Testing Binomiality of Chemical Reaction Networks Using Comprehensive Gr\"obner Systems

TL;DR

This paper investigates conditions under which the steady state ideals of biochemical reaction networks are binomial, using comprehensive Gr"obner systems to analyze parameter-dependent polynomial properties.

Contribution

It introduces a method employing comprehensive Gr"obner systems to automatically determine binomiality conditions for biochemical networks.

Findings

Computed comprehensive Gr"obner systems for various reactions.

Automated analysis on phosphorylation and biomodels.

Identified parameter conditions ensuring binomial steady state ideals.

Abstract

We consider the problem of binomiality of the steady state ideals of biochemical reaction networks. We are interested in finding polynomial conditions on the parameters such that the steady state ideal of a chemical reaction network is binomial under every specialisation of the parameters if the conditions on the parameters hold. We approach the binomiality problem using Comprehensive Gr\"obner systems. Considering rate constants as parameters, we compute comprehensive Gr\"obner systems for various reactions. In particular, we make automatic computations on n-site phosphorylations and biomodels from the Biomodels repository using the grobcov library of the computer algebra system Singular.