Combining Refinement of Parametric Models with Goal-Oriented Reduction of Dynamics

  • Stefan Haar
  • Juraj KolčákEmail author
  • Loïc Paulevé
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11388)


Parametric models abstract part of the specification of dynamical models by integral parameters. They are for example used in computational systems biology, notably with parametric regulatory networks, which specify the global architecture (interactions) of the networks, while parameterising the precise rules for drawing the possible temporal evolutions of the states of the components. A key challenge is then to identify the discrete parameters corresponding to concrete models with desired dynamical properties. This paper addresses the restriction of the abstract execution of parametric regulatory (discrete) networks by the means of static analysis of reachability properties (goal states). Initially defined at the level of concrete parameterised models, the goal-oriented reduction of dynamics is lifted to parametric networks, and is proven to preserve all the minimal traces to the specified goal states. It results that one can jointly perform the refinement of parametric networks (restriction of domain of parameters) while reducing the necessary transitions to explore and preserving reachability properties of interest.


  1. 1.
    Bartocci, E., Lió, P.: Computational modeling, formal analysis, and tools for systems biology. PLOS Comput. Biol. 12(1), 1–22 (2016). Scholar
  2. 2.
    Bernot, G., Comet, J.-P., Khalis, Z.: Gene regulatory networks with multiplexes. In: European Simulation and Modelling Conference Proceedings, pp. 423–432 (2008)Google Scholar
  3. 3.
    Bernot, G., Comet, J.-P., Khalis, Z., Richard, A., Roux, O.: A genetically modified hoare logic. Theor. Comput. Sci. (2018).
  4. 4.
    Bernot, G., Cassez, F., Comet, J.-P., Delaplace, F., Müller, C., Roux, O.: Semantics of biological regulatory networks. Electron. Notes Theor. Comput. Sci. 180(3), 3–14 (2007). Scholar
  5. 5.
    Chatain, T., Carmona, J.: Anti-alignments in conformance checking – the dark side of process models. In: Kordon, F., Moldt, D. (eds.) PETRI NETS 2016. LNCS, vol. 9698, pp. 240–258. Springer, Cham (2016). Scholar
  6. 6.
    Chatain, T., Paulevé, L.: Goal-driven unfolding of Petri nets. In: Meyer, R., Nestmann, U. (eds.) 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), vol. 85, pp. 18:1–18:16. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl (2017).
  7. 7.
    Cheng, A., Esparza, J., Palsberg, J.: Complexity results for 1-safe nets. Theor. Comput. Sci. 147(1&2), 117–136 (1995). Scholar
  8. 8.
    Cohen, D.P.A., Martignetti, L., Robine, S., Barillot, E., Zinovyev, A., Calzone, L.: Mathematical modelling of molecular pathways enabling tumour cell invasion and migration. PLoS Comput. Biol. 11(11), e1004571 (2015). Scholar
  9. 9.
    Collombet, S., et al.: Logical modeling of lymphoid and myeloid cell specification and transdifferentiation. Proc. Natl. Acad. Sci. 114(23), 5792–5799 (2017). Scholar
  10. 10.
    Corblin, F., Fanchon, E., Trilling, L., Chaouiya, C., Thieffry, D.: Automatic inference of regulatory and dynamical properties from incomplete gene interaction and expression data. In: Lones, M.A., Smith, S.L., Teichmann, S., Naef, F., Walker, J.A., Trefzer, M.A. (eds.) IPCAT 2012. LNCS, vol. 7223, pp. 25–30. Springer, Heidelberg (2012). Scholar
  11. 11.
    Haddad, S., Pradat-Peyre, J.-F.: New efficient Petri nets reductions for parallel programs verification. Parallel Process. Lett. 16(1), 101–116 (2006). Scholar
  12. 12.
    Helikar, T., et al.: The cell collective: toward an open and collaborative approach to systems biology. BMC Syst. Biol. 6, 96 (2012). Scholar
  13. 13.
    Khalis, Z., Comet, J.-P., Richard, A., Bernot, G.: The SMBioNet method for discovering models of gene regulatory networks. Genes Genomes Genomics 3(1), 15–22 (2009).
  14. 14.
    Klarner, H., Streck, A., Šafránek, D., Kolčák, J., Siebert, H.: Parameter identification and model ranking of thomas networks. In: Gilbert, D., Heiner, M. (eds.) CMSB 2012. LNCS, pp. 207–226. Springer, Heidelberg (2012). Scholar
  15. 15.
    Kolčák, J., Šafránek, D., Haar, S., Paulevé, L.: Parameter space abstraction and unfolding semantics of discrete regulatory networks. Theor. Comput. Sci. (2018).
  16. 16.
    Koutny, M., Desel, J., Kleijn, J. (eds.): Transactions on Petri Nets and Other Models of Concurrency XI. LNCS, vol. 9930. Springer, Heidelberg (2016). Scholar
  17. 17.
    Mokhov, A., Carmona, J., Beaumont, J.: Mining conditional partial order graphs from event logs. In: Koutny, M., Desel, J., Kleijn, J. (eds.) Transactions on Petri Nets and Other Models of Concurrency XI. LNCS, vol. 9930, pp. 114–136. Springer, Heidelberg (2016). Scholar
  18. 18.
    Naldi, A., et al.: The CoLoMoTo interactive notebook: accessible and reproducible computational analyses for qualitative biological networks. Front. Physiol. 9, 680 (2018). Scholar
  19. 19.
    Ostrowski, M., Paulevé, L., Schaub, T., Siegel, A., Guziolowski, C.: Boolean network identification from perturbation time series data combining dynamics abstraction and logic programming. Biosystems 149, 139–153 (2016). Scholar
  20. 20.
    Paulevé, L.: Reduction of qualitative models of biological networks for transient dynamics analysis. IEEE/ACM Trans. Comput. Biol. Bioinform. (2017). Scholar
  21. 21.
    Ponce-de-León, H., Rodríguez, C., Carmona, J., Heljanko, K., Haar, S.: Unfolding-based process discovery. In: Finkbeiner, B., Pu, G., Zhang, L. (eds.) ATVA 2015. LNCS, vol. 9364, pp. 31–47. Springer, Cham (2015). Scholar
  22. 22.
    Talcott, C., Dill, D.L.: Multiple representations of biological processes. In: Priami, C., Plotkin, G. (eds.) Transactions on Computational Systems Biology VI. LNCS, vol. 4220, pp. 221–245. Springer, Heidelberg (2006). Scholar
  23. 23.
    Thieffry, D., Thomas, R.: Dynamical behaviour of biological regulatory networks–II. Immunity control in bacteriophage lambda. Bull. Math. Biol. 57, 277–297 (1995). Scholar
  24. 24.
    Thomas, R.: Boolean formalization of genetic control circuits. J. Theor. Biol. 42(3), 563–585 (1973). Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.LSV, CNRS & ENS Paris-Saclay, Université Paris-SaclayCachanFrance
  2. 2.National Institute of InformaticsTokyoJapan
  3. 3.LRI UMR 8623, Univ. Paris-Sud – CNRS, Université Paris-SaclayOrsayFrance
  4. 4.Univ. Bordeaux, Bordeaux INP, CNRS, LaBRI, UMR5800TalenceFrance

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