| Summary: | Thesis (MSc)--University of Stellenbosch, 2004. === ENGLISH ABSTRACT: The complexity of microbial systems has presented serious obstacles to the quantification of
fermentation processes. Using computer modelling techniques progress has been made in
monitoring, controlling and optimising microbial systems using material balancing techniques and
empirical process models. The Monod equation is among the most commonly used models and is
based on empirical findings with no mechanistic basis. Monod presents a simple model to describe
the growth of a cell in a defined nutrient environment. The Monod equation is mathematically
analogous to the formula that was proposed by Michaelis and Menten to describe enzyme kinetics.
Both equations describe a hyperbolic function with a half-saturation constant (K_s in the monod
equation and K_m in the Michaelis Menten equation) but the meaning of the two saturation constants
K_s and K_m is different. In number of studies K_s and K_m are used as if they are equivalent. In
contrast to Michaelis-Menten kinetics, which describes a process catalysed by a single enzyme,
Monod kinetics describes an overall process involving thousands of enzymes.
The Monod equation describes the specific growth rate of a microbial cell as the function of a
limiting substrate concentration. The aim of this study was to test this principle, for Saccharomyces
cerevisiae VIN13 under glucose limited aerobic chemostat conditions. The VIN13 was observed to
follow the Monod description and when compared with other growth kinetic models gave one of the
best fits to the data. A functional relationship between the half-saturation constant, K_s, and
Michaelis Menten constant, K_m, was there after derived. This was achieved by using metabolic
control analysis (MCA) to explain when K_m of the transporter becomes equal to the K_s. Using the
deductions obtained from MCA a core kinetic model was then formulated to demonstrate that the
K_s can either be smaller, equal or higher than the K_m of the transporter, depending on the flux
control distribution in the model. === AFRIKAANSE OPSOMMING: Die kwantifisering van fermentasieprosesse word ernstig belemmer deur die kompleksiteit van
mikrobiale sisteme. Deur gebruik te maak van rekenaar-ondersteunde modelleringstechnieke vir die
opstelling van massa balans vergelykings en empiriese prosesmodelle is vordering gemaak in die
waarneming, beheer en optimalisering van mikrobiale sisteme. Die Monod vergelyking is een van
die mees gebruikte groeimodelle en is gebaseer op empiriese bevindings - die model het nie ‘n
meganistiese grondslag nie. Die Monod vergelyking is wiskundig ekwivalent aan die vergelyking
wat opgestel is deur Michaelis en Menten vir die beskrywing van ensiemkinetika. Beide
vergelykings beskryf ‘n hyperboliese kurwe met ‘n konstante wat die halfversadigingswaarde
aangee vir substraat (Ks in die Monod vergelyking en Km in die Michaelis-Menten vergelyking),
maar die betekenis van die twee versadigingskonstantes is verskillend. In ‘n aantal studies word die
Ks en Km waardes gebruik asof hulle gelyk is aan mekaar. In teenstelling met die Michaelis-
Menten kinetika wat ‘n enkel ensiem-gekataliseerde reaksie beskryf, beskryf die Monod
vergelyking ‘n proses wat duisende ensieme behels.
Die Monod vergelyking beskryf die spesifieke groeitempo van ‘n bakteriële sel as ‘n funksie van
die beperkende substraatkonsentrasie. Die doel van hierdie studie was om hierdie beginsel te toets
vir Saccharomyces cerevisiae VIN13 wat onder glukose beperkte, aerobiese kondisies in ‘n
chemostat gekweek word. Die VIN13 groei kon goed beskryf word met die Monod model, wat in
vergelyking met ander groeimodelle een van die beste passings vir die meetpunte het gegee.
Vervolgens is ‘n funksionele verwantskap afgelei tussen Ks en Km; deur gebruik te maak van
metabole kontrole analise (MCA) kon verduidelik word wanneer die Ks gelyk is aan die Km van die
transporter vir die beperkende substraat. Deur gebruik te maak van die MCA analise is ‘n
eenvoudige kinetiese model opgestel om aan te toon dat die Ks kleiner, gelyk aan of groter kan wees
as die Km van die transporter, afhanklik van die fluksie-kontrole verdeling in die model.
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