On an optimal setting of constant delays for the D-QSSA model reduction method applied to a class of chemical reaction networks. (English) Zbl 07613025

Summary: We develop and test a relatively simple enhancement of the classical model reduction method applied to a class of chemical networks with mass conservation properties. Both the methods, being (i) the standard quasi-steady-state approximation method, and (ii) the novel so-called delayed quasi-steady-state approximation method, firstly proposed by T. Vejchodský [Math. Bohem. 139, No. 4, 577–585 (2014; Zbl 1349.92030)], are extensively presented. Both theoretical and numerical issues related to the setting of delays are discussed. Namely, for one slightly modified variant of an enzyme-substrate reaction network (Michaelis-Menten kinetics), the comparison of the full non-reduced system behavior with respective variants of reduced model is presented and the results discussed. Finally, some future prospects related to further applications of the delayed quasi-steady-state approximation method are proposed.


92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
34A34 Nonlinear ordinary differential equations and systems
65K10 Numerical optimization and variational techniques


Zbl 1349.92030
Full Text: DOI


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