Effects of time delay on the dynamic of kinetic model of microbial fermentation process

Kasbawati -, Agus Yodi Gunawan, Rukman Hertadi, Kuntjoro Adji Sidarto


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.



fermentation process, single enzyme-substrate reaction mechanism, enzyme kinetic, time delay, Hopf bifurcation

DOI: http://dx.doi.org/10.21914/anziamj.v55i0.7167

Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.