Sustainability and Stability - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 831

y

0

þ0 < 10 8 ; Dm ¼ 0.1072/h;

m / þ ¼ 6.93 10 4 /h. Again at steady state, For D ¼ 0.67/h,

y

the dilution rate equals the specific growth rate,

m G ¼ D ¼ 0:67= h

The value of other growth parameters can be computed as

m G þ ¼ m G Dmþm =þ ¼ 0:670:1072þ6:9310 4

= h ¼ 0:5035= h

P =þ ¼ m =þ =m G þ ¼ 1:22910 3

Consider Eqn (16.38) for the random formation of plasmid-free cells,

P ¼ 2 1P R

(16.38)
where P R is the number of plasmid replicative units. Since the average plasmid copy number
for pDW17 is about 40 e 50, one can expect that P R 40. For P R ¼ 40,

P ¼ 2 1 40 ¼ 1:8210 12

Therefore, the data are consistent with the expectation. The observed probability is higher
due to the fact that not all the replicative units consist of single plasmid copies (as demon-
strated in Example 16-5).
Our discussion and example so far have been for continuous reactors. For most industrial
applications involving genetically engineered organisms, batch or fed-batch operations are
preferred. While continuous reactors are particularly sensitive to genetic instability, genetic
instability can be a significant limitation for batch systems. As we have seen that time evolu-
tion is required even for continuous systems, fed-batch or batch systems would not add any
complexity to the solution.
For a batch reactor, the mass balances on the cells yield:

d X þ
d t

m G þ X þ P =þ m G þ X þ ¼ (16.53)

d X
d t

m G X þP =þ m G þ X þ ¼ (16.54)

with initial conditions of t ¼ 0, X þ ¼ X þ 0 , and X ¼ 0. Assuming exponential growth
(i.e. substrate sufficient), Eqn (16.53) can be integrated to yield

X þ ¼ X þ0 exp½ð1P

=þ Þm Gþ

t (16.55)

Substituting Eqn (16.55) into Eqn (16.54) and integrating, we obtain

P =þ m G þ X þ0
ð1P

X ¼

=þ Þm G þ m G fexp½ð1P

=þ Þm G þ

texpðm G tÞg (16.56)