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A Bayesian Approach to Model Checking Biological Systems

  • Sumit K. Jha
  • Edmund M. Clarke
  • Christopher J. Langmead
  • Axel Legay
  • André Platzer
  • Paolo Zuliani
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5688)

Abstract

Recently, there has been considerable interest in the use of Model Checking for Systems Biology. Unfortunately, the state space of stochastic biological models is often too large for classical Model Checking techniques. For these models, a statistical approach to Model Checking has been shown to be an effective alternative. Extending our earlier work, we present the first algorithm for performing statistical Model Checking using Bayesian Sequential Hypothesis Testing. We show that our Bayesian approach outperforms current statistical Model Checking techniques, which rely on tests from Classical (aka Frequentist) statistics, by requiring fewer system simulations. Another advantage of our approach is the ability to incorporate prior Biological knowledge about the model being verified. We demonstrate our algorithm on a variety of models from the Systems Biology literature and show that it enables faster verification than state-of-the-art techniques, even when no prior knowledge is available.

Keywords

Model Check Power Curve Sequential Probability Ratio Test Symbolic Model Check Bayesian Algorithm 
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.

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References

  1. 1.
    Antoniotti, M., Policriti, A., Ugel, N., Mishra, B.: Model building and model checking for biochemical processes. Cell Biochem. Biophys. 38(3), 271–286 (2003)CrossRefPubMedGoogle Scholar
  2. 2.
    Baier, C., Clarke, E.M., Hartonas-Garmhausen, V., Kwiatkowska, M.Z., Ryan, M.: Symbolic model checking for probabilistic processes. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds.) ICALP 1997. LNCS, vol. 1256, pp. 430–440. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  3. 3.
    Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.-P.: Model-checking algorithms for continuous-time markov chains. IEEE Trans. Software Eng. 29(6), 524–541 (2003)CrossRefGoogle Scholar
  4. 4.
    Bailey, N.: The Elements of Stochastic Processes with Applications to the Natural Sciences. Wiley-IEEE (1990)Google Scholar
  5. 5.
    Barkai, N., Leibler, S.: Biological rhythms: Circadian clocks limited by noise. Nature 403, 267–268 (2000)PubMedGoogle Scholar
  6. 6.
    Batt, G., Ropers, D., de Jong, H., Geiselmann, J., Mateescu, R., Page, M., Schneider, D.: Validation of qualitative models of genetic regulatory networks by model checking: analysis of the nutritional stress response in Escherichia coli. Bioinformatics 25(1), i19–i28 (2005)CrossRefGoogle Scholar
  7. 7.
    Bechhofer, R.: A note on the limiting relative efficiency of the Wald sequential probability ratio test. J. Amer. Statist. Assoc. 55, 660–663 (1960)CrossRefGoogle Scholar
  8. 8.
    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 (2006) (in press)Google Scholar
  9. 9.
    Calder, M., Vyshemirsky, V., Gilbert, D., Orton, R.: Analysis of signalling pathways using the PRISM model checker. In: Proc. Computational Methods in Systems Biology (CMSB 2005), pp. 179–190 (2005)Google Scholar
  10. 10.
    Cardelli, L.: Abstract machines of systems biology. In: Priami, C., Merelli, E., Gonzalez, P., Omicini, A. (eds.) Transactions on Computational Systems Biology III. LNCS (LNBI), vol. 3737, pp. 145–168. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Chabrier, N., Fages, F.: Symbolic Model Checking of Biochemical Networks. In: Priami, C. (ed.) CMSB 2003. LNCS, vol. 2602, pp. 149–162. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  12. 12.
    Ciesinski, F., Größer, M.: On probabilistic computation tree logic. In: Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.-P., Siegle, M. (eds.) Validation of Stochastic Systems. LNCS, vol. 2925, pp. 147–188. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  13. 13.
    Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching-time temporal logic. In: Logic of Programs, Workshop, London, UK, pp. 52–71. Springer, Heidelberg (1982)CrossRefGoogle Scholar
  14. 14.
    Clarke, E.M., Faeder, J.R., Langmead, C.J., Harris, L.A., Jha, S.K., Legay, A.: Statistical model checking in biolab: Applications to the automated analysis of t-cell receptor signaling pathway. In: Heiner, M., Uhrmacher, A.M. (eds.) CMSB 2008. LNCS (LNBI), vol. 5307, pp. 231–250. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  15. 15.
    Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (1999)Google Scholar
  16. 16.
    Courcoubetis, C., Yannakakis, M.: The complexity of probabilistic verification. Journal of the ACM 42(4), 857–907 (1995)CrossRefGoogle Scholar
  17. 17.
    Diaconis, P., Ylvisaker, D.: Quantifying prior opinion. In: Bernardo, J.M., De Groot, M.H., Lindley, D.B., Smith, A.F.M. (eds.) Bayesian Statistics 2: Proceedings of the 2nd Valencia International Meeting. Elsevier Science Publisher, Amsterdam (1985)Google Scholar
  18. 18.
    Fages, F.: Temporal logic constraints in the biochemical abstract machine biocham. In: Hill, P.M. (ed.) LOPSTR 2005. LNCS, vol. 3901, pp. 1–5. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  19. 19.
    Finkbeiner, B., Sipma, H.: Checking finite traces using alternating automata. In: Proceedings of Runtime Verification (RV 2001), pp. 44–60 (2001)Google Scholar
  20. 20.
    Fisher, J., Piterman, N., Hubbard, E.J., Stern, M.J., Harel, D.: Computational insights into caenorhabditis elegans vulval development. Proc. Natl. Acad. Sci. U S A 102(6), 1951–1956 (2005)CrossRefPubMedPubMedCentralGoogle Scholar
  21. 21.
    Ghosh, B., Sen, P. (eds.): Handbook of sequential analysis. Dekker, New York (1991)Google Scholar
  22. 22.
    Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry 81(25), 2340–2361 (1977)CrossRefGoogle Scholar
  23. 23.
    Grosu, R., Smolka, S.: Monte Carlo Model Checking. In: CAV, pp. 271–286 (2005)Google Scholar
  24. 24.
    Heath, J., Kwiatkowska, M., Norman, G., Parker, D., Tymchyshyn, O.: Probabilistic model checking of complex biological pathways. In: Priami, C. (ed.) CMSB 2006. LNCS (LNBI), vol. 4210, pp. 32–47. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  25. 25.
    Heath, J., Kwiatkowska, M., Norman, G., Parker, D., Tymchyshyn, O.: Probabilistic model checking of complex biological pathways. Theoretical Computer Science 319(3), 239–257 (2008)CrossRefGoogle Scholar
  26. 26.
    Hérault, T., Lassaigne, R., Magniette, F., Peyronnet, S.: Approximate probabilistic model checking. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, pp. 73–84. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  27. 27.
    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. LNCS, vol. 3920, pp. 441–444. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  28. 28.
    Jeffreys, H.: Theory of Probability. Clarendon Press, Oxford (1961)Google Scholar
  29. 29.
    Jha, S.K., Clarke, E.M., Langmead, C.J., Legay, A., Platzer, A., Zuliani, P.: A bayesian approach to model checking biological systems. Technical Report CMU-CS-09-110, Computer Science Department, Carnegie Mellon University (2009)Google Scholar
  30. 30.
    Kam, N., Harel, D., Cohen, I.R.: Modeling biological reactivity: Statecharts vs. boolean logic. In: Proceedings of the Second International Conference on Systems Biology (2001)Google Scholar
  31. 31.
    Kwiatkowska, M.Z., Norman, G., Parker, D.: Prism 2.0: A tool for probabilistic model checking. In: QEST, pp. 322–323. IEEE, Los Alamitos (2004)Google Scholar
  32. 32.
    Langmead, C.J.: Generalized Queries and Bayesian Statistical Model Checking in Dynamic Bayesian Networks: Application to Personalized Medicine. In: Proc. 8th Ann. Intnl Conf. on Comput. Sys. Bioinf. (CSB), pp. 201–212 (2009)Google Scholar
  33. 33.
    Lecca, P., Priami, C.: Cell cycle control in eukaryotes: A BioSpi model. In: Proc. Workshop on Concurrent Models in Molecular Biology (BioConcur 2003). ENTCS (2003)Google Scholar
  34. 34.
    McAdams, H., Shapiro, L.: Circuit simulation of genetic networks. Science 269, 650–656 (1995)CrossRefPubMedGoogle Scholar
  35. 35.
    Owicki, S.S., Lamport, L.: Proving liveness properties of concurrent programs. ACM Trans. Program. Lang. Syst. 4(3), 455–495 (1982)CrossRefGoogle Scholar
  36. 36.
    Pnueli, A.: The temporal logic of programs. In: FOCS, pp. 46–57. IEEE, Los Alamitos (1977)Google Scholar
  37. 37.
    Priami, C., Regev, A., Shapiro, E., Silverman, W.: Application of a stochastic name-passing calculus to representation and simulation of molecular processes. Inf. Process. Lett. 80(1), 25–31 (2001)CrossRefGoogle Scholar
  38. 38.
    Sadot, A., Fisher, J., Barak, D., Admanit, Y., Stern, M.J., Hubbard, E.J.A., Harel, D.: Toward verified biological models. IEEE/ACM Transactions on Computational Biology and Bioinformatics 5(2), 223–234 (2008)CrossRefPubMedGoogle Scholar
  39. 39.
    Sen, K., Viswanathan, M., Agha, G.: Statistical model checking of black-box probabilistic systems. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 202–215. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  40. 40.
    Sen, K., Viswanathan, M., Agha, G.: On statistical model checking of stochastic systems. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 266–280. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  41. 41.
    Vilar, J., Kueh, H.-Y., Barkai, N., Leibler, S.: Mechanisms of noise-resistance in genetic oscillators. Proc. Nat. Acad. Sci. USA 99(9), 5988–5992 (2002)CrossRefPubMedPubMedCentralGoogle Scholar
  42. 42.
    Wald, A.: Sequential tests of statistical hypotheses. Annals of Mathematical Statistics 16(2), 117–186 (1945)CrossRefGoogle Scholar
  43. 43.
    Wald, A.: Sequential Analysis. Dover Publications (June 2004)Google Scholar
  44. 44.
    Yi, T.M., Kitano, H., Simon, M.I.: A quantitative characterization of the yeast heterotrimeric g protein cycle. Proc. Natl. Acad. Sci. USA 100(19), 10764–10769 (2003)CrossRefPubMedPubMedCentralGoogle Scholar
  45. 45.
    Younes, H.L.S., Kwiatkowska, M.Z., Norman, G., Parker, D.: Numerical vs. statistical probabilistic model checking. STTT 8(3), 216–228 (2006)CrossRefGoogle Scholar
  46. 46.
    Younes, H.L.S., Simmons, R.G.: Probabilistic verification of discrete event systems using acceptance sampling. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 223–235. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  47. 47.
    Younes, H.L.S., Simmons, R.G.: Statistical probabilistic model checking with a focus on time-bounded properties. Information and Computation 204(9), 1368–1409 (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Sumit K. Jha
    • 1
  • Edmund M. Clarke
    • 1
  • Christopher J. Langmead
    • 1
    • 2
  • Axel Legay
    • 3
  • André Platzer
    • 1
  • Paolo Zuliani
    • 1
  1. 1.Computer Science DepartmentCarnegie Mellon UniversityUSA
  2. 2.Lane Center for Computational BiologyCarnegie Mellon UniversityUSA
  3. 3.Institut d’Informatique INRIARennesFrance

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