324
Chapter 8
Figure 8.3 The age distribution for recombinant cells at
D
= 0.5 h'1
and for different values of the parameter
e
The solution to the balance in Eq. (3), subject to Eqs. (4) and (8.1) is
f( a ) = —— —Dn
e-£ta
(5)
J
1 —(9
Equation (5) gives the steady-state age distribution for plasmid-containing cells, and the distribution is
observed to be a function of the specific growth rate and the segregation parameter ® (see Fig. 8.3). The
doubling time rD
is also a function of the segregation parameter:
t
D
ln(2-0)
(
6
)
Thus, for a given specific growth rate E of the culture it is seen that the cell cycle time decreases when the
segregation parameter increases, i.e.f the cells have to speed up their growth rate in order to compensate for
the loss of a certain category of cells at cell division.
In order to find the distribution of plasmid content in the population of recombinant cells, it is necessary to
specify the distribution of plasmids to the two daughter cells upon cell division and the rate of plasmid
synthesis in the cells. First, the age distribution of cells with
p,,
plasmids at birth has a form similar to Eq.
(5), i.e.,
M<*) = chn e 'Da
(7)
where cb is determined by the applied model for the distribution of plasmids to the daughter cells. Three
models for
cb
were examined by Seo and Bailey:
*
Model
l.
In this model it is assumed that plasmids are distributed to daughter cells randomly at cell
division and that all cells contain
plasmids at cell division.
Model 2. The assumptions underlying this model are similar to those for Model 1, but here it is
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