Title

A Transformed Time-Dependent Michaelis-Menten Enzymatic Reaction Model And Its Asymptotic Stability

Keywords

Dynamic Michaelis-Menten model; Enzyme reactions; Nonlinear dynamics; Stability

Abstract

The dynamic form of the Michaelis-Menten enzymatic reaction equations provide a time-dependent model in which a substrate S reacts with an enzyme E to form a complex C which in turn is converted into a product P and the enzyme E. 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. © 2013 Springer Science+Business Media New York.

Publication Date

1-1-2014

Publication Title

Journal of Mathematical Chemistry

Volume

52

Issue

1

Number of Pages

222-230

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s10910-013-0257-1

Socpus ID

84891629540 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84891629540

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