Reaction Network Motifs for Static and Dynamic Absolute Concentration Robustness

Networks with absolute concentration robustness (ACR) have the property that a translation of a coordinate hyperplane either contains all steady states (static ACR) or attracts all trajectories (dy-namic ACR). The implication for the underlying biological system is robustness in the concentration of one of the species independent of the initial conditions as well as independent of the concentration of all other species. Identifying network conditions for dynamic ACR is a challenging problem. We lay the groundwork in this paper by studying small reaction networks, those with two reactions and two species. We give a complete classification by ACR properties of these minimal reaction networks. The dynamics are rich even within this simple setting. Insights obtained from this work will help illuminate the properties of more complex networks with dynamic ACR.

Automated summary

Networks with absolute concentration robustness exhibit stability in the concentration of one species regardless of the initial conditions and the concentrations of other species. By studying small reaction networks, we classified these networks based on their concentration robustness properties and observed rich dynamics even in this simple setting.