Biomedical Engineering Reference
In-Depth Information
process. You should point out any potential problems with the solution you have
proposed, as well as defend why your approach should be advantageous.
16.14.
Develop a model to describe the stability of a continuous culture for a plasmid-
containing culture. For some cultures, plasmids make a protein product (e.g. colicin in
E. coli) that kills plasmid-free cells but does not act on plasmid-containing cells.
Assume that the rate of killing by colicin is k
c
CX
, where k
c
is the rate constant for the
killing and C is the colicin concentration. Assume that the colicin production is first
order with respect to X
þ
.
16.15.
Consider the data in
Table P16.15
for E. coli BIr-pDWI7 grown in a minimal medium
supplemented with amino acids. Estimate
Dm
m
/
þ
. Compare the stability of this
system to one with a glucose-minimal medium (Example 16-6).
and
TABLE P16.15
0.3 h
L1
0.67 h
L1
D
[
D
[
Time, h
Generation
y
L
Time, h
Generation
y
L
0
0
0.003
0
0
0.003
4.6
2
0.010
5.2
5
0.010
11.5
5
0.04
10.3
10
0.015
16.0
7
0.08
16.5
15
0.05
23.1
10
0.30
20.6
20
0.13
27.7
12
0.43
31.0
30
0.34
34.7
15
0.55
41.4
40
0.68
46.2
20
0.96
51.7
50
0.95
16.16.
It has been claimed that gel immobilization stabilizes a plasmid-containing
population. A factor suggested to be responsible for the stabilization is
compartmentalization of the population into very small pockets. For example, the
pocket may start with an individual cell and grow to a level of 200 cells per cavity.
Develop a mathematical formula to compare the number of plasmid-free cells in a gel
to that in a large, well-mixed tank.
16.17.
You must design an operating strategy to allow an E. coli fermentation to achieve
a high cell density (
50 g/L) in a continuous culturing system. You have access to an
off-gas analyzer that will measure the pCO
2
in the exit gas. The glucose concentration
must be less than 100 mg/L to avoid the formation of acetate and other inhibitory
products. Develop an approach to control the glucose feed rate so as to maintain the
glucose level at 100
20 mg/L. What equations would you use and what assumptions
would you make?
16.18.
Develop a simple model for a population in which plasmids are present at division
with copy numbers 2, 4, 8, 16, 32, or 64. You can assume that dividing cells either
segregate plasmids perfectly or generate a plasmid-free cell.
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