  This paper presents an algebraic framework to study sign-sensitivities for
reaction networks modeled by means of systems of ordinary differential
equations. Specifically, we study the sign of the derivative of the
concentrations of the species in the network at steady state with respect to a
small perturbation on the parameter vector. We provide a closed formula for the
derivatives that accommodates common perturbations, and illustrate its form
with numerous examples. We argue that, mathematically, the study of the
response to the system with respect to changes in total amounts is not well
posed, and that one should rather consider perturbations with respect to the
initial conditions. We find a sign-based criterion to determine, without
computing the sensitivities, whether the sign depends on the steady state and
parameters of the system. This is based on earlier results of so-called
injective networks. Finally, we address systems with multiple steady states and
the restriction to stable steady states.
