Title

A transformed time-dependent Michaelis-Menten enzymatic reaction model and its asymptotic stability

Authors

Authors

K. Mallory;R. A. Van Gorder

Comments

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Abbreviated Journal Title

J. Math. Chem.

Keywords

Dynamic Michaelis-Menten model; Nonlinear dynamics; Stability; Enzyme; reactions; KINETICS; Chemistry, Multidisciplinary; Mathematics, Interdisciplinary; Applications

Abstract

The dynamic form of the Michaelis-Menten enzymatic reaction equations provide a time-dependent model in which a substrate reacts with an enzyme to form a complex which in turn is converted into a product and the enzyme . In the present paper, we show that this system of four nonlinear equations can be reduced to a single nonlinear differential equation, which is simpler to solve numerically than the system of four equations. Applying the Lyapunov stability theory, we prove that the non-zero equilibrium for this equation is globally asymptotically stable, and hence that the non-zero steady-state solution for the full Michaelis-Menten enzymatic reaction model is globally asymptotically stable for all values of the model parameters. As such, the steady-state solutions considered in the literature are stable. We finally discuss properties of the numerical solutions to the dynamic Michaelis-Menten enzymatic reaction model, and show that at small and large time scales the solutions may be approximated analytically.

Journal Title

Journal of Mathematical Chemistry

Volume

52

Issue/Number

1

Publication Date

1-1-2014

Document Type

Article

Language

English

First Page

222

Last Page

230

WOS Identifier

WOS:000329237100016

ISSN

0259-9791

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