Modeling of Growth Kinetics
263
Є
Є
+
H
є
2
+ 2 //
(7.29)
Figure
7.10
The
influence
of
temperature
on
the
maximum
specific growth rate of
E. coli
В/г.
The circles represent growth on a
glucose-rich
medium,
and
the
squares
represent growth
on a
glucose-minimal
medium.
The
lines
are
calculated
using
the
model
in
Eq.
(7.28)
with
the
parameters listed in Table 7.5. The
data are taken from Herendeen
et
al
(1979).
The model presented above for the temperature influence on the maximum specific growth rate has
a reasonable physical interpretation, and it may with some confidence also be used to express the
temperature dependence of rate constants in structured models for cellular kinetics. One important
aspect not considered is the influence of temperature on maintenance processes, which are normally
very temperature dependent. An expression similar to Eq. (7.28) can be used, but the activation
energy of the maintenance processes is likely to be different from that of the growth process. Thus
the relative rate of the two processes may vary with the temperature.
The influence of pH on cellular activity is determined by the sensitivity of the individual enzymes
to changes in the pH. Enzymes are normally active only within a certain pH interval, and the total
enzyme activity of the cell is therefore a complex function of the environmental pH. As an example
we shall consider the influence of pH on a single enzyme, which is taken to represent the cell
activity. The enzyme is assumed to exist in three forms:
Table 7.5 Model parameters in Eq. (7.28) for
K. pneumoniae
and
E. coli.1*
Parameter
K. pneumoniae
E. coli
(rich)
E. coli
(min)
86.40
58
58
kJ mole''
AGd
287.78
550
-
kJ mole'1
A
5.69
1014
1.0
10IU
6.3
109
h'1
В
1.38
1048
3.0
10*
-
-
Tor £
coli
the parameters are specified both for growth on a glucose-rich medium and a glucose-minimal medium.
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