Modeling of Growth Kinetics
297
hypothesis that is a mirror image of the Duboc-von Stockar hypothesis. Beuse
at al.
propose that some
daughter cells may take more than 2 (rb +
tm)
to develop into a mother cell while all mother cells can give
birth to daughter cells after rb +
tm.
Both hypotheses do however suffer from the weakness that it is difficult to understand why a fixed
proportion of the mother cells (or daughter cells) should choose to take “an extra day off’ and that they
should do so, generation after generation.______________________________________________________
If there is not really a finite number of subpopulations with stringently kept rules for the
generation time then the whole concept of synchrony falls apart. In a real culture of cells there
must be a statistical distribution of e.g generation times for the cells, and if synchrony should
prevail in the real culture there must be some mechanism by which e.g “slow” cells catch up with
faster proliferating cells. In mathematical terms there must exist an
attractor,
and in the case of
bioreactions the nature of the attractor must be biochemical. This is really where the
physiological interest in oscillating cultures is to be found: Through the study of spontaneous
oscillations in continuous cultures one may learn something about non-linear, feed forward cell
processes that influence the cell cycle. Hjortso and Nielsen (1994) proposed that the critical cell
size for budding or for cell division might oscillate. Experimentally it has been shown that the
critical cell size depends on the ethanol concentration. At high ethanol concentration the critical
mass for budding decreases while the critical mass for cell division increases (Martegani
et al.,
1990). Consequently, the attractor may function because of an oscillating ethanol concentration,
and it is known from experiments that this is actually so. At the start of the
S
phase (Fig. 7.17)
there is a burst of catabolic activity: A peak.in C 0 2 production and a corresponding ethanol peak
(more difficult to observe on the background of the ethanol already present in the medium)
signals the beginning of the “gestation phase”. Storage carbohydrates, accumulated by the
mother cells in the
tm
phase, are released to fuel the burst of catabolic activity. The daughter cells
(in the td phase) may take up the excreted ethanol and use it to speed up their passage through the
Gj phase. This was the hypothesis of Strassle
et a l
(1988), of Martegani
et al.
(1990) and of
Munch (1992) in their attempt to explain how the synchronization of the culture could happen.
There are, however many other groups who in the last ten years have contributed to the search for
a biological explanation of spontaneous oscillations in yeast. In general oscillations have never
been observed in anaerobic yeast cultures. Most studies are done in aerobic cultures with glucose
as substrate, but there are also examples of oscillations in aerobic yeast cultures fed with ethanol
(Murray
et al.,
2001). In the group of Kuriyama in Japan a number of biological attractors have
been suggested. It could be C 0 2 that possibly influences transport through the cell membrane
(but not ethanol in the exterior medium, since a pulse of ethanol added to the medium does not
change the oscillatory behavior (Keulers
et a l,
1996)), or oscillations could have a connection
with the sulfur metabolism of yeast ((Sohn and Kuriyama, 2001). It is tempting to suggest that
the possible inhibition of the respiratory system when ethanol is produced (but not by mere
addition of ethanol to the medium) by overflow at the pyruvate branch point could constitute a
feed back regulation that could lead to oscillations. As yet the correct mechanism (and there may
be several contributing mechanisms) has not been found, but in view of the importance o f the
yeast system as host for recombinant protein production the subject certainly merits much more
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