dorsal/arxiv
View SchemaSymbolic Reachability Analysis of Genetic Regulatory Networks using Qualitative Abstractions
| Authors | Grégory Batt, Delphine Ropers, Hidde De Jong, Michel Page, Johannes Geiselmann |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0702058 |
| URL | https://arxiv.org/abs/q-bio/0702058 |
Abstract
The switch-like character of gene regulation has motivated the use of hybrid, discrete-continuous models of genetic regulatory networks. While powerful techniques for the analysis, verification, and control of hybrid systems have been developed, the specificities of the biological application domain pose a number of challenges, notably the absence of quantitative information on parameter values and the size and complexity of networks of biological interest. We introduce a method for the analysis of reachability properties of genetic regulatory networks that is based on a class of discontinuous piecewise-affine (PA) differential equations well-adapted to the above constraints. More specifically, we introduce a hyperrectangular partition of the state space that forms the basis for a discrete abstraction preserving the sign of the derivatives of the state variables. The resulting discrete transition system provides a conservative approximation of the qualitative dynamics of the network and can be efficiently computed in a symbolic manner from inequality constraints on the parameters. The method has been implemented in the computer tool Genetic Network Analyzer (GNA), which has been applied to the analysis of a regulatory system whose functioning is not well-understood by biologists, the nutritional stress response in the bacterium Escherichia coli.
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"abstract": "The switch-like character of gene regulation has motivated the use of hybrid,\ndiscrete-continuous models of genetic regulatory networks. While powerful\ntechniques for the analysis, verification, and control of hybrid systems have\nbeen developed, the specificities of the biological application domain pose a\nnumber of challenges, notably the absence of quantitative information on\nparameter values and the size and complexity of networks of biological\ninterest. We introduce a method for the analysis of reachability properties of\ngenetic regulatory networks that is based on a class of discontinuous\npiecewise-affine (PA) differential equations well-adapted to the above\nconstraints. More specifically, we introduce a hyperrectangular partition of\nthe state space that forms the basis for a discrete abstraction preserving the\nsign of the derivatives of the state variables. The resulting discrete\ntransition system provides a conservative approximation of the qualitative\ndynamics of the network and can be efficiently computed in a symbolic manner\nfrom inequality constraints on the parameters. The method has been implemented\nin the computer tool Genetic Network Analyzer (GNA), which has been applied to\nthe analysis of a regulatory system whose functioning is not well-understood by\nbiologists, the nutritional stress response in the bacterium Escherichia coli.",
"arxiv_id": "q-bio/0702058",
"authors": [
"Gr\u00e9gory Batt",
"Delphine Ropers",
"Hidde De Jong",
"Michel Page",
"Johannes Geiselmann"
],
"categories": [
"q-bio.QM"
],
"title": "Symbolic Reachability Analysis of Genetic Regulatory Networks using Qualitative Abstractions",
"url": "https://arxiv.org/abs/q-bio/0702058"
},
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