Modeling of Growth Kinetics
Structuring at the cell level
Figure 7.2
Different types of model complexity, with increasing complexity from the upper left comer to
lower right comer. With structuring at the cell level, specific intracellular events or reactions are
considered in the model, and the biomass is structured into two or more variables. With structuring at the
population level, segregation of the population is considered,
it is recognized that not all the cells in
the population are identical.
From the above it is clear that a very important element in mathematical modeling ot
fermentation processes is to define the model structure (or specifying the complexity of the
model). A general rule can be stated as:
As simple os possible but not simpler.
This rule implies
that the basic mechanisms should always be included and that the model structure depends on the
aim of the model (see Note 7.2). Thus, if the aim is to simulate the biomass concentration in a
fermentation process, a simple unstructured model (Section 7.3) may be sufficient. Even though
these models are completely empirical, they are valuable for simple design problems and for
extracting key kinetic parameters of the growth kinetics. If on the other hand the aim is to
simulate dynamic growth conditions one may turn to simple structured models (Section 7.4),
the compartment models, which are also useful for illustrating the concept of structured
modeling. However, if the aim is to analyze a given system in further detail it is necessary to
include far more structure in the model, and in this case one often describes only selected
processes within the cell,
a certain pathway or gene transcription from a certain promoter.
Similarly if the aim is to investigate the interaction between different cellular processes,
influence of plasmid copy number on chromosomal DNA replication, a single cell model has to
be applied. A short introduction to these more detailed (or mechanistic) models is given in
Section 7.5. Finally, if the aim is to look at population distributions, which in some cases may
have an influence on growth or production kinetics, either a segregated or a morphologically
structured model has to be applied. In Section 7.6 we will consider simple cellular segregation -
here referred to as morphologically structured models, whereas population based models is the
topic of Chapter 8.
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