Population Balance Equations
Figure 8.6 Measurements of the length of the budding period
(■ ) and the traction of budded cells
(-*■) as functions of the dilution rate in a steady-state chemostat. Assuming that
a2 ~ tb,
the fraction of
budded cells is calculated using Eq. (13) (shown as line). Also shown is
= In 2
The data are taken from
Lievense and Lim (1982).
From Fig. 8.6, it is observed that the doubling time approaches the length of the budding period for high
specific growth rates. Consequently,
decreases for increasing
jj -
showing that the size of the daughter
cells resulting from the cell division increases with
and for high specific growth rates the cell division
becomes almost symmetric (two cells of almost equal size are formed).
Due to the formation of a bud scar on the cell envelope of the mother cell upon cell division it is expected
that mother cells would have a maximum age. Hjortso and Bailey (1982) introduced the concept of the
genealogical age of mother cells and calculated the distribution of cells with varying numbers of bud scars.
Thereby the effect of various hypotheses concerning the growth ability of mother cells with many bud scars
could be examined. Hjortso and Bailey (1983) also carried out experiments involving transient situations by
using the dynamic balance Eq. (14), which is derived from Eq. (8.2) with
0 for all
a ^a\ +a2
r(a) =
È+W + d № =
_D m
The dynamic balance was solved by the method of characteristics and again the influence of changing the
single-cell kinetics from zeroth to first order was examined.
Hjortso and Bailey (1984a) extended their segregated population model to predict plasmid stability at
steady-state growth. They assumed that the culture is under selection pressure, whereby only
plasmid-containing cells can survive in the environment. The population balance of Eq. (3) still holds, but
the cell balances relating to cell division in Eqs. (4) and (5) are modified to those of Eqs. (15) and (16) in
order to account for plasmid loss. 6k and
(the segregation parameters) are the probabilities of formation
of, respectively, a plasmid-free mother and a plasmid-free daughter cell at cell division.
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