Model Checking Genetic Regulatory Networks with Parameter Uncertainty

  • Grégory Batt
  • Calin Belta
  • Ron Weiss
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4416)


The lack of precise numerical information for the values of biological parameters severely limits the development and analysis of models of genetic regulatory networks. To deal with this problem, we propose a method for the analysis of genetic regulatory networks with parameter uncertainty. We consider models based on piecewise-multiaffine differential equations, dynamical properties expressed in temporal logic, and intervals for the values of uncertain parameters. The problem is then either to guarantee that the system satisfies the expected properties for every possible parameter value - the corresponding parameter set is then called valid - or to find valid subsets of a given parameter set. The proposed method uses discrete abstractions and model checking, and allows for efficient search of the parameter space. This approach has been implemented in a tool for robust verification of gene networks (RoVerGeNe) and applied to the tuning of a synthetic network build in E. coli.


Transition System Parameter Uncertainty Synthetic Biology Uncertain Parameter Linear Temporal Logic 
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.
    Kitano, H.: Systems biology: A brief overview. Science 295(5560), 1662–1664 (2002)CrossRefGoogle Scholar
  2. 2.
    Andrianantoandro, E., et al.: Synthetic biology: New engineering rules for an emerging discipline. Mol. Syst. Biol. (2006)Google Scholar
  3. 3.
    Szallasi, Z., Stelling, J., Periwal, V. (eds.): System Modeling in Cellular Biology: From Concepts to Nuts and Bolts. MIT Press, Cambridge (2006)Google Scholar
  4. 4.
    de Jong, H., Ropers, D.: Qualitative approaches to the analysis of genetic regulatory networks. In: Szallasi, Z., Stelling, J., Periwal, V. (eds.) System Modeling in Cellular Biology: From Concepts to Nuts and Bolts, pp. 125–148. MIT Press, Cambridge (2006)Google Scholar
  5. 5.
    Belta, C., Habets, L.C.G.J.M.: Controlling a class of nonlinear systems on rectangles. IEEE Trans. Aut. Control 51(11), 1749–1759 (2006)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Alur, R., et al.: Discrete abstractions of hybrid systems. Proc. IEEE 88(7), 971–984 (2000)CrossRefGoogle Scholar
  7. 7.
    Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (1999)Google Scholar
  8. 8.
    Batt, G., Belta, C.: Model checking genetic regulatory networks with applications to synthetic biology. CISE Tech. Rep. 2006-IR-0030, Boston University (2006)Google Scholar
  9. 9.
    de Jong, H., et al.: Qualitative simulation of genetic regulatory networks using piecewise-linear models. Bull. Math. Biol. 66(2), 301–340 (2004)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Abate, A., Tiwari, A.: Box invariance of hybrid and switched systems. In: Proc. ADHS’06 (2006)Google Scholar
  11. 11.
    Belta, C., Habets, L.C.G.J.M., Kumar, V.: Control of multi-affine systems on rectangles with applications to hybrid biomolecular networks. In: Proc. CDC’02 (2002)Google Scholar
  12. 12.
    Mestl, T., Plahte, E., Omholt, S.: A mathematical framework for describing and analysing gene regulatory networks. J. Theor. Biol. 176, 291–300 (1995)CrossRefGoogle Scholar
  13. 13.
    Glass, L., Kauffman, S.: The logical analysis of continuous non-linear biochemical control networks. J. Theor. Biol. 39(1), 103–129 (1973)CrossRefGoogle Scholar
  14. 14.
    Kloetzer, M., Belta, C.: Reachability analysis of multi-affine systems. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol. 3927, pp. 348–362. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  15. 15.
    Alur, R., Dang, T., Ivancic, F.: Progress on reachability analysis of hybrid systems using predicate abstraction. In: Maler, O., Pnueli, A. (eds.) HSCC 2003. LNCS, vol. 2623, pp. 4–19. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  16. 16.
    Koutsoukos, X., Antsaklis, P.J.: Safety and reachability of piecewise linear hybrid dynamical systems based on discrete abstractions. J. Discrete Event Dynamic Systems 13(3), 203–243 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Batt, G., et al.: Validation of qualitative models of genetic regulatory networks by model checking: Analysis of the nutritional stress response in E. coli. Bioinformatics 21(Suppl. 1), i19–i28 (2005)CrossRefGoogle Scholar
  18. 18.
    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, Springer, Heidelberg (2007)CrossRefGoogle Scholar
  19. 19.
    Hooshangi, S., Thiberge, S., Weiss, R.: Ultrasensitivity and noise propagation in a synthetic transcriptional cascade. Proc. Natl. Acad. Sci. USA 102(10), 3581–3586 (2005)CrossRefGoogle Scholar
  20. 20.
    Annichini, A., Asarin, E., Bouajjani, A.: Symbolic techniques for parametric reasoning about counter and clock systems. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 419–434. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  21. 21.
    Wang, F.: Symbolic parametric safety analysis of linear hybrid systems with BDD-like data-structures. IEEE Trans. Softw. Eng. 31(1), 38–51 (2005)CrossRefGoogle Scholar
  22. 22.
    Henzinger, T., Ho, P.-H., Wong-Toi, H.: HYTECH: A model checker for hybrid systems. Software Tools Technology Transfer 1(1-2), 110–122 (1997)zbMATHCrossRefGoogle Scholar
  23. 23.
    Ghosh, R., Tomlin, C.J.: Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modelling: Delta-Notch protein signalling. IEE Proc. Syst. Biol. 1(1), 170–183 (2004)Google Scholar
  24. 24.
    Lin, H., Antsaklis, P.J.: Robust regulation of polytopic uncertain linear hybrid systems with networked control system applications. In: Antsaklis, P., Liu, D. (eds.) Stability and Control of Dynamical Systems Applications, Birkhäuser, Basel (2003)Google Scholar
  25. 25.
    Antoniotti, M., et al.: Taming the complexity of biochemical models through bisimulation and collapsing: Theory and practice. Theor. Comput. Sci. 325(1), 45–67 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Calzone, L., et al.: Machine learning biochemical networks from temporal logic properties. In: Priami, C., Plotkin, G. (eds.) Transactions on Computational Systems Biology VI. LNCS (LNBI), vol. 4220, pp. 68–94. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  27. 27.
    Bernot, G., et al.: Application of formal methods to biological regulatory networks: Extending Thomas’ asynchronous logical approach with temporal logic. J. Theor. Biol. 229(3), 339–347 (2004)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Grégory Batt
    • 1
  • Calin Belta
    • 1
  • Ron Weiss
    • 2
  1. 1.Center for Information and Systems Engineering and Center for BioDynamics, Boston University, Brookline, MAUSA
  2. 2.Department of Electrical Engineering and Department of Molecular Biology, Princeton University, Princeton, NJUSA

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