Conservation Laws in Biochemical Reaction Networks
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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
APA
Vancouver
Author
Bibtex
}
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