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

Journal article
(Original article)


Publication Details

Author(s): Kram S, Schäfer M, Rabenstein R
Journal: Journal of Mathematical Chemistry
Publication year: 2017
Volume: 56
Journal issue: 4
Pages range: 1153-1183
ISSN: 0259-9791
Language: English


Abstract


This contribution presents an approximate solution of the enzyme kinetics problem for the case of excess of an enzyme over the substrate. A rst 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 identication 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 denition 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 rst 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.


FAU Authors / FAU Editors

Rabenstein, Rudolf Prof. Dr.
Lehrstuhl für Multimediakommunikation und Signalverarbeitung
Schäfer, Maximilian
Lehrstuhl für Multimediakommunikation und Signalverarbeitung


How to cite

APA:
Kram, S., Schäfer, M., & Rabenstein, R. (2017). Approximation of enzyme kinetics for high enzyme concentration by a first order perturbation approach. Journal of Mathematical Chemistry, 56(4), 1153-1183. https://dx.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 (2017): 1153-1183.

BibTeX: 

Last updated on 2018-17-06 at 16:10