# The effect of conservation on the dynamics of chemical reaction networks

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The Effect of Conservation on the Dynamics of Chemical Reaction Networks The effect of conservation on the dynamics of chemical reaction networks Katalin M. Hangos ∗ Gábor Szederkényi ∗,∗∗ ∗ Process Control Research Group, Systems and Control Laboratory, Computer and Automation Research Institute, Hungarian Academy of Sciences P.O. Box 63, H-1518 Budapest, Hungary e-mail:{hangos,[email protected] ∗∗ PPKE-ITK, 1083 Budapest, Práter u. 50/a, Hungary (e-mail: [email protected]) Abstract: Component mass conservation gives a linear first integral to the dynamic reaction kinetic equations and greatly influences the set of admissible reactions. Therefore, mass conservation can be related to the deficiency of the reaction network and thus to its dynamic properties. In particular, it is shown that a mass conserving CRN without isomers and with a full rank complex composition matrix has zero deficiency. The concepts and results are illustrated on the example of the original and the lumped version of Michaelis-Menten kinetics. Keywords: Process control; Chemical variables control; Modelling; Graph theoretic models; Structural stability; 1. INTRODUCTION It is well-known that kinetic systems form a wide class of nolinear models with good dynamical descriptive proper- ties [3]. Therefore (bio)chemical reaction networks (CRNs) are often used to model complex biological mechanisms [11], or even to describe dynamical systems in application fields seemingly far from chemistry such as mechanical or electrical systems [12]. The increasing and extended inter- est towards this field is shown by the fact that numerous surveys and tutorials have been published even in journals where the primary scope is not chemistry [1, 2, 13]. The classical chemical theory of deterministic CRNs obey- ing the mass action law (MAL CRNs) assumes closed isotherm and isobaric conditions, where the total mass is conserved. This mass conservation applies also for the set of species that participate i

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