Gröbner bases of reaction networks with intermediate species

Amir Hossein Sadeghimanesh; Elisenda Feliu

doi:10.1016/j.aam.2019.02.006

Gröbner bases of reaction networks with intermediate species

Amir Hossein Sadeghimanesh, Elisenda Feliu

Department of Mathematical Sciences

3 Citations (Scopus)

Abstract

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 language	English
Journal	Advances in Applied Mathematics
Volume	107
Pages (from-to)	74-101
ISSN	0196-8858
DOIs	https://doi.org/10.1016/j.aam.2019.02.006
Publication status	Published - Jun 2019

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FeliuIntermediatesGroebnerBases_ResubmissionAccepted author manuscript, 397 KBLicence: CC BY-NC-ND

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title = "Gr{\"o}bner bases of reaction networks with intermediate species",

abstract = "In this work we consider the computation of Gr{\"o}bner 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 Gr{\"o}bner basis of the steady state ideal of the core network always lifts to a Gr{\"o}bner 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.",

author = "Sadeghimanesh, {Amir Hossein} and Elisenda Feliu",

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TY - JOUR

T1 - Gröbner bases of reaction networks with intermediate species

AU - Sadeghimanesh, Amir Hossein

AU - Feliu, Elisenda

PY - 2019/6

Y1 - 2019/6

N2 - 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.

AB - 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.

U2 - 10.1016/j.aam.2019.02.006

DO - 10.1016/j.aam.2019.02.006

M3 - Journal article

SN - 0196-8858

VL - 107

SP - 74

EP - 101

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

ER -

Gröbner bases of reaction networks with intermediate species

Abstract

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