Compositional Reachability Analysis of Genetic Networks

  • Gregor Gössler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4210)


Genetic regulatory networks have been modeled as discrete transition systems by many approaches, benefiting from a large number of formal verification algorithms available for the analysis of discrete transition systems. However, most of these approaches do not scale up well. In this article, we explore the use of compositionality for the analysis of genetic regulatory networks. We present a framework for modeling genetic regulatory networks in a modular yet faithful manner based on the mathematically well-founded formalism of differential inclusions. We then propose a compositional algorithm to efficiently analyze reachability properties of the model. A case study shows the potential of this approach.


Transition System Genetic Network Action Constraint Switching Domain Reachability Analysis 
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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  1. 1.
    Alur, R., Dang, T., Ivancić, F.: Reachability analysis of hybrid systems via predicate abstraction. Trans. on Embedded Computing Systems (2004)Google Scholar
  2. 2.
    Batt, G., Bergamini, D., de Jong, H., Garavel, H., Mateescu, R.: Model checking genetic regulatory networks using GNA and CADP. In: Graf, S., Mounier, L. (eds.) SPIN 2004. LNCS, vol. 2989, pp. 158–163. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    Batt, G., de Jong, H., Geiselmann, J., Page, M., Ropers, D., Schneider, D.: Symbolic reachability analysis of genetic regulatory networks using qualitative abstraction. Research Report 5362, INRIA, France (2004)Google Scholar
  4. 4.
    Batt, G., Ropers, D., de Jong, H., Geiselmann, J., Page, M., Schneider, D.: Qualitative analysis and verification of hybrid models of genetic regulatory networks: Nutritional stress response in escherichia coli. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 134–150. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Bernot, G., Comet, J.-P., Richard, A., Guespin, J.: Application of formal methods to biological regulatory networks: Extending Thomas asynchronous logical approach with temporal logic. Journal of Theoretical Biology 229(3), 339–348 (2004)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Blossey, R., Cardelli, L., Phillips, A.: A compositional approach to the stochastic dynamics of gene networks. Trans. on Comput. Syst. Biol. 4, 99–122 (2006)MathSciNetGoogle Scholar
  7. 7.
    Casey, R., de Jong, H., Gouzé, J.-L.: Piecewise-linear models of genetic regulatory networks: Equilibria and their stability. Mathematical Biology 52(1), 27–56 (2006)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    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
  9. 9.
    Chaouiya, C., Remy, E., Ruet, P., Thieffry, D.: Qualitative modelling of genetic networks: From logical regulatory graphs to standard petri nets. In: Cortadella, J., Reisig, W. (eds.) ICATPN 2004. LNCS, vol. 3099, pp. 137–156. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  10. 10.
    Comet, J.-P., Klaudel, H., Liauzu, S.: Modeling multi-valued genetic regulatory networks using high-level petri nets. In: Ciardo, G., Darondeau, P. (eds.) ICATPN 2005. LNCS, vol. 3536, pp. 208–227. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    de Jong, H.: Modeling and simulation of genetic regulatory systems: A literature review. Journal of Computational Biology 9(1), 69–105 (2002)Google Scholar
  12. 12.
    de Jong, H., Geiselmann, J., Batt, G., Hernandez, C., Page, M.: Qualitative simulation of the initiation of sporulation in Bacillus subtilis. Bulletin of Mathematical Biology 66(2), 261–300 (2004)CrossRefMathSciNetGoogle Scholar
  13. 13.
    de Jong, H., Geiselmann, J., Hernandez, C., Page, M.: Genetic Network Analyzer: Qualitative simulation of genetic regulatory networks. Bioinformatics 19(3), 336–344 (2003)CrossRefGoogle Scholar
  14. 14.
    de Jong, H., Gouzé, J.-L., Hernandez, C., Page, M., Sari, T., Geiselmann, J.: Qualitative simulation of genetic regulatory networks using piecewise-linear models. Bulletin of Mathematical Biology 66, 301–340 (2004)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Eker, S., Knapp, M., Laderoute, K., Lincoln, P., Talcott, C.: Pathway logic: Executable models of biological networks. ENTCS 71 (2002)Google Scholar
  16. 16.
    Fages, F., Soliman, S., Chabrier-Rivier, N.: Modelling and querying interaction networks in the biochemical abstract machine BIOCHAM. J. of Biological Physics and Chemistry 4(2), 64–72 (2004)CrossRefGoogle Scholar
  17. 17.
    Filippov, A.F.: Differential equations with discontinuous righthand side. Mathematics and its Applications 18 (1988)Google Scholar
  18. 18.
    Ghosh, R., Tiwari, A., Tomlin, C.: Automated symbolic reachability analysis; with application to delta-notch signaling automata. In: Maler, O., Pnueli, A. (eds.) HSCC 2003. LNCS, vol. 2623, pp. 233–248. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  19. 19.
    Glass, L., Kauffman, S.A.: The logical analysis of continuous, non-linear biochemical control networks. Journal of Theoretical Biology 39(1), 103–129 (1973)CrossRefGoogle Scholar
  20. 20.
    Gössler, G., Sifakis, J.: Component-based construction of deadlock-free systems (extended abstract). In: Pandya, P.K., Radhakrishnan, J. (eds.) FSTTCS 2003. LNCS, vol. 2914, Springer, Heidelberg (2003)Google Scholar
  21. 21.
    Gouzé, J.-L., Sari, T.: A class of piecewise linear differential equations arising in biological models. Dynamical Systems 17(4), 299–316 (2003)CrossRefGoogle Scholar
  22. 22.
    Heiner, M., Koch, I.: Petri net based model validation in systems biology. In: Cortadella, J., Reisig, W. (eds.) ICATPN 2004. LNCS, vol. 3099, pp. 216–237. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  23. 23.
    Larrinaga, A., Naldi, A., Sánchez, L., Thieffry, D., Chaouiya, C.: GINsim: a software suite for the qualitative modelling, simulation and analysis of regulatory networks. Biosystems (2005)Google Scholar
  24. 24.
    Marnellos, G., Deblandre, G.A., Mjolsness, E., Kintner, G.: Delta-Notch lateral inhibitory patterning in the emergence of ciliated cells in Xenopus: Experimental observations and a gene network model. In: Proc. PSB 2000, vol. 5, pp. 326–337. World Scientific Publishing, Singapore (2000)Google Scholar
  25. 25.
    Oltvai, Z.N., Barabási, A.L.: Life’s complexity pyramid. Science 298, 763–764 (2002)CrossRefGoogle Scholar
  26. 26.
    Piazza, C., Antoniotti, M., Mysore, V., Policriti, A., Winkler, F., Mishra, B.: Algorithmic algebraic model checking I: Challenges form systems biology. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 5–19. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  27. 27.
    Resendis-Antonio, O., Freyre-González, J.A., Menchaca-Méndez, R., Gutiérrez-Ríos, R.M., Martínez-Antonio, A., Avila-Sánchez, C., Collado-Vides, J.: Modular analysis of the transcriptional regulatory network of e. coli. Trends in Genetics 21(1), 16–20 (2005)CrossRefGoogle Scholar
  28. 28.
    Simão, E., Remy, E., Thieffry, D., Chaouiya, C.: Qualitative modelling of regulated metabolic pathways: application to the tryptophan biosynthesis in e.coli. Bioinformatics 21(suppl. 2), ii190–ii196 (2005)Google Scholar
  29. 29.
    Thomas, R.: Boolean formalisation of genetic control circuits. J. Theor. Biol. 42, 565–583 (1973)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Gregor Gössler
    • 1
  1. 1.POP ART project, INRIA Rhône-AlpesFrance

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