Symbolic reachability analysis of genetic regulatory networks using discrete abstractions

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.