328
Chapter 8
r(m) = km
(10)
r(m
) =
k
(11)
With these two models for the single-cell growth rate the steady-state distribution function
(jiw)
can be
calculated, and the results are shown in Fig. 8.5. It is observed that the distribution function is completely
different in the two models, and with measurements of the cell size distribution (e.g,, by flow cytometry), it
should be possible to distinguish between the two models.
With the distribution function in Eq. (9), one can calculate the number fraction of daughter and mother
cells, respectively, (here termed Z* in order to avoid confusion with the mass fraction Z used in Section 7.6):
z ; = J
0(a)da =
(12)
0
0,+fll
Z ;=
J
0(a)da = e ^ - l
(13)
The length
tb
of the budding phase is often considered to be independent of the specific growth rate
(tb
* 1.8
h), even though it decreases slightly with
p
(see Fig. 8.6). If the same holds for the time for maturation, i.e.,
rm
approximately constant, then it is concluded that
a2
is independent of the specific growth rate. Thus from
Eq. (13) the fraction of mother cells in the culture increases with the specific growth rate. This corresponds
well with experimental data given by Lievense and Lim (1982), who found that the budding index, i.e., the
fraction of budded cells, increases with
D
in a steady-state chemostat (Fig. 8.6).
Dimensionless cell mass
Figure 8.5 Cell mass distribution function with, respectively, first- and zeroth-order growth kinetics of the
individual cells. The model parameters are:
D =
0.2 h'1;
k
(zeroth) = 0.13 and
k
(first) = 0.2. The cell mass
has been rendered dimensionless by
wt,
which is set to 1.
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