# Robustness in power law kinetic systems with reactant-determined interactions

## TL;DR

This paper extends the concept of absolute concentration robustness (ACR) from mass-action systems to more general power-law kinetic systems with reactant-determined interactions, providing new insights into system robustness.

## Contribution

It generalizes ACR conditions to power-law kinetic systems with reactant-determined interactions, broadening the applicability of robustness analysis beyond mass-action models.

## Key findings

- Power-law kinetic systems with reactant-determined interactions can exhibit ACR.
- A power-law approximation of the global carbon cycle model shows ACR properties.
- The extended framework helps identify robustness components in complex chemical networks.

## Abstract

Robustness against the presence of environmental disruptions can be observed in many systems of chemical reaction network. However, identifying the underlying components of a system that give rise to robustness is often elusive. The influential work of Shinar and Feinberg established simple yet subtle network-based conditions for absolute concentration robustness (ACR), a phenomena in which a species in a mass-action system has the same concentration for any steady state the network may admit. In this contribution, we extend this result to embrace kinetic systems more general than mass-action systems, namely, power-law kinetic systems with reactant-determined interactions (denoted by "PL-RDK"). In PL-RDK, the kinetic order vectors (which we call "interactions") of reactions with the same reactant complex are identical. As illustration, we considered a scenario in the pre-industrial state of global carbon cycle. A power-law approximation of the dynamical system of this scenario is found to be dynamically equivalent to an ACR-possessing PL-RDK system.