Reaction Network Motifs for Static and Dynamic Absolute Concentration Robustness

TL;DR

This paper classifies small reaction networks with two reactions and species to understand static and dynamic absolute concentration robustness, providing foundational insights for analyzing more complex biological systems.

Contribution

It offers a complete classification of minimal reaction networks based on ACR properties, advancing understanding of dynamic robustness in biological networks.

Findings

Complete classification of 2-reaction, 2-species networks by ACR properties

Rich dynamics observed even in simple networks

Insights to inform analysis of complex networks with ACR

Abstract

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 (dynamic 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 2 reactions and 2 species. We give a complete classification by ACR properties of these minimal reaction networks. The dynamics is rich even within this simple setting. Insights obtained from this work will help illuminate the properties of more complex networks with dynamic ACR.