On the Use of Temporal Formal Logic to Model Gene Regulatory Networks

  • Gilles Bernot
  • Jean-Paul Comet
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6160)

Abstract

Modelling activities in molecular biology face the difficulty of prediction to link molecular knowledge with cell phenotypes. Even when the interaction graph between molecules is known, the deduction of the cellular dynamics from this graph remains a strong corner stone of the modelling activity, in particular one has to face the parameter identification problem. This article is devoted to convince the reader that computers can be used not only to simulate a model of the studied biological system but also to deduce the sets of parameter values that lead to a behaviour compatible with the biological knowledge (or hypotheses) about dynamics. This approach is based on formal logic. It is illustrated in the discrete modelling framework of genetic regulatory networks due to René Thomas.

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References

  1. 1.
    Ahmad, J., Bourdon, J., Eveillard, J., Fromentin, D., Roux, O., Sinoquet, C.: Temporal constraints of a gene regulatory network: refining a qualitative simulation. Biosystems 98(3), 149–159 (2009)CrossRefGoogle Scholar
  2. 2.
    Bernot, G., Comet, J.-P., Khalis, Z.: Gene regulatory networks with multiplexes. In: European Simulation and Modelling Conference Proceedings, France, October 27-29, pp. 423–432 (2008) ISBN 978-90-77381-44-1Google Scholar
  3. 3.
    Bernot, G., Gaudel, M.C., Marre, B.: Software testing based on formal specifications: A theory and a tool. Software Engineering Journal 6(6), 387–405 (1991)CrossRefGoogle Scholar
  4. 4.
    Cardelli, L., Caron, E., Gardner, P., Kahramanogulları, O., Phillips, A.: A process model of rho gtp-binding proteins. Theoretical Computer Science 410(33-34), 3166–3185 (2009)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Cimatti, A., Clarke, E., Giunchiglia, E., Giunchiglia, F., Pistore, M., Roveri, M., Sebastiani, R., Tacchella, A.: NuSMV Version 2: An OpenSource Tool for Symbolic Model Checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, p. 359. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  6. 6.
    Collado-Vides, J., Magasanik, B., Smith, T.: Integrative approaches to molecular biology. The MIT press, Cambridge (1996)Google Scholar
  7. 7.
    Curti, M., Degano, P., Priami, C., Baldari, C.T.: Modelling biochemical pathways through enhanced π-calculus. Theoretical Computer Science 325(1), 111–140 (2004)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    de Jong, H.: Qualitative modeling and simulation of bacterial regulatory networks. In: Heiner, M., Uhrmacher, A. (eds.) CMSB 2008. LNCS (LNBI), vol. 5307, p. 1. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  9. 9.
    Fanchon, E., Corblin, F., Trilling, L., Hermant, B., Gulino, D.: Modeling the molecular network controlling adhesion between human endothelial cells: Inference and simulation using constraint logic programming. In: Danos, V., Schachter, V. (eds.) CMSB 2004. LNCS (LNBI), vol. 3082, pp. 104–118. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Gouzé, J.-L.: Positive and negative circuits in dynamical systems. Journal of Biological Systems 6, 11–15 (1998)MATHCrossRefGoogle Scholar
  11. 11.
    Jacob, F., Monod, J.: Genetic regulatory mechanisms in the synthesis of proteins. Journal of molecular biology 3, 318–356 (1961)CrossRefGoogle Scholar
  12. 12.
    Jard, C., Jéron, T.: TGV: theory, principles and algorithms. a tool for the automatic synthesis of conformance test cases for non-deterministic reactive systems. Software Tools for Technology Transfert 7(4), 297–315 (2005)CrossRefGoogle Scholar
  13. 13.
    Khalis, Z., Bernot, G., Comet, J.-P.: Gene Regulatory Networks: Introduction of multiplexes into R. Thomas’ modelling. In: Proc. of the Nice Spring school on Modelling and simulation of biological processes in the context of genomics, EDP Science, pp. 139–151 (2009) ISBN : 978-2-7598-0437-5Google Scholar
  14. 14.
    Khalis, Z., Comet, J.-P., Richard, A., Bernot, G.: The smbionet method for discovering models of gene regulatory networks. Genes, Genomes and Genomics (2009)Google Scholar
  15. 15.
    Kügler, P., Gaubitzer, E., Müller, S.: Parameter identification for chemical reaction systems using sparsity enforcing regularization: A case study for the chlorite-iodide reaction. Journal of Physical Chemistry A 113(12), 2775–2785 (2009)CrossRefGoogle Scholar
  16. 16.
    Little, J.W.: Threshold effects in gene regulation: When some is not enough. PNAS 102(15), 5310–5311 (2005)CrossRefGoogle Scholar
  17. 17.
    Mateus, D., Gallois, J.-P., Comet, J.-P., Le Gall, P.: Symbolic modeling of genetic regulatory networks. Journal of Bioinformatics and Computational Biology 5(2B), 627–640 (2007)CrossRefGoogle Scholar
  18. 18.
    Naldi, A., Remy, E., Thieffry, D., Chaouiya, C.: A reduction of logical regulatory graphs preserving essential dynamical properties. In: Degano, P., Gorrieri, R. (eds.) CMSB 2009. LNCS (LNBI), vol. 5688, pp. 266–280. Springer, Heidelberg (2009)Google Scholar
  19. 19.
    Plahte, E., Mestl, T., Omholt, S.W.: Feedback loops, stability and multistationarity in dynamical systems. Journal Biological Systems 3, 409–413 (1995)CrossRefGoogle Scholar
  20. 20.
    Popper, K.R.: Conjectures and refutations: the growth of scientific knowledge. Routledge & Kegan Paul, London (1965)Google Scholar
  21. 21.
    Richard, A., Comet, J.-P.: Necessary conditions for multistationarity in discrete dynamical systems. Discrete Applied Mathematics 155(18), 2403–2413 (2007)MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Rizk, A., Batt, G., Fages, F., Soliman, S.: A general computational method for robustness analysis with applications to synthetic gene networks. Bioinformatics 25(12), i169–i178 (2009)CrossRefGoogle Scholar
  23. 23.
    Siebert, H., Bockmayr, A.: Temporal constraints in the logical analysis of regulatory networks. Theoretical Computer Science 391(3), 258–275 (2008)MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Snoussi, E.H.: Necessary conditions for multistationarity and stable periodicity. Journal of Biological Systems 6, 3–9 (1998)MATHCrossRefGoogle Scholar
  25. 25.
    Snoussi, E.H.: Qualitative dynamics of a piecewise-linear differential equations: a discrete mapping approach. Dynamics and stability of Systems 4, 189–207 (1989)MATHMathSciNetGoogle Scholar
  26. 26.
    Snoussi, E.H., Thomas, R.: Logical identification of all steady states: the concept of feedback loop caracteristic states. Bull. Math. Biol. 55(5), 973–991 (1993)MATHGoogle Scholar
  27. 27.
    Soulé, C.: Graphical requirements for multistationarity. ComPlexUs 1, 123–133 (2003)CrossRefGoogle Scholar
  28. 28.
    Thomas, R.: On the relation between the logical structure of systems and their ability to generate multiple steady states and sustained oscillations. In: Series in Synergetics, vol. 9, pp. 180–193. Springer, Heidelberg (1981)Google Scholar
  29. 29.
    Thomas, R., d’Ari, R.: Biological Feedback. CRC Press, Boca Raton (1990)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Gilles Bernot
    • 1
  • Jean-Paul Comet
    • 1
  1. 1.Algorithmes-Euclide-BLaboratoire I3S, UMR 6070 UNS-CNRSSophia Antipolis Cedex

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