2026/04/16 by Xinyi Si, Xiaoxian Tang · 1 voice
Biochemistry, Genetics and Molecular Biology · #q-bio.MN
arxiv published 2026/04/16 · arxiv updated 2026/07/03
Absolute concentration robustness (ACR) characterizes systems where the steady-state concentration of a specific species remains invariant across all positive steady states. While ACR is a desirable property in biochemical network design, its structural compatibility with conservation laws remains a critical open question. This paper investigates the interplay between conservation laws and non-vacuous ACR in reaction networks, specifically analyzing whether ACR can be preserved or suppressed by augmenting the system with dependent species. We establish two main theoretical results regarding the structural obstructions to ACR. First, for networks governed by conservation laws, we derive a generic criterion demonstrating that augmenting a nondegenerate network with a single dependent species inevitably eliminates non-vacuous ACR for that species under generic rate constants. Second, we provide a complete characterization of non-redundant zero-one networks with dimension at most two. Despite their low dimensionality, these networks capture rich dynamical mechanisms and are sufficient to exhibit non-vacuous ACR, which we classify based on the structural properties of their stoichiometric matrices. A key finding is that all ACR networks contain no more than three different stoichiometric rows. This result rigorously establishes that an abundance of distinct conservation laws acts as a fundamental obstruction to ACR in non-redundant networks.