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The concept of robustness of regulatory networks has been closely related tothe nature of the interactions among genes, and the capability of patternmaintenance or reproducibility. Defining this robustness property is achallenging task, but mathematical models have often associated it to thevolume of the space of admissible parameters. Not only the volume of the spacebut also its topology and geometry contain information on essential aspects ofthe network, including feasible pathways, switching between two parallelpathways or distinct/disconnected active regions of parameters. A generalmethod is presented here to characterize the space of admissible parameters, bywriting it as a semi-algebraic set, and then theoretically analyzing itstopology and geometry, as well as volume. This method provides a more objectiveand complete measure of the robustness of a developmental module. As anillustration, the segment polarity gene network is analyzed.

Shape, size and robustness: feasible regions in the parameter space of biochemical networks