  We present a systematic mathematical analysis of the qualitative steady-state
response to rate perturbations in large classes of reaction networks. This
includes multimolecular reactions and allows for catalysis, enzymatic
reactions, multiple reaction products, nonmonotone rate functions, and
non-closed autonomous systems. Our structural sensitivity analysis is based on
the stoichiometry of the reaction network, only. It does not require numerical
data on reaction rates. Instead, we impose mild and generic nondegeneracy
conditions of algebraic type. From the structural data, only, we derive which
steady-state concentrations are sensitive to, and hence influenced by, changes
of any particular reaction rate - and which are not. We also establish
transitivity properties for influences involving rate perturbations. This
allows us to derive an influence graph which globally summarizes the influence
pattern of the given network. The influence graph allows the computational, but
meaningful, automatic identification of functional subunits in general
networks, which hierarchically influence each other. We illustrate our results
for several variants of the glycolytic citric acid cycle. Biological
applications include enzyme knockout experiments, and metabolic control.
