Subnetwork analysis for multistationarity in mass action kinetics

Abstract

Since quantitative knowledge of the complex (bio)chemical reaction networks is often very limited, formal methods that connect network structure and dynamic behavior are needed in mathematical modeling and analysis. Feinberg's Chemical Reaction Network Theory allows for the classification of the potential network behavior, for instance, with respect to the existence of multiple steady states, but is computationally limited to small systems. Here, we show that by analyzing subnetworks associated to stoichiometric generators, the applicability of the theory can be extended to more complex networks. Moreover, based on mild conditions regarding multiststionarity of such subnetworks, we present an algorithm which establishes multistationarity in the overall network.For example-networks inspired by cell cycle control in budding yeast, the approach allows for identification of key mechanisms for multistationarity, for model discrimination and for robustness analysis. The present paper continues and extends our work that has appeared in PNAS (cf. [6]).