# Families of Toric Chemical Reaction Networks

## TL;DR

This paper investigates families of chemical reaction networks with toric steady states, providing algebraic tools to analyze their multistationarity, model distinguishability, and implications for experimental design, exemplified by phosphorylation networks.

## Contribution

It introduces an algorithmic construction of reaction network families with toric steady states and uses matroids to analyze their steady state behavior and distinguishability.

## Key findings

- Multistationarity propagates through network families.
- Matroids encode steady state dependencies and model distinguishability.
- Necessary conditions for network family distinguishability are established.

## Abstract

We study families of chemical reaction networks whose positive steady states are toric, and therefore can be parameterized by monomials. Families are constructed algorithmically from a core network; we show that if a family member is multistationary, then so are all subsequent networks in the family. Further, we address the questions of model selection and experimental design for families by investigating the algebraic dependencies of the chemical concentrations using matroids. Given a family with toric steady states and a constant number of conservation relations, we construct a matroid that encodes important information regarding the steady state behaviour of the entire family. Among other things, this gives necessary conditions for the distinguishability of families of reaction networks with respect to a data set of measured chemical concentrations. We illustrate our results using multi-site phosphorylation networks.