Robustness in chemical reaction networks with low-dimensional stoichiometric space

Autoregulatory processes are present in several biochemical systems and their main characteristic is the capacity to mitigate the effect of external input on the system. When these processes are modeled with Chemical Reaction Networks, the robustness with respect to external input is called Absolute Concentration Robustness (ACR), and under mass action kinetics, detecting ACR corresponds to deciding whether the real "positive" part of an algebraic variety is contained in a hyperplane parallel to a coordinate hyperplane. In this talk, I will introduce the concept of ACR, give an overview of available tools for detecting ACR, and then focus on detecting ACR in small networks. For networks with low-dimensional stoichiometric space, we provide a full classification of the networks that have ACR for every set of parameters. This is joint work with Anne Shiu and Nicolette Meshkat.