Linear elimination in chemical reaction networks

Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review

Standard

Linear elimination in chemical reaction networks. / Sáez, Meritxell; Feliu, Elisenda; Wiuf, Carsten.

Recent Advances in Differential Equations and Applications. ed. / Juan Luis García Guirao; José Alberto Murillo Hernández; Francisco Periago Esparza. Springer, 2019. p. 177-193 (SEMA SIMAI Springer Series, Vol. 18).

Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review

Harvard

Sáez, M, Feliu, E & Wiuf, C 2019, Linear elimination in chemical reaction networks. in JLG Guirao, JAM Hernández & FP Esparza (eds), Recent Advances in Differential Equations and Applications. Springer, SEMA SIMAI Springer Series, vol. 18, pp. 177-193, 25th Congress on Differential Equations and Applications / 15th Congress on Applied Mathematics , Cartagena, Spain, 26/06/2017. https://doi.org/10.1007/978-3-030-00341-8_11

APA

Sáez, M., Feliu, E., & Wiuf, C. (2019). Linear elimination in chemical reaction networks. In J. L. G. Guirao, J. A. M. Hernández, & F. P. Esparza (Eds.), Recent Advances in Differential Equations and Applications (pp. 177-193). Springer. SEMA SIMAI Springer Series Vol. 18 https://doi.org/10.1007/978-3-030-00341-8_11

Vancouver

Sáez M, Feliu E, Wiuf C. Linear elimination in chemical reaction networks. In Guirao JLG, Hernández JAM, Esparza FP, editors, Recent Advances in Differential Equations and Applications. Springer. 2019. p. 177-193. (SEMA SIMAI Springer Series, Vol. 18). https://doi.org/10.1007/978-3-030-00341-8_11

Author

Sáez, Meritxell ; Feliu, Elisenda ; Wiuf, Carsten. / Linear elimination in chemical reaction networks. Recent Advances in Differential Equations and Applications. editor / Juan Luis García Guirao ; José Alberto Murillo Hernández ; Francisco Periago Esparza. Springer, 2019. pp. 177-193 (SEMA SIMAI Springer Series, Vol. 18).

Bibtex

@inbook{73134eca98b84834af68ac55ee672e18,
title = "Linear elimination in chemical reaction networks",
abstract = "We consider dynamical systems arising in biochemistry and systems biology that model the evolution of the concentrations of biochemical species described by chemical reactions. These systems are typically confined to an invariant linear subspace of ℝn. The steady states of the system are solutions to a system of polynomial equations for which only non-negative solutions are of interest. Here we study the set of non-negative solutions and provide a method for simplification of this polynomial system by means of linear elimination of variables. We take a graphical approach. The interactions among the species are represented by an edge labelled graph. Subgraphs with only certain labels correspond to sets of species concentrations that can be eliminated from the steady state equations using linear algebra. To assess positivity of the eliminated variables in terms of the non-eliminated variables, a multigraph is introduced that encodes the connections between the eliminated species in the reactions. We give graphical conditions on the multigraph that ensure the eliminated variables are expressed as positive functions of the non-eliminated variables. We interpret these conditions in terms of the reaction network. The results are illustrated by examples.",
keywords = "Conservation law, Elimination, Linear system, Noninteracting, Reaction network, Steady states",
author = "Meritxell S{\'a}ez and Elisenda Feliu and Carsten Wiuf",
year = "2019",
doi = "10.1007/978-3-030-00341-8_11",
language = "English",
series = "SEMA SIMAI Springer Series",
publisher = "Springer",
pages = "177--193",
editor = "Guirao, {Juan Luis Garc{\'i}a } and Hern{\'a}ndez, {Jos{\'e} Alberto Murillo } and Esparza, {Francisco Periago}",
booktitle = "Recent Advances in Differential Equations and Applications",
address = "Switzerland",
note = "25th Congress on Differential Equations and Applications / 15th Congress on Applied Mathematics ; Conference date: 26-06-2017 Through 30-06-2017",

}

RIS

TY - CHAP

T1 - Linear elimination in chemical reaction networks

AU - Sáez, Meritxell

AU - Feliu, Elisenda

AU - Wiuf, Carsten

PY - 2019

Y1 - 2019

N2 - We consider dynamical systems arising in biochemistry and systems biology that model the evolution of the concentrations of biochemical species described by chemical reactions. These systems are typically confined to an invariant linear subspace of ℝn. The steady states of the system are solutions to a system of polynomial equations for which only non-negative solutions are of interest. Here we study the set of non-negative solutions and provide a method for simplification of this polynomial system by means of linear elimination of variables. We take a graphical approach. The interactions among the species are represented by an edge labelled graph. Subgraphs with only certain labels correspond to sets of species concentrations that can be eliminated from the steady state equations using linear algebra. To assess positivity of the eliminated variables in terms of the non-eliminated variables, a multigraph is introduced that encodes the connections between the eliminated species in the reactions. We give graphical conditions on the multigraph that ensure the eliminated variables are expressed as positive functions of the non-eliminated variables. We interpret these conditions in terms of the reaction network. The results are illustrated by examples.

AB - We consider dynamical systems arising in biochemistry and systems biology that model the evolution of the concentrations of biochemical species described by chemical reactions. These systems are typically confined to an invariant linear subspace of ℝn. The steady states of the system are solutions to a system of polynomial equations for which only non-negative solutions are of interest. Here we study the set of non-negative solutions and provide a method for simplification of this polynomial system by means of linear elimination of variables. We take a graphical approach. The interactions among the species are represented by an edge labelled graph. Subgraphs with only certain labels correspond to sets of species concentrations that can be eliminated from the steady state equations using linear algebra. To assess positivity of the eliminated variables in terms of the non-eliminated variables, a multigraph is introduced that encodes the connections between the eliminated species in the reactions. We give graphical conditions on the multigraph that ensure the eliminated variables are expressed as positive functions of the non-eliminated variables. We interpret these conditions in terms of the reaction network. The results are illustrated by examples.

KW - Conservation law

KW - Elimination

KW - Linear system

KW - Noninteracting

KW - Reaction network

KW - Steady states

UR - http://www.scopus.com/inward/record.url?scp=85060280858&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-00341-8_11

DO - 10.1007/978-3-030-00341-8_11

M3 - Book chapter

AN - SCOPUS:85060280858

T3 - SEMA SIMAI Springer Series

SP - 177

EP - 193

BT - Recent Advances in Differential Equations and Applications

A2 - Guirao, Juan Luis García

A2 - Hernández, José Alberto Murillo

A2 - Esparza, Francisco Periago

PB - Springer

T2 - 25th Congress on Differential Equations and Applications / 15th Congress on Applied Mathematics

Y2 - 26 June 2017 through 30 June 2017

ER -

ID: 212679414