Inhibitory effect of lactic acid. Bibal et al.(1988,1989) studied the inhibition of lactic acid on..

Inhibitory effect of lactic acid. Bibal et al.(1988,1989)
studied the inhibition of lactic acid on Streptococcus cremoris, and in this
exercise we willanalyze 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:

As discussed in Example 7.11, it is mainly the un-dissociated
form of lactic acid that passes through the cellular membrane, and we will therefore
assume that it is

Inhibitory effect of lactic acid. Bibal et al.(1988,1989)
studied the inhibition of lactic acid on Streptococcus cremoris, and in this
exercise we willanalyze 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:

As discussed in Example 7.11, it is mainly the un-dissociated
form of lactic acid that passes through the cellular membrane, and we will therefore
assume that it is only the un-dissociated acid that has a toxic effect on the
cells. Plot the relative specific growth rate, i.e.,m max(p)/m max(p = 0),
versus the concentration of the un-dissociated acid concentration (in mM). pH =
6.3 was used and pK a for lactic acid is 3.88. Assume that the inhibition model
given by (7.19) holds. Find the inhibition constant i. Plot the model together
with the experiments.

(b) From the results in (a) you conclude that (7.19) 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 un-dissociated
lactic acid concentrations (pu). There seems to be a certain maximum
concentration of un-dissociated acid above which growth stops. Next try the
model (7.20) to find the influence of puonm, and estimate the model parameter.
At what concentration of lactic acid will growth stop?

(c) Plot the maximum specific growth rate as a function
of the pH in a medium containing 1 and 10 g L1of 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 et al.
(1988,1989) found the data below:

How can you explain the decrease in the yield coefficient
with increasing lactic acid concentration?

(e) Assume that the maintenance coefficient 0.05 h1.
Calculate the true yield coefficient in (7.27) for p = 0. Using the model
derived in

(b), calculate the maintenance coefficient as a function
of pu. Explain the results.