Conservation Laws in Biochemical Reaction Networks

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Standard

Conservation Laws in Biochemical Reaction Networks. / Mahdi, Adam; Ferragut, Antoni; Valls, Claudia; Wiuf, Carsten.

I: S I A M Journal on Applied Dynamical Systems, Bind 16, Nr. 4, 2017, s. 2213-2232.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Mahdi, A, Ferragut, A, Valls, C & Wiuf, C 2017, 'Conservation Laws in Biochemical Reaction Networks', S I A M Journal on Applied Dynamical Systems, bind 16, nr. 4, s. 2213-2232. https://doi.org/10.1137/17M1138418

APA

Mahdi, A., Ferragut, A., Valls, C., & Wiuf, C. (2017). Conservation Laws in Biochemical Reaction Networks. S I A M Journal on Applied Dynamical Systems, 16(4), 2213-2232. https://doi.org/10.1137/17M1138418

Vancouver

Mahdi A, Ferragut A, Valls C, Wiuf C. Conservation Laws in Biochemical Reaction Networks. S I A M Journal on Applied Dynamical Systems. 2017;16(4):2213-2232. https://doi.org/10.1137/17M1138418

Author

Mahdi, Adam ; Ferragut, Antoni ; Valls, Claudia ; Wiuf, Carsten. / Conservation Laws in Biochemical Reaction Networks. I: S I A M Journal on Applied Dynamical Systems. 2017 ; Bind 16, Nr. 4. s. 2213-2232.

Bibtex

@article{019e1910d5e848598a1ee79730de1201,
title = "Conservation Laws in Biochemical Reaction Networks",
abstract = "We study the existence of linear and nonlinear conservation laws in biochemical reaction networkswith mass-action kinetics. It is straightforward to compute the linear conservation laws as theyare related to the left null-space of the stoichiometry matrix. The nonlinear conservation laws aredifficult to identify and have rarely been considered in the context of mass-action reaction networks.Here, using the Darboux theory of integrability, we provide necessary structural (i.e., parameterindependent)conditions on a reaction network to guarantee the existence of nonlinear conservationlaws of a certain type. We give necessary and sufficient structural conditions for the existence ofexponential factors with linear exponents and univariate linear Darboux polynomials. This allowsus to conclude that nonlinear first integrals only exist under the same structural condition (as inthe case of the Lotka–Volterra system). We finally show that the existence of such a first integralgenerally implies that the system is persistent and has stable steady states. We illustrate our resultsby examples.",
keywords = "Darboux polynomials, dynamical systems, mass-action kinetics, nonlinear conservation law, persistence, Lotka-Volterra system",
author = "Adam Mahdi and Antoni Ferragut and Claudia Valls and Carsten Wiuf",
year = "2017",
doi = "10.1137/17M1138418",
language = "English",
volume = "16",
pages = "2213--2232",
journal = "SIAM Journal on Applied Dynamical Systems",
issn = "1536-0040",
publisher = "Society for Industrial and Applied Mathematics",
number = "4",

}

RIS

TY - JOUR

T1 - Conservation Laws in Biochemical Reaction Networks

AU - Mahdi, Adam

AU - Ferragut, Antoni

AU - Valls, Claudia

AU - Wiuf, Carsten

PY - 2017

Y1 - 2017

N2 - We study the existence of linear and nonlinear conservation laws in biochemical reaction networkswith mass-action kinetics. It is straightforward to compute the linear conservation laws as theyare related to the left null-space of the stoichiometry matrix. The nonlinear conservation laws aredifficult to identify and have rarely been considered in the context of mass-action reaction networks.Here, using the Darboux theory of integrability, we provide necessary structural (i.e., parameterindependent)conditions on a reaction network to guarantee the existence of nonlinear conservationlaws of a certain type. We give necessary and sufficient structural conditions for the existence ofexponential factors with linear exponents and univariate linear Darboux polynomials. This allowsus to conclude that nonlinear first integrals only exist under the same structural condition (as inthe case of the Lotka–Volterra system). We finally show that the existence of such a first integralgenerally implies that the system is persistent and has stable steady states. We illustrate our resultsby examples.

AB - We study the existence of linear and nonlinear conservation laws in biochemical reaction networkswith mass-action kinetics. It is straightforward to compute the linear conservation laws as theyare related to the left null-space of the stoichiometry matrix. The nonlinear conservation laws aredifficult to identify and have rarely been considered in the context of mass-action reaction networks.Here, using the Darboux theory of integrability, we provide necessary structural (i.e., parameterindependent)conditions on a reaction network to guarantee the existence of nonlinear conservationlaws of a certain type. We give necessary and sufficient structural conditions for the existence ofexponential factors with linear exponents and univariate linear Darboux polynomials. This allowsus to conclude that nonlinear first integrals only exist under the same structural condition (as inthe case of the Lotka–Volterra system). We finally show that the existence of such a first integralgenerally implies that the system is persistent and has stable steady states. We illustrate our resultsby examples.

KW - Darboux polynomials

KW - dynamical systems

KW - mass-action kinetics

KW - nonlinear conservation law

KW - persistence

KW - Lotka-Volterra system

U2 - 10.1137/17M1138418

DO - 10.1137/17M1138418

M3 - Journal article

VL - 16

SP - 2213

EP - 2232

JO - SIAM Journal on Applied Dynamical Systems

JF - SIAM Journal on Applied Dynamical Systems

SN - 1536-0040

IS - 4

ER -

ID: 187663377