In this paper we study the mathematical model of auxiliary (or coupled) reactions, a mechanism which describes several chemical reactions. In order to apply singular perturbation techniques, we determine an appropriate perturbation parameter ǫ (which is related to the kinetic constants and initial conditions of the model), the inner and outer solutions and the matched expansions of the solutions, up to the first order in ǫ, in the total quasi-steady-state approximation (tQSSA) framework. The contribution of these expansions can be useful for the estimation of the kinetic parameters of the reaction by means of the interpolation of experimental data with the explicit approximations of the solutions. Some numerical results are discussed, showing the high reliability of the tQSSA with respect to the standard QSSA.

Asymptotics and numerical analysis for enzymatic auxiliary reactions / Bersani, Alberto Maria; Borri, Alessandro; Tosti, Maria Elisa. - In: CONTINUUM MECHANICS AND THERMODYNAMICS. - ISSN 0935-1175. - 33:(2021), pp. 851-872. [10.1007/s00161-020-00962-5]

Asymptotics and numerical analysis for enzymatic auxiliary reactions

Alberto Maria Bersani
;
Maria Elisa Tosti
2021

Abstract

In this paper we study the mathematical model of auxiliary (or coupled) reactions, a mechanism which describes several chemical reactions. In order to apply singular perturbation techniques, we determine an appropriate perturbation parameter ǫ (which is related to the kinetic constants and initial conditions of the model), the inner and outer solutions and the matched expansions of the solutions, up to the first order in ǫ, in the total quasi-steady-state approximation (tQSSA) framework. The contribution of these expansions can be useful for the estimation of the kinetic parameters of the reaction by means of the interpolation of experimental data with the explicit approximations of the solutions. Some numerical results are discussed, showing the high reliability of the tQSSA with respect to the standard QSSA.
2021
auxiliary; reactions; Michaelis–Menten; kinetics; singular; perturbations; asymptotic; expansions; total quasi-steady-state approximation
01 Pubblicazione su rivista::01a Articolo in rivista
Asymptotics and numerical analysis for enzymatic auxiliary reactions / Bersani, Alberto Maria; Borri, Alessandro; Tosti, Maria Elisa. - In: CONTINUUM MECHANICS AND THERMODYNAMICS. - ISSN 0935-1175. - 33:(2021), pp. 851-872. [10.1007/s00161-020-00962-5]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1471557
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