Homeostasis and injectivity: a reaction network perspective

TL;DR

This paper explores the relationship between homeostasis and injectivity in reaction networks, showing that injectivity of a modified network prevents homeostasis, with analysis and examples provided.

Contribution

It establishes a novel connection between homeostasis and injectivity in reaction networks, introducing the concept of the homeostasis-associated reaction network.

Findings

Injectivity of the homeostasis-associated network prevents homeostasis.

Examples demonstrate reaction networks that can or cannot exhibit homeostasis.

Theoretical framework links singularity theory with reaction network analysis.

Abstract

Homeostasis is a mechanism by which a feature can remain invariant with change in external parameters. We adopt the definition of homeostasis in the context of singularity theory. We make a connection between homeostasis and the theory of injective reaction networks. In particular, we show that a reaction network cannot exhibit homeostasis if a modified reaction network (which we call the homeostasis-associated reaction network) is injective. We provide examples of reaction networks which can or cannot exhibit homeostasis by analyzing the injectivity of the homeostasis-associated reaction network.