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The total quasi-steady-state for multiple alternative substrate reactions

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Abstract

The Michaelis–Menten–Briggs–Haldane approximation and its extension, the total quasi-steady-state approximation (tQSSA) are famous assumptions for simplification of mathematical modeling of enzyme-substrate reactions. These approximations and their validity conditions are well studied for a single substrate reaction system. However, the extension of these studies for the tQSSA of the general case of multiple substrate reactions is yet to be performed precisely due to the consequent non-linear expressions for tQSSA. In this paper, we introduce a linearization method for equations governing the tQSSA of multiple substrate reactions to obtain an analytical solution for the evolution of concentrations of reactants that is valid throughout the whole time period. In addition, we provide the validity conditions of the tQSSA for multiple substrate reaction systems using the singular perturbation analysis method.

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Authors and Affiliations

  1. Center for Biosystems and Biotech Data Science, Ghent University Global Campus, 119 Songdomunhwa-ro, Incheon, Yeonsu-gu, 21985, South Korea

    Azimberdy Besya & Shodhan Rao

  2. Department of Data Analysis and Mathematical Modelling, Ghent University, Coupure links 653, 9000, Gent, Belgium

    Shodhan Rao

Authors
  1. Azimberdy Besya
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  2. Shodhan Rao
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Correspondence to Azimberdy Besya.

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Besya, A., Rao, S. The total quasi-steady-state for multiple alternative substrate reactions. J Math Chem 60, 841–861 (2022). https://doi.org/10.1007/s10910-022-01339-6

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  • DOI: https://doi.org/10.1007/s10910-022-01339-6

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