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Qualitative simulation of genetic regulatory networks using piecewise-linear models

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Abstract

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.

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Authors and Affiliations

  1. Institut National de Recherche en Informatique et en Automatique (INRIA), Unité de recherche Rhône-Alpes, 655 avenue de l’Europe Montbonnot, 38334, Saint Ismier Cedex, France

    Hidde de Jong & Michel Page

  2. Institut National de Recherche en Informatique et en Automatique (INRIA), Unité de recherche Sophia Antipolis, 2004 route des Lucioles, BP 93, 06902, Sophia Antipolis, France

    Jean-Luc Gouzé

  3. Swiss Institute of Bioinformatics (SIB), CMU-Rue Michel-Servet 1, 1211, Geneva 4, Switzerland

    Céline Hernandez

  4. École Supérieure des Affaires, Université Pierre Mendès France, Grenoble, France

    Michel Page

  5. Laboratoire de Mathématiques, Université de Haute Alsace, 4 rue des Frères Lumière, 68093, Mulhouse, France

    Tewfik Sari

  6. Laboratoire Adaptation et Pathogénie des Microorganismes (CNRS UMR 5163), Université Joseph Fourier, 460 rue de la Piscine, BP53 38041, Grenoble Cedex 9, France

    Johannes Geiselmann

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  1. Hidde de Jong
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  2. Jean-Luc Gouzé
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  3. Céline Hernandez
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  4. Michel Page
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Correspondence to Hidde de Jong.

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de Jong, H., Gouzé, JL., Hernandez, C. et al. Qualitative simulation of genetic regulatory networks using piecewise-linear models. Bull. Math. Biol. 66, 301–340 (2004). https://doi.org/10.1016/j.bulm.2003.08.010

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