Genetically Regulated Metabolic Networks: Gale-Nikaido Modules and Differential Inequalities

We propose an approach to study static properties of metabolic networks with genetic regulation. We base our results on differential inequalities which are constraints on the values of the partial derivatives of the reaction rate functions. The approach uses an iterative elimination method for the steady state equations involving algebraic modules that satisfy the Gale-Nikaido global univalence property. The same method allows to find conditions for unique steady state. In the case of metabolic pathways, partial elimination of variables can produce several alternative models, allowing to compare steady state changes of metabolites with and without genetic regulation.