Modeling of Growth Kinetics
273
wash out when the shift is from a low dilution rate. When the dilution rate is changed to
0.99 h'1
the
glucose concentration increases rapidly to a value much higher than
Ky[
and
K,_2,
and this allows growth
at the maximum rate. However, when the cells have been grown at a low dilution rate the size of the
active compartment is not sufficiently large to allow rapid growth, and
XA
therefore has to be built up
before the maximum specific growth rate is attained. On the other hand if the cells have been grown at a
high dilution rate
XA
is already near its maximum value and the cells immediately attain their maximum
specific growth rate. It is observed that the model is able to correctly describe the two experiments (all
parameters were estimated from steady state experiments), and the model correctly incorporates
information about the previous history of the cells.
The model also included formation of lactic acid and the kinetics was described with a rate equation
similar to Eq. (3). Thus, the lactic acid formation increases when the activity of the cells increases, and
hereby it is ensured that there is a close coupling between formation of this primary metabolite and
growth of the cells.
It is interesting to note that even though the model does not include a specific maintenance reaction, it
can actually describe a decrease in the yield coefficient of biomass on glucose at low specific growth
rates. The yield coefficient is given by:
/
\k-> s + K
,
^ = r 21
M
w
J - r — ;^
(
7
)
Since
KlA
is larger than
Ky2
the last term in the parenthesis decreases for increasing specific growth rate,
1
C
o
c
3
§
2
I
0,1 I—
-50
0
50
100
150
200
Tims (min)
Figure 7.14 Measurement of the biomass concentration in two transient experiments in a glucose limited
chemostat cultures with
L. cremoris.
The dilution rate was shifted from an initial value of 0.10 h'1
(* ) or
0.50 h'1
(■ ) to 0.99 h'1, respectively. The biomass concentration is normalized by the steady state
biomass concentration before the step change, which was made at time zero. The lines are model
simulations. The data are taken from Nielsen
et ai
(1991b),
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