Brief paper: Symbolic reachability analysis of genetic regulatory networks using discrete abstractions

Authors:
Grégory Batt;Hidde de Jong;Michel Page;Johannes Geiselmann
Affiliations:
INRIA Grenoble - Rhône-Alpes, 655 avenue de l'Europe, Montbonnot, 38334 Saint Ismier Cedex, France and Center for Information and Systems Engineering, Boston University, USA and Verimag, Gren ...;INRIA Grenoble - Rhône-Alpes, 655 avenue de l'Europe, Montbonnot, 38334 Saint Ismier Cedex, France;INRIA Grenoble - Rhône-Alpes, 655 avenue de l'Europe, Montbonnot, 38334 Saint Ismier Cedex, France and Ecole Supérieure des Affaires, Université Pierre Mendès France, Grenoble, ...;INRIA Grenoble - Rhône-Alpes, 655 avenue de l'Europe, Montbonnot, 38334 Saint Ismier Cedex, France and Laboratoire Adaptation et Pathogénie des Microorganismes (CNRS UMR 5163), Universit ...
Venue:
Automatica (Journal of IFAC)
Year:
2008

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Abstract

We use hybrid-systems techniques for the analysis of reachability properties of a class of piecewise-affine (PA) differential equations that are particularly suitable for the modeling of genetic regulatory networks. 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 qualitative description of the network dynamics that is well-adapted to available experimental data and that can be efficiently computed in a symbolic manner from inequality constraints on the parameters.