Modeling of Growth Kinetics
295
B
l
J
J
0
2
4
6
8
12
14
16
Time (h)
Figure 7.18 Spontaneous oscillation of
S. cerevisiae.
A. Measurements of carbon dioxide in the exhaust gas and the dissolved oxygen concentration (DOT) in %
of the equilibrium value.
B. Measurements of the concentrations of ethanol ( ■ ) and acetate (^ ).
The data are taken from Frandsen (1993).
The cellular metabolism of the daughter cells (or
unbudded cells
) and the mother cells (or
budded
cells
) is very different, and to give a correct description of the overall growth kinetics of yeast
cultures it is therefore necessary to apply a morphologically structured model. In many cases one
may, however, describe the average metabolism of the culture with an intracellularly structured
model, i.e., assume that the population is homogeneous and still get a satisfactory description of
many experimental data (see Example 7.3). These models can, however, not describe a fascinating
phenomenon observed in a glucose-limited chemostat with
S. cerevisiae
: Spontaneous oscillations
of many easily measured process variables such as the dissolved oxygen, ethanol and glucose
concentrations; oxygen uptake rate; and carbon dioxide evolution rate, as well as intracellular
variables (e.g., NADH and DNA). Figure 7.18 shows some typical results. The literature contains
numerous experimental investigations of the oscillations [see in particular Strassle
et a l
(1989) and
Munch (1992)]. These oscillations can be maintained for many generations, especially when one
uses high-performance bioreactors,
in which the environment is practically homogeneous
throughout the reactor (Strassle
et al.
1988; Duboc
et al
., 1996; Duboc and von Stockar, 2000;
Beuse
et a l,
1999).
Spontaneous oscillations can only be maintained if the growth of the culture is
synchronous
,
since after completion of one cycle the fraction of each morphological form in the cell mass must
be the same as it was at
t
-
Tosc,
where
Tmc
is the length of the oscillation period. With the
asymmetric cell division of
S. cerevisiae
it is not immediately clear how the synchrony can be
maintained for many generations. If, however the population can be divided into a discrete
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