Testing Binomiality of Chemical Reaction Networks Using Comprehensive Gröbner Systems

Hamid Rahkooy (1) , Thomas Sturm (2, 3, 4, 1, 5)

1 MPII - Max-Planck-Institut für Informatik
2 CNRS - Centre National de la Recherche Scientifique
3 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
4 MOSEL - Proof-oriented development of computer-based systems
5 Saarland University [Saarbrücken]

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 Gröbner systems. Considering rate constants as parameters, we compute comprehensive Gröbner 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.

Mots clés: Binomial ideals; Toric varieties; Chemical reaction networks; Mass action kinetics; Scientific computation; Symbolic computation Gröbner bases Comprehensive Gröbner bases

Domaines: Calcul formel [cs.SC]; Logique en informatique [cs.LO]; Réseaux moléculaires [q-bio.MN]; Géométrie algébrique [math.AG]; Systèmes dynamiques [math.DS]

Hamid Rahkooy, Thomas Sturm. Testing Binomiality of Chemical Reaction Networks Using Comprehensive Gröbner Systems. CASC 2021 - Computer Algebra in Scientific Computing, Sep 2021, Sochi, Russia. pp.334-352, ⟨10.1007/978-3-030-85165-1_19⟩. ⟨hal-03438171⟩