Modeling of Growth Kinetics
275
of other carbon sources like galactose, lactose, maltose, sucrose, ethanol, acetate and carbohydrate
polymers. The reason is that glucose is the preferred substrate for most organisms as it supports
rapid growth, and the microorganism will therefore attempt to use this carbon and energy source
first. Some of the characteristics of microbial growth on sequentially metabolized substrates are
compiled in Table 7.6. They capture in a simple fashion the overall consequences for the sequential
utilization of carbon and energy sources as a result of the complex regulatory mechanisms behind
carbon catabolite repression.
It is possible to set up detailed mechanistic models describing the regulatory phenomena behind
glucose repression, and hereby describe how enzymes involved in utilization of other carbon
sources are synthesized. In Section 7.5.1 we will illustrate this with a model for the lac-operon in£.
coli,
i.e., the genes involved in lactose utilization. However, the complexity of these models is
substantial, and if the aim is to simply simulate biomass growth on multiple substrates a simpler
modeling concept is to be preferred. Ramkrishna and co-workers have developed an ingenious
modeling concept, which is especially suited for description of growth on multiple carbon and
energy sources. Their cybernetic modeling approach is based on the hypothesis that while the
detailed modeling of regulatory processes is complicated, it may be possible to interpret the
functioning of the cell as being guided by a strategy of optimal allocation of resources
{Ramkrishna, 1982; Ramkrishna
et a i
, 1984). Since there is no direct way of confirming whether
microorganisms really optimize the allocation of their resources towards growth, the cybernetic
models should be accepted on the same basis as other simple structured models: They provide a
good modeling framework that can be used to simulate growth on multiple substrates and hereby be
used for design of fermentation processes.
The basic idea of the cybernetic model is that one
key enzyme
plays a bottleneck role in growth on a
Table'7.6
Characteristics of microbial growth on truly substitutable substrates (Ramkrishna
et al.,
19871._________________________________________________________________________________
1.
Given multiple substrates, microorganisms prefer to utilize the substrate on which they can grow
the fastest, commonly resulting in a sequential utilization of the substrates in a batch culture.
2.
Sequential utilization may turn into simultaneous utilization when another substrate, e.g., the
nitrogen source, becomes limiting.
3.
Even during simultaneous utilization of multiple substrates, the specific growth rate is never higher
than that which can be obtained with growth on any substrate alone.
4.
If during growth on a “slower” substrate, a “faster” substrate is added to the medium, the growth on
the slower substrate quickly stops.
5.
In continuous cultures, multiple substrates are consumed simultaneously at low dilution rates, and
the faster substrate is preferentially consumed at high dilution rates.___________________________
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