Absolute concentration robustness in power law kinetic systems

TL;DR

This paper extends the understanding of absolute concentration robustness (ACR) in chemical kinetic systems, especially for power law kinetics with various deficiencies, using network equivalence and decomposition techniques.

Contribution

It introduces novel criteria for ACR in deficiency zero power law systems and higher deficiency networks through network decomposition and kinetic analysis.

Findings

ACR can be guaranteed in deficiency zero power law systems.

Higher deficiency networks can exhibit ACR via low deficiency subnetworks.

A weaker form of robustness, 'balanced concentration robustness', is identified.

Abstract

Absolute concentration robustness (ACR) is a condition wherein a species in a chemical kinetic system possesses the same value for any positive steady state the network may admit regardless of initial conditions. Thus far, results on ACR center on chemical kinetic systems with deficiency one. In this contribution, we use the idea of dynamic equivalence of chemical reaction networks to derive novel results that guarantee ACR for some classes of power law kinetic systems with deficiency zero. Furthermore, using network decomposition, we identify ACR in higher deficiency networks (i.e. deficiency $\geq$ 2) by considering the presence of a low deficiency subnetwork with ACR. Network decomposition also enabled us to recognize and define a weaker form of concentration robustness than ACR, which we named as `balanced concentration robustness'. Finally, we also discuss and emphasize our view of ACR as a primarily kinetic character rather than a condition that arises from structural sources.