On an optimal setting of constant delays for the D-QSSA model reduction method applied to a class of chemical reaction networks

Ctirad Matonoha; Štěpán Papáček; Volodymyr Lynnyk

Applications of Mathematics (2022)

  • Volume: 67, Issue: 6, page 831-857
  • ISSN: 0862-7940

Abstract

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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 Vejchodský (2014), 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.

How to cite

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Matonoha, Ctirad, Papáček, Štěpán, and Lynnyk, Volodymyr. "On an optimal setting of constant delays for the D-QSSA model reduction method applied to a class of chemical reaction networks." Applications of Mathematics 67.6 (2022): 831-857. <http://eudml.org/doc/298520>.

@article{Matonoha2022,
abstract = {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 Vejchodský (2014), 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.},
author = {Matonoha, Ctirad, Papáček, Štěpán, Lynnyk, Volodymyr},
journal = {Applications of Mathematics},
keywords = {reaction network; model reduction; singular perturbation; quasi-steady-state approximation; D-QSSA method; optimization},
language = {eng},
number = {6},
pages = {831-857},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On an optimal setting of constant delays for the D-QSSA model reduction method applied to a class of chemical reaction networks},
url = {http://eudml.org/doc/298520},
volume = {67},
year = {2022},
}

TY - JOUR
AU - Matonoha, Ctirad
AU - Papáček, Štěpán
AU - Lynnyk, Volodymyr
TI - On an optimal setting of constant delays for the D-QSSA model reduction method applied to a class of chemical reaction networks
JO - Applications of Mathematics
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 6
SP - 831
EP - 857
AB - 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 Vejchodský (2014), 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.
LA - eng
KW - reaction network; model reduction; singular perturbation; quasi-steady-state approximation; D-QSSA method; optimization
UR - http://eudml.org/doc/298520
ER -

References

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