Sensitivity of chemical reaction networks : a structural approach . 2 . Regular monomolecular systems

For the deceptively innocent case of monomolecular reactions, only, we embark on a systematic mathematical analysis of the steady state response to perturbations of reaction rates. Our structural sensitivity analysis is based on the directed graph structure of the monomolecular reaction network, only. In fact, our function-free approach does not require numerical input. We work with general, not necessarily monotone reaction rate functions. Based on the graph structure alone, we derive which steady state concentrations and reaction fluxes are sensitive to, and thus affected by, a rate change – and which are not. Moreover, we establish a transitivity property for the influence of a rate perturbation, at any reaction, on all reaction fluxes. The results and concepts developed here, from a mathematical view point, are of applied relevance including metabolic networks in biology; see our companion paper [MoFi14].