Conservation Laws in Biochemical Reaction Networks
Scholar | Other documents of the author: Adam, Mahdi; Ferragut, Antoni; Valls, Claudia; Carsten, Wiuf
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TitleConservation Laws in Biochemical Reaction Networks
PublisherSociety for Industrial and Applied Mathematics
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. [-]
Investigation projectAM 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.
Bibliographic citationMAHDI, Adam, et al. Conservation Laws in Biochemical Reaction Networks. SIAM Journal on Applied Dynamical Systems, 2017, vol. 16 núm. 4, p. 2213-2232.
© 2017, Society for Industrial and Applied Mathematics
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