Understanding Multistationarity of Fully Open Reaction Networks

TL;DR

This paper investigates the conditions for multistationarity in fully open reaction networks, introduces a novel method to generate non-multistationary networks, and applies machine learning to predict multistationarity using graph neural networks.

Contribution

It provides new theoretical insights, a deterministic operation for generating non-multistationary networks, and pioneers the use of machine learning for classifying reaction network multistationarity.

Findings

New operation to generate non-multistationary networks

Successful training of graph attention neural network for prediction

First application of machine learning to reaction network classification

Abstract

This work addresses multistationarity of fully open reaction networks equipped with mass action kinetics. We improve upon the existing results relating existence of positive feedback loops in a reaction network and multistationarity; and we provide a novel deterministic operation to generate new non-multistationary networks. This is interesting because while there were many operations to create infinitely many new multistationary networks from a multistationary example, this is the first such operation for the non-multistationary counterpart. Such tools for the generation of example networks have a use-case in the application of data science to reaction network theory. We demonstrate this by using the new data, along with a novel graph representation of reaction networks that is unique up to a permutation on the name of species of the network, to train a graph attention neural network model to predict multistationarity of reaction networks. This is the first time machine learning tools are used for studying classification problems of reaction networks.