Parameter Synthesis by Parallel Coloured CTL Model Checking

  • Luboš Brim
  • Milan ČeškaEmail author
  • Martin Demko
  • Samuel Pastva
  • David Šafránek
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9308)


We propose a new distributed-memory parallel algorithm for parameter synthesis from CTL hypotheses. The algorithm colours the state space transitions by different parameterisations and extends CTL model checking to identify the maximal set of parameters that guarantee the satisfaction of the given CTL property. We experimentally confirm good scalability of our approach and demonstrate its applicability in the case study of a genetic switch controlling decisions in the cell cycle.


  1. 1.
    Ballarini, P., Guido, R., Mazza, T., Prandi, D.: Taming the complexity of biological pathways through parallel computing. Brief. Bioinform 10(3), 278–288 (2009)CrossRefGoogle Scholar
  2. 2.
    Barnat, J., Brim, L., Krejci, A., Streck, A., Safranek, D., Vejnar, M., Vejpustek, T.: On parameter synthesis by parallel model checking. IEEE/ACM Trans. Comput. Bio. Bioinform. 9(3), 693–705 (2012)CrossRefGoogle Scholar
  3. 3.
    Barnat, J., Brim, L., Safránek, D.: High-performance analysis of biological systems dynamics with the divine model checker. Brief. Bioinform. 11(3), 301–312 (2010)CrossRefGoogle Scholar
  4. 4.
    Batt, G., Belta, C., Weiss, R.: Model checking liveness properties of genetic regulatory networks. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 323–338. Springer, Heidelberg (2007) CrossRefGoogle Scholar
  5. 5.
    Batt, G., Page, M., Cantone, I., Gössler, G., Monteiro, P., de Jong, H.: Efficient parameter search for qualitative models of regulatory networks using symbolic model checking. Bioinformatics 26(18), 603–610 (2010)CrossRefGoogle Scholar
  6. 6.
    Batt, G., Ropers, D., Jong, H.D., Geiselmann, J., Mateescu, R., Schneider, D.: Validation of qualitative models of genetic regulatory networks by model checking: analysis of the nutritional stress response in escherichia coli. Bioinformatics 21, 19–28 (2005)CrossRefGoogle Scholar
  7. 7.
    Brim, L., Češka, M., Šafránek, D.: Model checking of biological systems. In: Bernardo, M., de Vink, E., Di Pierro, A., Wiklicky, H. (eds.) SFM 2013. LNCS, vol. 7938, pp. 63–112. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  8. 8.
    Brim, L., Yorav, K., Zidkova, J.: Assumption-based distribution of CTL model checking. STTT 7(1), 61–73 (2005)CrossRefGoogle Scholar
  9. 9.
    Clarke, E.M., Emerson, E.A., Sistla, A.P.: Automatic verification of finite-state concurrent systems using temporal logic specifications. ACM Trans. Program. Lang. Syst. 8, 244–263 (1986)CrossRefzbMATHGoogle Scholar
  10. 10.
    Collins, P., Habets, L.C., van Schuppen, J.H., Černá, I., Fabriková, J., Šafránek, D.: Abstraction of biochemical reaction systems on polytopes. In: IFAC World Congress, pp. 14869–14875. IFAC (2011)Google Scholar
  11. 11.
    Donaldson, R., Gilbert, D.: A model checking approach to the parameter estimation of biochemical pathways. In: Heiner, M., Uhrmacher, A.M. (eds.) CMSB 2008. LNCS (LNBI), vol. 5307, pp. 269–287. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  12. 12.
    Donzé, A., Clermont, G., Langmead, C.J.: Parameter synthesis in nonlinear dynamical systems: application to systems biology. J. Comput. Biol. 17(3), 325–336 (2010)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Donzé, A., Fanchon, E., Gattepaille, L.M., Maler, O., Tracqui, P.: Robustness analysis and behavior discrimination in enzymatic reaction networks. PLoS ONE 6(9), e24246 (2011)CrossRefGoogle Scholar
  14. 14.
    Fages, F., Soliman, S.: Formal cell biology in biocham. In: Bernardo, M., Degano, P., Zavattaro, G. (eds.) SFM 2008. LNCS, vol. 5016, pp. 54–80. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  15. 15.
    Fröhlich, F., Theis, F.J., Hasenauer, J.: Uncertainty analysis for non-identifiable dynamical systems: profile likelihoods, bootstrapping and more. In: Mendes, P., Dada, J.O., Smallbone, K. (eds.) CMSB 2014. LNCS, vol. 8859, pp. 61–72. Springer, Heidelberg (2014) Google Scholar
  16. 16.
    Gábor, A., Banga, J.R.: Improved parameter estimation in kinetic models: selection and tuning of regularization methods. In: Mendes, P., Dada, J.O., Smallbone, K. (eds.) CMSB 2014. LNCS, vol. 8859, pp. 45–60. Springer, Heidelberg (2014) Google Scholar
  17. 17.
    Gilbert, D., Breitling, R., Heiner, M., Donaldson, R.: An introduction to biomodel engineering, illustrated for signal transduction pathways. In: Corne, D.W., Frisco, P., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2008. LNCS, vol. 5391, pp. 13–28. Springer, Heidelberg (2009) CrossRefGoogle Scholar
  18. 18.
    Grosu, R., Batt, G., Fenton, F.H., Glimm, J., Le Guernic, C., Smolka, S.A., Bartocci, E.: From cardiac cells to genetic regulatory networks. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 396–411. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  19. 19.
    Jha, S.K., Langmead, C.J.: Synthesis and infeasibility analysis for stochastic models of biochemical systems using statistical model checking and abstraction refinement. Theor. Comput. Sci. 412(21), 2162–2187 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Jha, S., Shyamasundar, R.K.: Adapting biochemical kripke structures for distributed model checking. In: Priami, C., Ingólfsdóttir, A., Mishra, B., Riis Nielson, H. (eds.) Transactions on Computational Systems Biology VII. LNCS (LNBI), vol. 4230, pp. 107–122. Springer, Heidelberg (2006) CrossRefGoogle Scholar
  21. 21.
    Liu, B., Kong, S., Gao, S., Zuliani, P., Clarke, E.M.: Parameter synthesis for cardiac cell hybrid models using \(\delta \)-decisions. In: Mendes, P., Dada, J.O., Smallbone, K. (eds.) CMSB 2014. LNCS, vol. 8859, pp. 99–113. Springer, Heidelberg (2014) Google Scholar
  22. 22.
    Mittnacht, S.: Control of prb phosphorylation. Curr. Opin. Genet. Dev. 8(1), 21–27 (1998)CrossRefGoogle Scholar
  23. 23.
    Monteiro, P.T., Ropers, D., Mateescu, R., Freitas, A.T., de Jong, H.: Temporal logic patterns for querying qualitative models of genetic regulatory networks. In: ECAI. FAIA, vol. 178, pp. 229–233. IOS Press (2008)Google Scholar
  24. 24.
    Raue, A., Karlsson, J., Saccomani, M.P., Jirstrand, M., Timmer, J.: Comparison of approaches for parameter identifiability analysis of biological systems. Bioinformatics 30, 1440–1448 (2014)CrossRefGoogle Scholar
  25. 25.
    Rizk, A., Batt, G., Fages, F., Soliman, S.: A general computational method for robustness analysis with applications to synthetic gene networks. Bioinformatics 25(12), 169–178 (2009)CrossRefGoogle Scholar
  26. 26.
    Swat, M., Kel, A., Herzel, H.: Bifurcation analysis of the regulatory modules of the mammalian G1/S transition. Bioinformatics 20(10), 1506–1511 (2004)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Luboš Brim
    • 1
  • Milan Češka
    • 1
    Email author
  • Martin Demko
    • 1
  • Samuel Pastva
    • 1
  • David Šafránek
    • 1
  1. 1.Systems Biology Laboratory, Faculty of InformaticsMasaryk UniversityBrnoCzech Republic

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