We apply to Michaelis–Menten kinetics an alternative approach to the study of Singularly Perturbed Differential Equations, that is based on the Renormalization Group (SPDERG). To this aim, we first rebuild the perturbation expansion for Michaelis–Menten kinetics, beyond the standard Quasi-Steady-State Approximation (sQSSA), determining the 2nd order contributions to the inner solutions, that are presented here for the first time to our knowledge. Our main result is that the SPDERG 2nd order uniform approximations reproduce the numerical solutions of the original problem in a better way than the known results of the perturbation expansion, even in the critical matching region. Indeed, we obtain analytical results nearly indistinguishable from the numerical solutions of the original problem in a large part of the whole relevant time window, even in the case in which the kinetic constants produce an expansion parameter value as large as ɛ=0.5.

An alternative approach to Michaelis-Menten kinetics that is based on the renormalization group / Coluzzi, Barbara; Bersani, Alberto M.; Bersani, Enrico. - In: MATHEMATICAL BIOSCIENCES. - ISSN 0025-5564. - STAMPA. - 299:(2018), pp. 28-50. [10.1016/j.mbs.2017.11.012]

An alternative approach to Michaelis-Menten kinetics that is based on the renormalization group

Coluzzi, Barbara
;
Bersani, Alberto M.
;
Bersani, Enrico
2018

Abstract

We apply to Michaelis–Menten kinetics an alternative approach to the study of Singularly Perturbed Differential Equations, that is based on the Renormalization Group (SPDERG). To this aim, we first rebuild the perturbation expansion for Michaelis–Menten kinetics, beyond the standard Quasi-Steady-State Approximation (sQSSA), determining the 2nd order contributions to the inner solutions, that are presented here for the first time to our knowledge. Our main result is that the SPDERG 2nd order uniform approximations reproduce the numerical solutions of the original problem in a better way than the known results of the perturbation expansion, even in the critical matching region. Indeed, we obtain analytical results nearly indistinguishable from the numerical solutions of the original problem in a large part of the whole relevant time window, even in the case in which the kinetic constants produce an expansion parameter value as large as ɛ=0.5.
Enzyme kinetics; Perturbation expansion; Renormalization group approach; Singular perturbation; Statistics and Probability; Modeling and Simulation; Biochemistry, Genetics and Molecular Biology (all); Immunology and Microbiology (all); Agricultural and Biological Sciences (all); Applied Mathematics
01 Pubblicazione su rivista::01a Articolo in rivista
An alternative approach to Michaelis-Menten kinetics that is based on the renormalization group / Coluzzi, Barbara; Bersani, Alberto M.; Bersani, Enrico. - In: MATHEMATICAL BIOSCIENCES. - ISSN 0025-5564. - STAMPA. - 299:(2018), pp. 28-50. [10.1016/j.mbs.2017.11.012]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1101931
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