Gröbner bases of reaction networks with intermediate species

AmirHosein Sadeghimanesh, Elisenda Feliu

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
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In this work we consider the computation of Gröbner bases of the steady state ideal of reaction networks equipped with mass-action kinetics. Specifically, we focus on the role of intermediate species and the relation between the extended network (with intermediate species) and the core network (without intermediate species).

We show that a Gröbner basis of the steady state ideal of the core network always lifts to a Gröbner basis of the steady state ideal of the extended network by means of linear algebra, with a suitable choice of monomial order. As illustrated with examples, this contributes to a substantial reduction of the computation time, due mainly to the reduction in the number of variables and polynomials. We further show that if the steady state ideal of the core network is binomial, then so is the case for the extended network, as long as an extra condition is fulfilled. For standard networks, this extra condition can be visually explored from the network structure alone.
Original languageEnglish
Pages (from-to)74-101
Number of pages28
JournalAdvances in Applied Mathematics
Early online date7 Mar 2019
Publication statusPublished - Jun 2019
Externally publishedYes

Bibliographical note

NOTICE: this is the author’s version of a work that was accepted for publication in Advances in Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Advances in Applied Mathematics, 107, (2019)
DOI: 10.1016/j.aam.2019.02.006

© 2019, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International


  • Binomial ideals
  • Mass-action kinetics
  • Steady state ideal
  • Invariant
  • Gröbner basis


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