Conservation Laws in Biochemical Reaction Networks
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Altres documents de l'autoria: Adam, Mahdi; Ferragut, Antoni; Valls, Claudia; Carsten, Wiuf
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Títol
Conservation Laws in Biochemical Reaction NetworksData de publicació
2017Editor
Society for Industrial and Applied MathematicsISSN
1536-0040; 1536-0040Cita bibliogràfica
MAHDI, Adam, et al. Conservation Laws in Biochemical Reaction Networks. SIAM Journal on Applied Dynamical Systems, 2017, vol. 16 núm. 4, p. 2213-2232.Tipus de document
info:eu-repo/semantics/articleVersió de l'editorial
https://epubs.siam.org/doi/abs/10.1137/17M1138418Versió
info:eu-repo/semantics/submittedVersionParaules clau / Matèries
Resum
We study the existence of linear and non-linear conservation laws in biochemical
reaction networks with mass-action kinetics. It is straightforward to compute
the linear conservation laws as they are related to the ... [+]
We study the existence of linear and non-linear conservation laws in biochemical
reaction networks with mass-action kinetics. It is straightforward to compute
the linear conservation laws as they are related to the left null-space of the
stoichiometry matrix. The non-linear conservation laws are difficult to identify
and have rarely been considered in the context of mass-action reaction networks.
Here, using Darboux theory of integrability we provide necessary structural
(i.e. parameter independent) conditions on a reaction network to guarantee the
existence of non-linear conservation laws of certain type. We give necessary
and sufficient structural conditions for the existence of exponential factors with
linear exponents and univariate linear Darboux polynomials. This allows us to
conclude that a non-linear first integrals (similar to Lotka-Volterra system) only
exists under the same structural condition. We finally show that the existence
of such a first integral generally implies that the system is persistent and has
stable steady states. We illustrate our results by examples. [-]
Publicat a
SIAM Journal on Applied Dynamical Systems, 2017, vol. 16 núm. 4, p. 2213-2232.Proyecto de investigación
AM acknowledges the support of EPSRC project EP/K036157/1. AF is partially supported by the MINECO grants MTM2013-40998-P and MTM2016- 77278-P and by the Universitat Jaume I grant P1-1B2015-16. CV is partially 385 supported by FCT/Portugal through UID/MAT/04459/2013. CW is supported by the Lundbeck Foundation, Denmark, the Danish Research Council and Dr.phil. Ragna Rask-Nielsen Grundforskningsfond (administered by the Royal Danish Academy of Sciences and Letters). This work was finalised while CW was visiting Universitat Politècnica de Catalunya in Spring 2017.Drets d'accés
© 2017, Society for Industrial and Applied Mathematics
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