Computing Weakly Reversible Deficiency Zero Network Translations Using Elementary Flux Modes

TL;DR

This paper introduces a computational method using binary linear programming to construct reaction-to-reaction graphs for biochemical networks, aiding in analyzing steady states and dynamical behaviors.

Contribution

The authors develop an efficient algorithm for structural translation of reaction networks, enabling analysis of weakly reversible deficiency zero networks.

Findings

Successfully applied to 508 biochemical networks from BioModels database.

Facilitates establishing multistationarity in reaction systems.

Provides a formal link between reaction graphs and original networks.

Abstract

We present a computational method for performing structural translation, which has been studied recently in the context of analyzing the steady states and dynamical behavior of mass-action systems derived from biochemical reaction networks. Our procedure involves solving a binary linear programming problem where the decision variables correspond to interactions between the reactions of the original network. We call the resulting network a reaction-to-reaction graph and formalize how such a construction relates to the original reaction network and the structural translation. We demonstrate the efficacy and efficiency of the algorithm by running it on 508 networks from the European Bioinformatics Institutes' BioModels database. We also summarize how this work can be incorporated into recently proposed algorithms for establishing mono and multistationarity in biochemical reaction systems.