillespie, D.: Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry 81(25), 2340–2361 (1977)CrossRefGoogle Scholar
  8. 8.
    Hillston, J.: A Compositional Approach to Performance Modelling. Cambridge University Press, Cambridge (1996)CrossRefGoogle Scholar
  9. 9.
    Hinton, A., Kwiatkowska, M., Norman, G., Parker, D.: PRISM: A tool for automatic verification of probabilistic systems. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006 and ETAPS 2006. LNCS, vol. 3920, pp. 441–444. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    Kwiatkowska, M., Norman, G., Parker, D.: Probabilistic symbolic model checking with PRISM: A hybrid approach. International Journal on Software Tools for Technology Transfer (STTT) 6(2), 128–142 (2004)Google Scholar
  11. 11.
    Kwiatkowska, M., Norman, G., Parker, D.: Probabilistic model checking in practice: Case studies with PRISM. ACM SIGMETRICS Performance Evaluation Review 32(4), 16–21 (2005)CrossRefGoogle Scholar
  12. 12.
    Phillips, A., Cardelli, L.: A correct abstract machine for the stochastic pi-calculus. In: Proc. BioCONCUR 2004. ENTCS. Elsevier, Amsterdam (2004)Google Scholar
  13. 13.
  14. 14.
  15. 15.
    Priami, C.: Stochastic π-calculus. The Computer Journal 38(7), 578–589 (1995)CrossRefGoogle Scholar
  16. 16.
    Priami, C., Regev, A., Silverman, W., Shapiro, E.: Application of a stochastic name passing calculus to representation and simulation of molecular processes. Information Processing Letters 80, 25–31 (2001)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Regev, A., Shapiro, E.: Cellular abstractions: Cells as computation. Nature 419(6905), 343 (2002)CrossRefGoogle Scholar
  18. 18.
    Regev, A., Silverman, W., Shapiro, E.: Representation and simulation of biochemical processes using the pi- calculus process algebra. In: Altman, R., Dunker, A., Hunter, L., Klein, T. (eds.) Pacific Symposium on Biocomputing, 2001, vol. 6, pp. 459–470. World Scientific Press, Singapore (2001)Google Scholar
  19. 19.
    Rutten, J., Kwiatkowska, M., Norman, G., Parker, D.: Mathematical Techniques for Analyzing Concurrent and Probabilistic Systems. CRM Monograph Series, vol. 23. AMS (2004)Google Scholar
  20. 20.
    Schlessinger, J.: Epidermal growth factor receptor pathway. Sci. STKE (Connections Map), http://stke.sciencemag.org/cgi/cm/stkecm;CMP_14987
  21. 21.
    Tsang, M., Dawid, I.: Promotion and attenuation of FGF signaling through the Ras-MAPK pathway. Science STKE, 17 (2004)Google Scholar
  22. 22.
    Tymchyshyn, O., Norman, G., Heath, J., Kwiatkowska, M.: Computer assisted biological reasoning: The simulation and analysis of FGF signalling pathway dynamics (submitted for publication)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • J. Heath
    • 1
  • M. Kwiatkowska
    • 2
  • G. Norman
    • 2
  • D. Parker
    • 2
  • O. Tymchyshyn
    • 2
  1. 1.School of Biosciences 
  2. 2.School of Computer ScienceUniversity of BirminghamBirminghamUK

Personalised recommendations