ON QUALITATIVE REPRESENTATIONS OF A PIECEWISE-LINEAR MODEL OF A TWO GENES REGULATORY NETWORK – COMPARATIVE APPROACHES
There is an increasing interest in the study of genetic regulatory networks, and in addition to experimental tools, specific tools for modelling and simulation recently emerged, allowing systematic behaviour prediction of large complex systems. Since there is a usual lack of information of biochemical reaction networks, qualitative simulation tools, requiring only specification of inequality-like algebraic constraints, are preferred to quantitative ones. Starting from a simple piecewise-linear model of a two genes regulatory network (TGNR) described in the literature, this paper proposes an alternate qualitative modelling technique, which extends a hybrid control systems (HCS) framework classic in control engineering. The thresholds protein concentrations partition the state space into hyperrectangular open regions and the resulting qualitative model is basically a logical abstraction of the families of continuous trajectories mapped to this partition. The relations of this model to numerical simulation results and a comparison with the corresponding qualitative model in the GNA (Generic Network Analyse) approach are presented.