Absolute Concentration Robustness of Non-Redundant Zero-One Networks with Conservation Laws

TL;DR

This paper investigates how conservation laws influence the presence of absolute concentration robustness (ACR) in reaction networks, providing criteria and characterizations for when non-vacuous ACR can or cannot occur.

Contribution

It offers a criterion showing adding a dependent species eliminates non-vacuous ACR in nondegenerate networks with conservation laws and characterizes zero-one networks with low dimension exhibiting universal ACR.

Findings

Adding a dependent species precludes non-vacuous ACR in certain networks.

Zero-one networks with at most two dimensions can exhibit universal ACR.

Networks with four or more distinct stoichiometric rows lack non-vacuous ACR.

Abstract

Absolute concentration robustness (ACR) means the concentration of certain species stays the same in all the steady states. In this work, we study how conservation laws might effect non-vacuous ACR in reaction networks. The goal is to show whether non-vacuous ACR can be preserved or precluded by adding species that depend on the existing species. We have the following two main results. (i) For networks with conservation laws, we prove a criterion: for a nondegenerate network, augmenting it with one new species that depends on the original species leads to the resulting network having no non-vacuous ACR for any generic choice of rate constants in the new species. (ii) We characterize all non-redundant zero-one networks with dimension of at most two that exhibit non-vacuous ACR for any generic choice of rate constants according to the number of distinct rows in the stoichiometric matrices. An important finding is that if there are at least four distinct rows in the stoichiometric matrix, then the corresponding network has no non-vacuous ACR for any generic choice of rate constants, which implies that many conservation laws prevent non-vacuous ACR in non-redundant zero-one reaction networks.