  Motivated by the question of how biological systems maintain homeostasis in
changing environments, Shinar and Feinberg introduced in 2010 the concept of
absolute concentration robustness (ACR). A biochemical system exhibits ACR in
some species if the steady-state value of that species does not depend on
initial conditions. Thus, a system with ACR can maintain a constant level of
one species even as the environment changes. Despite a great deal of interest
in ACR in recent years, the following basic question remains open: How can we
determine quickly whether a given biochemical system has ACR? Although various
approaches to this problem have been proposed, we show that they are
incomplete. Accordingly, we present new methods for deciding ACR, which harness
computational algebra. We illustrate our results on several biochemical
signaling networks.
