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

    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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