Control structure and limitations of biochemical networks

Biochemical networks typically exhibit intricate topologies that hinder their analysis with control-theoretic tools. In this work we present a systematic methodology for the identification of the control structure of a reaction network. The method is based on a bandwidth reduction technique applied to the incidence matrix of the network's graph. In addition, in the case of mass-action and stable networks we show that it is possible to identify linear algebraic dependencies between the time-domain integrals of some species' concentrations. We consider the extrinsic apoptosis pathway and an activation-inhibition mechanism to illustrate the application of our results.