254
Chapter 7
which for a constant
shows that F,* decreases to zero for p“ *0 where an increasing fraction of
the substrate is used to meet the maintenance requirements of the cell. For large specific growth
rates
Ysx
approaches (î^™*)'1
=
.
This corresponds to the situation where the maintenance
substrate consumption becomes negligible compared with the substrate consumption for biomass
growth, and the model reduces to the black box model of Section
7.3.1.
Despite its simple structure the linear rate equation (7.24) of Pirt is found to mimic the
results of many fermentation processes quite well. Table 7.3 compiles true yield coefficients and
maintenance coefficients for various microbial species with glucose and oxygen as substrates.
This table is a complement to Table 5.1 that gives values for the corresponding energetic
parameters F ^ p and mATP.
Example 7.2 Steady-state chemostat described by the Monod model including maintenance
We now reconsider the experimental data from Example 7.1, but include maintenance requirements. The
steady-state balances are
Y ,n“u
xs
“ max
s + K ,
+ ms
x =
D(sf ~s)
(
1
)
s+ K
.
x
=
D x
(1)
Table 7.3 A compilation of "true" yield and maintenance coefficients for different microbial species
growing at aerobic growth conditions. Data are shown for growth on glucose or glycerol.*
Species
Substrate
^ XS
(g (g DWy1)
■ytrue
1 xo
(mmoles
(s.
DWV1!
ms
(g(gDWh)1)
m0
(mmoles
(g DW h)'1)
Aspergillus awamori
Glucose
1.92
68
0.016
0.62
Aspergillus nidulans
1.67
111
0.020
0.54
Aspergillus niger
Aspergillus oryzae
Bacillus clausii
1.82
24
0.043
1,49
Candida utilis
2.00
84
0.031
0.87
Escherichia coli
2.27
70
0.057
0.45
Klebsiella aerogenes
2.27
74
0.063
0.99
Pénicillium chrysogenum
2.17
70
0.021
0.87
Saccharomyces cerevisiae
1.85
47
0.015
0.62
Aerobacter aerogenes
Glycerol
1.79
63
0.089
2.52
Bacillus megatarium
1.67
90
-
0.70
Klebsiella aero eenes
2.13
58
0.074
2.52
* The yield coefficients are all for growth with no formation of metabolites, i.e., carbon dioxide is the only metabolic
product. The coefficients are specified both for the listed limiting substrate and for oxygen. NH3 is the nitrogen source.
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