Sensitivity of chemical reaction networks: a structural approach 3. Regular multimolecular systems

摘要

We present a systematic mathematical analysis of the qualitative steady-stateresponse to rate perturbations in large classes of reaction networks. Thisincludes multimolecular reactions and allows for catalysis, enzymaticreactions, multiple reaction products, nonmonotone rate functions, andnon-closed autonomous systems. Our structural sensitivity analysis is based onthe stoichiometry of the reaction network, only. It does not require numericaldata on reaction rates. Instead, we impose mild and generic nondegeneracyconditions of algebraic type. From the structural data, only, we derive whichsteady-state concentrations are sensitive to, and hence influenced by, changesof any particular reaction rate - and which are not. We also establishtransitivity properties for influences involving rate perturbations. Thisallows us to derive an influence graph which globally summarizes the influencepattern of the given network. The influence graph allows the computational, butmeaningful, automatic identification of functional subunits in generalnetworks, which hierarchically influence each other. We illustrate our resultsfor several variants of the glycolytic citric acid cycle. Biologicalapplications include enzyme knockout experiments, and metabolic control.