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Topic: Continuous culture – x(t), s(t) graphs versus x(D),
s(D) diagrams
After working on this topic you will be able to...
-
prepare x(D) und s(D) diagrams for chemostat cultures starting from
experimental data.
-
predict the influence of sin and of the growth parameters on x(D) and
s(D) curves.
-
analyse and interpret the time course of the substrate and biomass
concentrations in a chemostat culture and to name the underlying
mechanisms.
-
recognise steady-state conditions in a continuous culture.
Kayser et al. (2005) cultivated E. coli K12 strain TG1 in aerobic, carbonlimited continuous cultures at 28ºC. They used a defined mineral medium
containing 10 g/l glucose as sole source of carbon and energy. Depending on
the specific growth rate the biomass and residual substrate concentrations
were
measured.
The
results
are
summarised
in
table
Table_x,s(D)_Kayseretal_2005. Based on these results you ought to
determine the growth parameters for E. coli TG1 at 28ºC by using the Monod
model. In addition, you are asked to simulate the possible time course of the
biomass and residual substrate concentrations in a chemostat culture of strain
TG1 when changing D several times.
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Table_x,s(D)_Kayseretal_2005. Concentrations of biomass and glucose
during steady-state growth of E. coli K12 strain TG1 at various dilutions rates
in glucose-limited continuous culture.
D (h-1)
x (g/l)
glucose (g/l)
0.044
5.07
0.000
0.066
5.05
0.000
0.134
5.29
0.000
0.150
5.24
0.000
0.17
5.23
0.000
0.203
5.41
0.000
0.265
5.28
0.000
0.28
5.53
0.000
0.3
5.53
0.000
0.347
5.61
0.229
0.375
5.69
0.295
0.388
5.88
0.259
0.397
5.27
0.398
0.410
3.82
1.822
0.415
1.05
6.048
The following exercises have to be worked on:
A. With the help of which model can you describe the experimental data
of Kayser et al. (2005)?
B. What was the possible time course x(t), s(t) during a chemostat
experiment, based on which the x(D) and s(D) diagrams were
constructed?
C. How do sin and the growth parameters affect x(t), s(t) and x(D), s(D)?
D. How do the biomass productivity, catalase productivity and the
specific glucose consumption rate behave as function of D?
E. How can the wash-out of a chemostat culture be described?
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HOW TO PROCEED
A. With the help of which model can you describe the experimental data
of Kayser et al. (2005)?
1. Find out what the exercise is about.
2. Open the x,s(D)-simulation (Excel).
3. Introduce under “experimental data“ the values determined by Kayser
et al. (2005).
4. Introduce under “parameter 1 and 2” the substrate concentration in the
medium feed sin used in the chemostat experiments of Kayser et al.
(2005).
5. Model the experimental x,s(D) data by successively changing the
growth parameters.
6. Based on the results of your fit formulate a mathematical model to
describe the experimental results of Kayser et al. (2005).
7. Answer the question.
B What was the possible time course x(t), s(t) during a chemostat
experiment, based on which the x(D) and s(D) diagrams were
constructed?
1. Find out what the exercise is about.
2. Open the simulation applet and chose the cultivation system
“continuous culture”. Open the scenario “ESBS_continuous_culture“.
3. Change the scenario by applying the growth parameters as determined
under A and by applying sin as used by Kayser et al. (2005).
4. Simulate the temporal development x(t), s(t) for a chemostat
experiment with an initial batch phase und subsequent successive
increase of D. Use the following dilution rates: 0.15 h-1, 0.3 h-1, 0.388
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h-1, 0.41 h-1, 0.415 h-1. Each phase should be long enough so that
steady-state
can
be
reached.
In
the
scenario
“ESBS_continuous_culture” change the tables for Fin und Fout
accordingly.
5. Determine the phases of steady-state growth. Compare the steadystate biomass and glucose concentrations with the experimental
results of Kayser et al. 2005.
6. Answer the question.
C. How do sin and the growth parameters affect x(t), s(t) and x(D), s(D)?
1. Find out what the exercise is about.
2. In similar chemostat experiments with E. coli ML 30 at 28.4ºC
Kovarova et al. (1996) determined the following growth parameters:
μmax = 0.54 h-1, Ks = 33.3 μg/l and Yx/s = 0.45 g/g.
3. Change the growth parameters individually in the under B
constructed scenario (see exercise B, steps 3 and 4) using the
values as reported by Kovarova et al. (1996).
4. Describe the newly simulated x(t), s(t) curves in comparison with the
curve determined under B.
5. Simulate for E. coli ML 30 the temporal development of s(t) and x(t)
by using simultaneously the growth parameters reported by
Kovarova et al. (1996).
6. Determine the phases of steady-state growth and the biomass and
glucose concentrations in these phases.
7. Open the x,s(D)-simulation (Excel).
8. Introduce under „experimental data“ the dilution rates D and the
corresponding biomass and glucose concentrations as determined
for E. coli ML 30 in step 6.
9. Simulate x(D) and s(D) for E. coli ML30 and E. coli TG1 by using the
growth parameters given in step 2 or determined in exercise A,
respectively. (sin = 10 g/l).
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10. Compare x,s(D) for E. coli ML 30 with x,s(D) for E. coli TG1
11. Introduce under both parameter 1 and 2 the growth parameters as
determined for E. coli TG1. Under parameter 1, individually change
the growth parameters to the ones determined by Kovarova et al.
(1996) for E. coli ML 30: 1. μmax, 2. Yx/s and 3. Ks. Depict for each
growth parameter changed the effects on the x,s(D) diagrams.
12. Determine the influence of sin on x,s(D) by decreasing sin to 1 g/l.
13. Answer the question.
D. How do the biomass productivity, catalase productivity and the
specific glucose consumption rate behave as a function of D?
1.
Find out what the exercise is about.
2.
Calculate the specific biomass formation rate rx for each dilution rate.
3.
Represent rx as a function of D in an Excel graph.
4.
Determine Dopt when rx is maximal, i.e. the highest biomass
concentration is formed in the shortest time.
5.
Ihssen and Egli (2004) determined catalase (HPII) activity in
chemostat cultures of E. coli growing at different dilutions rates
(Table_HPII_activity_Ihssen&Egli_2004). Based on this data deduce
the specific HPII activity for the dilution rates used by Kayser et al.
(2005).
6.
Calculate the enzyme productivity rp for catalase.
7.
Represent rp as a function of D in an Excel graph.
8.
Determine Dopt when rp is maximal.
9.
Calculate the specific glucose consumption rate qs for each dilution
rate.
10. Represent qs as a function of D in an Excel graph. Describe the
graph
11. Answer the question.
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Table_HPII_activity_Ihssen&Egli_2004. Specific HPII activity in cultures of
E. coli K12 strain MG1655 grown in chemostats (T = 37ºC) at different dilution
rates with a glucose mineral medium.
Dilution rate
Specific HPII activity
(h-1)
(μmol H2O2 min-1 mgtotal protein-1)
0.03
82
0.1
54
0.3
27
0.5
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E. How can the wash-out of a chemostat culture be described?
1. Find out what the exercise is about.
2. Open the simulation applet and chose the cultivation system
“continuous culture”. Open the scenario “ESBS_continuous_culture“.
3. Change the scenario by applying the growth parameters as determined
under A and by applying sin as used by Kayser et al. (2005).
4. Simulate the temporal development x(t), s(t) for a chemostat
experiment with an initial batch phase und subsequent successive
increase of D. Use the following dilution rates: 0.3 h-1 und 0.41 h-1.
Each phase should be long enough so that steady-state can be
reached. In the scenario “ESBS_continuous_culture“ change the tables
for Fin und Fout accordingly.
5. Change the highest dilution rate in the chemostat experiment in a way
that the culture washes out and no stable steady-state is reached.
6. Describe the wash-out of biomass and the wash-in of glucose with
mathematical formulas.
7. With the formulas proposed calculate a wash-in and wash-out curve in
Excel.
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8. Export the simulated curves into Excel and compare with the curves
calculated under 6.
9. Answer the question.
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