Acta Biotheoretica

, Volume 58, Issue 2–3, pp 217–232 | Cite as

Comparing Boolean and Piecewise Affine Differential Models for Genetic Networks

  • Madalena ChavesEmail author
  • Laurent Tournier
  • Jean-Luc Gouzé
Regular Article


Multi-level discrete models of genetic networks, or the more general piecewise affine differential models, provide qualitative information on the dynamics of the system, based on a small number of parameters (such as synthesis and degradation rates). Boolean models also provide qualitative information, but are based simply on the structure of interconnections. To explore the relationship between the two formalisms, a piecewise affine differential model and a Boolean model are compared, for the carbon starvation response network in E. coli. The asymptotic dynamics of both models are shown to be quite similar. This study suggests new tools for analysis and reduction of biological networks.


Boolean models Piecewise affine models Genetic networks Model reduction 



This work was supported in part by the French National Research Agency through the BioSys project MetaGenoReg.

Supplementary material

10441_2010_9097_MOESM1_ESM.pdf (76 kb)
PDF (76 KB)


  1. Bagley R, Glass L (1996) Counting and classifying attractors in high dimensional dynamical systems. J Theor Biol 183:269–284CrossRefGoogle Scholar
  2. Casey R, de Jong H, Gouzé J (2006) Piecewise linear models of genetic regulatory networks: equilibria and their stability. J Math Biol 52:27–56CrossRefGoogle Scholar
  3. Chaves M, Sontag E, Albert R (2006) Methods of robustness analysis for boolean models of gene control networks. IEE Proc Syst Biol 235:154–167CrossRefGoogle Scholar
  4. Chaves M, Eißing T, Allgöwer F (2009) Regulation of apoptosis via the nfkb pathway: modeling and analysis. In: N Ganguly, Deutsch A, Mukherjee A (eds) Dynamics on and of complex networks: applications to biology, computer science and the social sciences, Modeling and Simulation in Science, Engineering and Technology. Birkhauser, Boston, pp 19–34Google Scholar
  5. Glass L (1975) Classification of biological networks by their qualitative dynamics. J Theor Biol 54:85–107CrossRefGoogle Scholar
  6. Glass L, Kauffman S (1973) The logical analysis of continuous, nonlinear biochemical control networks. J Theor Biol 39:103–129CrossRefGoogle Scholar
  7. Gouzé J, Sari T (2002) A class of piecewise linear differential equations arising in biological models. Dyn Syst 17(4):299–316CrossRefGoogle Scholar
  8. Grognard F, Gouzé JL, de Jong H (2007) Piecewise-linear models of genetic regulatory networks: theory and example. In: Queinnec I, Tarbouriech S, Garcia G, Niculescu S (eds), Biology and control theory: current challenges, Lecture Notes in Control and Information Sciences (LNCIS) 357, Springer, Berlin, pp 137–159Google Scholar
  9. Liang S, Fuhrman S, Somogyi R (1998) REVEAL, a general reverse engineering algorithm for inference of genetic network architecture. In: Pacific Symposium on Biocomputing, vol 3. pp 18–29Google Scholar
  10. Ropers D, de Jong H, Page M, Schneider D, Geiselmann J (2006) Qualitative simulation of the carbon starvation response in Escherichia coli. Biosystems 84(2):124–152CrossRefGoogle Scholar
  11. Sánchez L, Thieffry D (2001) A logical analysis of the Drosophila gap-gene system. J Theor Biol 211:115–141CrossRefGoogle Scholar
  12. Snoussi E, Thomas R (1993) Logical identification of all steady states: the concept of feedback loop characteristic states. Bull Math Biol 55(5):973–991Google Scholar
  13. Thomas R, D’Ari R (1990) Biological feedback. CRC PressGoogle Scholar
  14. Tournier L, Chaves M (2009) Uncovering operational interactions in genetic networks using asynchronous boolean dynamics. J Theor Biol 260(2):196–209CrossRefGoogle Scholar
  15. Tournier L, Gouzé JL (2008) Hierarchical analysis of piecewise affine models of gene regulatory networks. Theory Biosci 127:125–134CrossRefGoogle Scholar
  16. van Ham P (1979) How to deal with more than two levels. In: Thomas R (ed), Kinetic logic: a boolean approach to the analysis of complex regulatory systems. Lecture Notes in Biomathematics, vol 29. Springer, Berlin, pp 326–343Google Scholar
  17. von Dassow G, Meir E, Munro E, Odell G (2000) The segment polarity network is a robust developmental module. Nature 406:188–192CrossRefGoogle Scholar
  18. Zhang J, Johansson K, Lygeros J, Sastry S (2001) Zeno hybrid systems. Int J Robust Nonlinear Control 11:435–451CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Madalena Chaves
    • 1
    Email author
  • Laurent Tournier
    • 2
  • Jean-Luc Gouzé
    • 1
  1. 1.INRIA, project-team COMORESophia AntipolisFrance
  2. 2.INRA, Unit MIG (UR 1077)Jouy-en-JosasFrance

Personalised recommendations