Bulletin of Mathematical Biology

, Volume 66, Issue 2, pp 301–340 | Cite as

Qualitative simulation of genetic regulatory networks using piecewise-linear models

  • Hidde de JongEmail author
  • Jean-Luc Gouzé
  • Céline Hernandez
  • Michel Page
  • Tewfik Sari
  • Johannes Geiselmann


In order to cope with the large amounts of data that have become available in genomics, mathematical tools for the analysis of networks of interactions between genes, proteins, and other molecules are indispensable. We present a method for the qualitative simulation of genetic regulatory networks, based on a class of piecewise-linear (PL) differential equations that has been well-studied in mathematical biology. The simulation method is well-adapted to state-of-the-art measurement techniques in genomics, which often provide qualitative and coarse-grained descriptions of genetic regulatory networks. Given a qualitative model of a genetic regulatory network, consisting of a system of PL differential equations and inequality constraints on the parameter values, the method produces a graph of qualitative states and transitions between qualitative states, summarizing the qualitative dynamics of the system. The qualitative simulation method has been implemented in Java in the computer tool Genetic Network Analyzer.


Regulatory Domain Switching Domain Genetic Regulatory Network Qualitative State Solution Trajectory 
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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Copyright information

© Society for Mathematical Biology 2004

Authors and Affiliations

  • Hidde de Jong
    • 1
    Email author
  • Jean-Luc Gouzé
    • 2
  • Céline Hernandez
    • 3
  • Michel Page
    • 1
    • 4
  • Tewfik Sari
    • 5
  • Johannes Geiselmann
    • 6
  1. 1.Institut National de Recherche en Informatique et en Automatique (INRIA)Unité de recherche Rhône-AlpesSaint Ismier CedexFrance
  2. 2.Institut National de Recherche en Informatique et en Automatique (INRIA)Unité de recherche Sophia AntipolisSophia AntipolisFrance
  3. 3.Swiss Institute of Bioinformatics (SIB)Geneva 4Switzerland
  4. 4.École Supérieure des AffairesUniversité Pierre Mendès FranceGrenobleFrance
  5. 5.Laboratoire de MathématiquesUniversité de Haute AlsaceMulhouseFrance
  6. 6.Laboratoire Adaptation et Pathogénie des Microorganismes (CNRS UMR 5163)Université Joseph FourierGrenoble Cedex 9France

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