Chapter 9
The major objection that can be raised against the models treated hitherto is that the real culture
does not respond instantaneously to a change in substrate concentration as has been tacitly
assumed. The compartment models of Section 7.4.1, e.g. the lactic acid kinetics of example 7.6
do include a factor
which responds with a much larger time constant than s when the dilution
rate or the feed concentration is changed. Just as was done for the batch reactor model in Section
9.1.1 {Eqs 9.15 to 9.19) the dynamics of the stirred tank can be studied if the correct rate
expressions are used in Eq (9.85 a,b,c). A series of model studies have recently been made in
which the concepts of the simple structured model of example 7.6 have been further developed.
The main improvement is that the cellular processes are grouped into catabolic and anabolic
processes which are taken to be uncoupled in a transient experiment. Hence two time constants,
one for the catabolic processes
and one for the anabolic processes
(t^ m)
are introduced.
Both time constants are much larger than the time constant for mixing new feed into the medium.
In the model of Duboc et al.(1998) it was hypothesized that a culture that has operated in steady
state at a low
value has a “hidden catabolic capability” which springs into action as soon as
more substrate becomes available due to an up-shift o f
or when a substrate pulse is added.
Experiments confirm the existence of this rapid- access catabolic capacity, since the rate of C 02
production immediately increases when
is up-shifted from a low value. The jump in rcaub is
furthermore independent of
in an anaerobic yeast fermentation, but depends only on
If an
anthropomorphic explanation is permitted one could say that the first duty of the metabolism of
an organism that suddenly finds itself in a more pleasant environment is to start ATP production
(the jump in rcatab), next to use the ATP to build up more catabolic machinery, and finally to use
the reconstituted catabolic machinery to increase cellular growth. The experimental evidence
supports that this happens, r^ b may be around I hour while ranaboi is more than 2 hours.
In a recent study by Melchiorsen et al. (2001) the same concept is used. Here the dynamics of the
pyruvate metabolism is investigated in shift-up or shift-down experiments. A culture of
Lactococcus lactis
that has grown at steady state with a small
value immediately stops
producing mixed acids when
is changed to a higher value. Obviously the PFL enzyme is
inhibited by the higher glucose flux through the EMP pathway. But also, and with a time
constant of about 1 hour, the catabolic machinery increases (as witnessed by an increasing lactic
acid production). More slowly the specific growth rate catches up. The same phenomenon is
observed when the
value is decreased.
There is no doubt that the subject of bioreactor dynamics will continue to supply many
interesting research topics. The experimental techniques are now so strong that one is able to
discriminate between models and thereby introduce a new level of investigation of microbial
physiology. At the same time phenomena that at the present seem mysterious, such as the
oscillations of a continuous aerobic yeast culture (Section 7.6.1) may find an acceptable
explanation. New model studies, particularly of dynamic models, will reveal if assumptions that
we make concerning the cell physiology (such as “the respiratory capacity of the yeast cell
decreases when it starts to make ethanol by the overflow mechanism”) can be supported by
model simulation studies and finally confirmed by experiments.
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