260
Chapter 7
RQ =
'cch
%
P x\V rm
+AlV
ûflsv.
(
11
)
If there is no fermentative metabolism RQ becomes equal to 0M
/a i2, which is close to 1, whereas if there
is fermentative metabolism RQ increases above 1. Since it is relatively easy to measure the carbon
dioxide production rate and the oxygen uptake rate by head space gas analysis, the RQ can be evaluated
almost continuously, and a value above 1 will indicate some fermentative metabolism. This can be used
in the control of e.g. the feed of glucose to the reactor, i.e., if the feed is too fast the glucose uptake rate
will be above the critical value and there will be fermentative metabolism. The feed has to be reduced in
order to avoid this.
With the specific rates given for all the major substrates, metabolic products, and biomass, it is possible
to simulate the concentration of the variables in a bioreactor (see Fig. 7.8) with the model parameters
listed in Table 7.4. The model predicts that when the glucose uptake rate increases above the critical
value rojm»x/a']j2
(corresponding to a certain value of the specific growth rate), ethanol is formed by the
cells. In a steady state chemostat this is seen as the presence of ethanol in the medium at specific growth
rates above this critical value. When the critical value is exceeded and ethanol is produced the biomass
yield drops dramatically, and this results in a rapid decrease in the biomass concentrations.
The Sonnleitner and Kappeli (1986) model is an excellent example of how mechanistic concepts can be
incorporated into an unstructured model to give a fairly simple and in many situations adequate description
of the complex growth of
S, cerevisiae.
With its limited structure the model does, however, give a poor
description of transient operating conditions, e.g., the lag phase between growth on glucose and the
subsequent growth on ethanol in a batch fermentation can not be predicted. It would not be difficult to
include intracellular structure to describe, e.g., the level of the oxidative machinery, but this was not the
target of Sonnleitner and Kappeli. Any basically sound model can be made to fit new experiments when
more structure is added._____________________________________________________________________
Example 7.4 Extension of the Sonnleitner and Kappeli model to describe protein production
As mentioned in Chapter 2
S. cerevisiae
is used to produce heterologous proteins, and in particular it is used
to produce human insulin. Strong glycolytic promoters often drive the production of heterologous proteins,
and the productivity of the protein is therefore closely associated with the biomass production. Carlsen
et al.
(1997) studied the kinetics of proteinase A production by
S. cerevisiae,
and used a recombinant system very
similar to that used for industrial insulin production (proteinase A was taken as a model protein for insulin).
Table 7.4 Model parameters in the Sonnleitner and Kappeli model.
Stoichiometric coefficients___________________
Kinetic param eters
ot
12
12.4 mmoles/g of glucose
K
3.50 g glucose (g DW h)'
P.,
13.4 mmoles/g of glucose
*0
8.00 mmoles (g DW h)'1
v,
0.49 g/g of glucose
0.1 g U1
K
0*
Yi
10.5 mmoles/g of glucose
0.48 g/g of glucose
0.05
e/e.
of elucose
K>
0.1 mgL'1
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