Title

Solution Method For The Transformed Time-Dependent Michaelis–Menten Enzymatic Reaction Model

Keywords

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

Abstract

The dynamic form of the Michaelis–Menten enzymatic reaction equations provides a time-dependent model in which a substrate(Formula presented) reacts with an enzyme (Formula presented) to form a complex (Formula presentd) which is in turn converted into a product (Formula presented) and the enzyme (Formula presented). In the recent paper [Mallory and Van Gorder in J Math Chem 52: 222–230, 2014], it was shown 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. Qualitative properties of solutions were discussed, and stability results were given. In the present paper, we apply the optimal homotopy analysis method to the solution of this problem in order to obtain quantitative results. To do so, we transform the governing equation into a form that is more amenable to analysis. From the homotopy solutions, we are then able to study the effects of the model parameters on the solutions to the dynamic Michaelis–Menten enzymatic reaction equations. The results demonstrate the accuracy and efficiency of the approach, with residual errors of(Formula presented) by considering relatively few iterations of the method. Therefore, the optimal homotopy analysis method is shown to be a rather useful tool for constructing analytical solutions to the dynamic Michaelis–Menten enzymatic reaction equations.

Publication Date

10-31-2014

Publication Title

Journal of Mathematical Chemistry

Volume

52

Issue

10

Number of Pages

2494-2506

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s10910-014-0397-y

Socpus ID

84939873471 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84939873471

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