Modeling of Growth Kinetics
307
Time
(hi
X
(2 I/')
0
5.1
0.5
4.5
1.0
3.7
2.0
2.8
3.0
2,1
4.0
1.4
Determine Pmax from this experiment. Discuss the applied method [see also Esener
et al.
(1981c)].
Problem 7,2 Inhibitory effect of lactic acid
Bibal
et al.
(1988, 1989) studied the inhibition of lactic acid on
Streptococcus cremoris,
and in this exercise
we will analyze their data.
a.
The influence of lactic acid on the growth of
S. cremoris
was examined by measuring the maximum
specific growth rate during batch growth of the bacterium in media containing various
concentrations of lactic acid (
p
). The results are summarized below:
o
( e L 1)
,i
(hA)
0
0.90
12.0
0.68
39.0
.
0.52
55.0
0.13
According to Section 2.1.2.1 (see also Example 2.1), it is mainly the undissociated form of lactic
acid that can pass the cellular membrane, and we will therefore assume that it is only the
undissociated acid that has a toxic effect on the cells. Plot the relative specific growth rate, i.e.,
Pmax(py<Pma*(/7=0), versus the concentration of the undissociated acid concentration (in mM). pH =
6.3 was used and pK,, for lactic acid is 3.88. Assume that the inhibition model given by Eq. (7.22)
holds. Find the inhibition constant
K,.
Plot the model together with the experiments.
b.
From the results in a. you conclude that Eq. (7.22) is not well suited for description of the
experimental data, since the inhibition by lactic acid seems to be stronger, especially at high values
of undissociated lactic acid concentrations (pu), i.e., there seems to be a certain maximum
concentration of undissociated acid above which growth stops.
Specify another simple
one-parameter model for the influence of
p v
on P, and estimate the model parameter. What
concentration of lactic acid
ip)
does this maximum value correspond to?
c.
Plot the maximum specific growth rate as a function of the pH in a medium containing 1 g L'1
and
10 g L 1
of lactic acid (total concentration), using the model found in (b).
d.
Measuring the yield coefficient on lactose in a steady-state chemostat at different concentrations of
lactic acid, Bibal
etal.
(1988; 1989) found the data below