Weakly reversible deficiency zero realizations of reaction networks

TL;DR

This paper proves the uniqueness of weakly reversible deficiency zero realizations for reaction networks that admit such realizations under all rate constants and introduces an algorithm to find this realization.

Contribution

It establishes the uniqueness of weakly reversible deficiency zero realizations and provides an algorithm to identify this network when it exists.

Findings

Uniqueness of weakly reversible deficiency zero realizations

Algorithm for finding the unique realization

Applicable to all rate constants scenarios

Abstract

We prove that if a given reaction network $\mathcal{N}$ has a weakly reversible deficiency zero realization for all choice of rate constants, then there exists a $\textit{unique}$ weakly reversible deficiency zero network $\mathcal{N}'$ such that $\mathcal{N}$ is realizable by $\mathcal{N}'$. Additionally, we propose an algorithm to find this weakly reversible deficiency zero network $\mathcal{N}'$ when it exists.