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

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 in the new species for any generic choice of rate constants. (ii) We characterize all non-redundant zero-one networks with dimension of at most two that exhibit non-vacuous ACR 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.