Approximation of enzyme kinetics for high enzyme concentration by a ﬁrst order perturbation approach

Kram S, Schäfer M, Rabenstein R (2018)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2018

Journal

Journal of Mathematical Chemistry Springer Verlag (Germany)

Book Volume: 56

Pages Range: 1153-1183

Journal Issue: 4

DOI: 10.1007/s10910-017-0848-3

Abstract

This contribution presents an approximate solution of the enzyme kinetics problem for the case of excess of an enzyme over the substrate. A ﬁrst order perturbation approach is adopted where the perturbation parameter is the relation of the substrate concentration to the total amount of enzyme. As a generalization over existing solutions for the same problem, the presented approximation allows for nonzero initial conditions for the substrate and the enzyme concentrations as well as for nonzero initial complex concentration. Nevertheless, the approximate solution is obtained in analytical form involving only elementary functions like exponentials and logarithms.

The presentation discusses all steps of the procedure, starting from amplitude and

time scaling for a non-dimensional representation and for the identiﬁcation of the

perturbation parameter. Suitable time constants lead to the short term and long term

behaviour, also known as the inner and outer solution. Special attention is paid to the

matching process by the deﬁnition of a suitable intermediate layer. The results are

presented in concise form as a summary of the required calculations. An extended

example compares the zero order and ﬁrst order perturbation approximations for the

short term and long term solution as well as the uniform solution. A comparison to

the numerical solution of the initial set of nonlinear ordinary differential equations

demonstrates the achievable accuracy.

Authors with CRIS profile

Sebastian Kram Professur für Signalverarbeitung Maximilian Schäfer Lehrstuhl für Multimediakommunikation und Signalverarbeitung Rudolf Rabenstein Lehrstuhl für Multimediakommunikation und Signalverarbeitung

How to cite

APA:

Kram, S., Schäfer, M., & Rabenstein, R. (2018). Approximation of enzyme kinetics for high enzyme concentration by a ﬁrst order perturbation approach. Journal of Mathematical Chemistry, 56(4), 1153-1183. https://doi.org/10.1007/s10910-017-0848-3

MLA:

Kram, Sebastian, Maximilian Schäfer, and Rudolf Rabenstein. "Approximation of enzyme kinetics for high enzyme concentration by a ﬁrst order perturbation approach." Journal of Mathematical Chemistry 56.4 (2018): 1153-1183.

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