Modeling of Growth Kinetics
261
From analysis of the production kinetics in chemostat cultures they found that the specific proteinase A
production could be describe as:
V o r =
+ P
i l fer
(1)
where
vm
and vf„ are given by eq. (5) and (6) in Example 7.3, respectively. When this production kinetics
was applied it was found that the model could be fitted quite well to experimental data. Using the model
they predicted the volumetric productivity of proteinase A as a function of the specific growth rate, and
found the results shown in Fig. 7.9. It is interesting to see that the volumetric productivity, which is the
quantity of interest in connection with heterolous protein production, has a very distinct maximum at the
critical dilution rate. Thus, in order to ensure optimal productivity it is necessary to operate at (or very
close) to the critical dilution rate. Even small changes in the dilution rate results in a significant decrease in
the volumetric productivity. The reason for the very distinct optimum is that the protein production is
related to biomass production, which also decreases drastically around the critical dilution rate.___________
7.3.3 The Influence of Temperature and pH
The reaction temperature and the pH of the growth medium are other process variables with a
bearing on growth kinetics. It is normally desired to keep both of these variables constant (and at
their optimal values) throughout the fermentation process - hence they are often called
culture
parameters
to distinguish them from other variables such as reactant concentrations, stirring rate,
oxygen supply rate, etc., which can change dramatically from the start to the end of a fermentation.
The influence of temperature
T
and pH on individual cell processes can be very different, and since
the growth process is the result of many enzymatic processes the influence of both temperature and
pH on the overall bioreaction is quite complex.
Figure 7.9 The volumetric production of protease A by a recombinant strain of
S. cerevisiae
at different
dilution rates.
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