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

Matonoha, Ctirad; Papáček, Štěpán; Lynnyk, Volodymyr

Appl. Math., Praha 67, No. 6, 831-857 (2022).

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.

MSC:

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

Keywords:

reaction network; model reduction; singular perturbation; quasi-steady-state approximation; D-QSSA method; optimization

Citations:

Zbl 1349.92030

References:

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