  We study the response of chemical reaction networks driven far from
equilibrium to logarithmic perturbations of reaction rates. The response of the
mean number of a chemical species is observed to be quantitively limited by
number fluctuations as well as the maximum thermodynamic driving force. We
prove these trade-offs for linear chemical reaction networks and a class of
nonlinear chemical reaction networks with a single chemical species. Numerical
results for several model systems support the conclusion that these trade-offs
continue to hold for a broad class of chemical reaction networks, though their
precise form appears to depend sensitively on the deficiency of the network.
