  We study two specific measures of quality of chemical reaction networks,
Precision and Sensitivity. The two measures arise in the study of sensory
adaptation, in which the reaction network is viewed as an input-output system.
Given a step change in input, Sensitivity is a measure of the magnitude of the
response, while Precision is a measure of the degree to which the system
returns to its original output for large time. High values of both are
necessary for high-quality adaptation.
  We focus on reaction networks without dissipation, which we interpret as
detailed-balance, mass-action networks. We give various upper and lower bounds
on the optimal values of Sensitivity and Precision, characterized in terms of
the stoichiometry, by using a combination of ideas from matroid theory and
differential-equation theory.
  Among other results, we show that this class of non-dissipative systems
contains networks with arbitrarily high values of both Sensitivity and
Precision. This good performance does come at a cost, however, since certain
ratios of concentrations need to be large, the network has to be extensive, or
the network should show strongly different time scales.
