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

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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.

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Acknowledgment

The authors are grateful to Branislav Rehák for his worthy suggestions and discussions relevant to this paper. The authors would like to express their sincere thanks to anonymous reviewers for their constructive comments and valuable suggestions that have contributed to the improved version of the paper. The authors thank the corresponding editor for his valuable comments, encouragement, and patience.

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Authors and Affiliations

  1. Czech Academy of Sciences, Institute of Computer Science, Pod Vodárenskou věží 2, 182 07, Praha 8, Czech Republic

    Ctirad Matonoha

  2. Czech Academy of Sciences, Institute of Information Theory and Automation, Pod Vodárenskou věží 4, 182 00, Praha 8, Czech Republic

    Štěpán Papáček & Volodymyr Lynnyk

Authors
  1. Ctirad Matonoha
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  2. Štěpán Papáček
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  3. Volodymyr Lynnyk
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Correspondence to Ctirad Matonoha.

Additional information

The work of Ctirad Matonoha was supported by the long-term strategic development financing of the Institute of Computer Science of the Czech Academy of Sciences (RVO:67985807). The work of Štěpán Papáček and Volodymyr Lynnyk was supported by the Czech Science Foundation through the research grant No. 19-05872S.

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Matonoha, C., Papáček, Š. & Lynnyk, V. On an optimal setting of constant delays for the D-QSSA model reduction method applied to a class of chemical reaction networks. Appl Math 67, 831–857 (2022). https://doi.org/10.21136/AM.2022.0136-21

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