Applying Mechanistic Models in Bioprocess Development - Measurement, Monitoring, Modelling, and Control of Bioprocesses - page 141

Fig. 1 Schematic workflow for the model analysis

2.1 Model Formulation

Under aerobic conditions, budding yeast may exclusively oxidize glucose (respi-
ratory metabolism), or simultaneously oxidize and reduce glucose (fermentative
metabolism) if the respiratory capacity of the cells is exceeded. The described
overflow metabolism is commonly referred to as the Crabtree effect. Cells pref-
erably oxidize glucose, as the energetic yield is more favorable for respiration than
fermentation. In case the respiratory capacity is reached, the excess of glucose
(i.e., overflow of glucose) is reduced using fermentative pathways that result in the
production of ethanol. Moreover, in a second growth phase, yeast will then con-
sume the produced ethanol, but only after depletion of glucose, as the latter
inhibits the consumption of any other carbon source. Also acetate and glycerol are
formed and consumed, although the corresponding concentrations are typically
much lower than for ethanol.
The Sonnleitner and Käppeli [ 1 ] model describes the glucose-limited growth of
Saccharomyces cerevisiae. This model is able to account for the overflow
metabolism, and to predict the concentrations of biomass, glucose, ethanol, and
oxygen throughout an aerobic cultivation in a stirred tank reactor. Acetate and
glycerol are not included for simplification purposes. The model relies on three
stoichiometric reactions describing the growth of biomass on glucose by respira-
tion (Eq. 1 ) and by fermentation (Eq. 2 ), as well as the growth of biomass on
ethanol by respiration (Eq. 3 ). The stoichiometry of the three different pathways
can be summarized in a matrix form (Table 1 ) describing how the consumption of
glucose, ethanol, and oxygen are correlated with the production of biomass and
ethanol, i.e., the yields of the reactions. The mol-based stoichiometric coefficients
can be converted into the corresponding mass-based yields, e.g., Y X Oxid

= b 9

MW(biomass)/MW(glucose).

C 6 H 12 O 6 þ aO 2 þ b 0 : 15 NH 3 ½ ! bC 1 H 1 : 79 O 0 : 57 N 0 : 15 þ cCO 2 þ dH 2 O ð 1 Þ

C 6 H 12 O 6 þ g 0 : 15 NH 3 ½ ! gC 1 H 1 : 79 O 0 : 57 N 0 : 15 þ hCO 2 þ iH 2 O þ jC 2 H 6 O

ð 2 Þ