326
Chapter 8
With this model Seo and Bailey calculated the plasmid content distribution for the population of
recombinant cells using Models 1 and 3. The results are shown in Fig. 8.4. For Model 1, there is a distinct
maximum plasmid copy number of
N=
20, whereas for Model 3 there is broad distribution of plasmid copy
number in the population.
Using the plasmid copy number distribution found from the above model, Seo and Bailey calculated the
productivity of the recombinant culture, i.e., the rate of formation of the recombinant product. For the
individual cells the product formation kinetics was taken to be
re( p ) = keP
Ï--
max
J
(
12
)
which is an analogue of Eq. (7.64). The total productivity for the culture is
<i*
= J
f( p ) r e(p )d p
(13)
o
and with the plasmid copy number distribution in Fig. 8.4,
qe
was found to have a maximum when it is
specified as a function of the average plasmid copy number (calculated as the first moment of the
distribution function). Thus, for production of a recombinant protein there is an optimal average plasmid
copy number for the population.
Finally, Seo and Bailey examined the instability of the recombinant population by using the dynamic age
distribution for two subpopulations: (1) plasmid-containing cells and (2) plasmid-free cells. Depending on
the parameters
N
and
K
in Models 1 and 3, the stability of the recombinant culture was examined.
Obviously the stability increases for increasing values of both parameters.
The Seo and Bailey model represents a detailed analysis of recombinant cultures, and it has served as a
useful guide for setting up simple models where homogeneity in the cell population is assumed._________
Example 8.3 Age distribution model for
S. cerevisiae
The asymmetric cell division of budding yeast (see Fig. 7.16) has been modeled by Hjortso and Bailey
(1982). Their model is based on an age distribution. Cells having an age smaller than
at ~ td
are defined as
daughter cells, and cells with an age larger than
a,
are called mother cells. Since cell division occurs only at
a=a\+a2
(where
a2=
a balance similar to that of Eq. (3) of Example 8.2 holds for the steady-state age
distribution:
df(a)
da
= -D f(a )
In their model Hjortso and Bailey used a normalized distribution function
* (« ) «
m
(i)
n
(2)
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