Biomedical Engineering Reference
In-Depth Information
Example 16-6.
Genetic instability of a continuous culture
The data in
Table E16-6.1
were obtained for E. coli B/r-pDW17 at two different dilution
rates in glucose-limited chemostats. The average plasmid copy number for pDW17 is about
40
e
50 copies per cell. About 12% of the total protein synthesized is due to the plasmid. The
proteins are retained intracellularly in soluble form. Use these data to estimate
Dm
,
m
/
þ
,
m
G
þ
,
m
G
, and P
/
þ
.
Solution.
Note that data on plasmid stability are usually given in terms of the number of
generations, which is a nondimensionless time based on (ln2)/D
¼
1 generation. To estimate
the growth parameters, the easiest way to do is use a spreadsheet program such as Excel to fit
the experimental data with the model,
Eqn (16.52)
. As one can observe from
Eqn (16.52)
, there
are two parameters can be obtained from the plasmid-free cell fractions versus time data:
Dm
and
m
/
þ
. Other parameters would need to be obtained from other data. For example, the
growth rate for the plasmid-free cells can be determined by the dilution rate in this case.
TABLE E16-6.1
Experimental Values for Plasmid Stability of Escherichia coli B/r-pDW17 in a Glucose-Limited
Chemostat
D
[
0.30/h
D
[
0.67/h
Time, h
No. of generations
y
L
Time, h
No. of generations
y
L
0
0
0.002
0
0
0.002
11.6
5
0.010
10.3
10
0.010
23.1
10
0.030
20.7
20
0.035
46.2
20
0.13
31.0
30
0.15
57.8
25
0.22
41.4
40
0.34
69.3
30
0.39
51.7
50
0.65
80.9
35
0.76
62.1
60
0.81
92.4
40
0.88
72.4
70
0.93
104.0
45
0.97
82.8
80
0.98
116.5
50
1.00
93.1
90
1.0
138.6
60
1.00
103.5
100
1.0
Data source: Shuler & Kargi 2006.
Table E16-6.2
shows the least-square fit of the experimental data with
Eqn (16.52)
. The vari-
ance between the computed values of y
and those of experimental data are shown in the
last row. One can observe that the fit for the higher dilution rate is better than that for the
lower dilution rate. The results are plotted in
Fig. E16-6
. One can observe that the sigmoidal
curves captured the data quite well. For D
¼
0.3/h,
y
0
y
þ0
¼ 9:5810
4
;
Dm ¼
0.09733/h;
10
8
/h. Since at steady state, the dilution rate equals the specific growth rate, that is
m
/
þ
<
m
G
¼ D ¼ 0:3=
h
Search WWH ::
Custom Search