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EFFECTS OF TIME DELAY ON THE DYNAMICS OF A KINETIC MODEL OF A MICROBIAL FERMENTATION PROCESS

Part of: Physiological, cellular and medical topics Functional-differential and differential-difference equations

Published online by Cambridge University Press:  10 September 2014

KASBAWATI ,
A. Y. GUNAWAN ,
R. HERTADI  and
K. A. SIDARTO
KASBAWATI
Affiliation:
Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung, Indonesia email [email protected] email [email protected] Department of Mathematics, Faculty of Mathematics and Natural Sciences, Hasanuddin University, Jl. Perintis Kemerdekaan Km. 10, Makassar, Indonesia email [email protected]
A. Y. GUNAWAN*
Affiliation:
Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung, Indonesia email [email protected] email [email protected]
R. HERTADI
Affiliation:
Biochemistry Research Division, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung, Indonesia email [email protected]
K. A. SIDARTO
Affiliation:
Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung, Indonesia email [email protected] email [email protected]
*
✉[email protected]
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Abstract

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We examine the dynamics of fermentation process in a yeast cell. Our investigation focuses on the main branch pathway: pyruvate and acetaldehyde branch points. We formulate the kinetics for all enzymatic reactions as Michaelis–Menten models. Since the activity of an enzyme mainly depends on the conformational changes of the enzyme structure, the enzyme requires a certain period of time to reset its structure, until it is ready to bind substrates again. For this situation, a rate-limiting step exists, for which the catalytic process suffers a delay. Since all conversion processes are catalysed by enzymes, each reaction can experience a delay at a different time. To investigate how the delay affects the reaction processes, especially at the branch points, we propose that the rate-limiting step takes place at the first reaction. For this reason, a discrete time delay is introduced to the first kinetic model. We find a bifurcation diagram for the delay that depends on the rate of glucose supply and kinetic parameters of the first enzyme. By comparison, our analysis agrees with the numerical solution. Our numerical simulations also show that there is a certain glucose supply that may optimize ethanol production.

Keywords

fermentation processsingle enzyme–substrate reaction mechanismenzyme kinetictime delayHopf bifurcation

MSC classification

Secondary: 92C45: Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) 34K60: Qualitative investigation and simulation of models 34K99: None of the above, but in this section
Type
Research Article
Information
The ANZIAM Journal , Volume 55 , Issue 4 , April 2014 , pp. 336 - 356
Copyright
Copyright © 2014 Australian Mathematical Society 

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