Modeling of Growth Kinetics
265
7.4 Simple Structured Models
As discussed in the introduction to this chapter, the unstructured models are quite adequate for
steady-state conditions, and as shown in Example 7.3 even complex growth patterns can be
incorporated. Unstructured models do, however, give a poor description of dynamic experiments
where the biomass composition changes and the activity of the biomass therefore varies. The poor
fit of unstructured models to dynamic changes in fermentations has been confirmed by many
different fermentation studies, see e.g. Esener
et al.
(1981b) who illustrated that the Monod model
(including maintenance) could not fit biomass concentration data both in the exponential growth
phase and in the transition phase from exponential growth to a phase with slower growth in a
fed-batch fermentation of
K. pneumoniae.
It must be realized that unstructured models are primarily
data fitters for a restricted set of data, and they can rarely be used at significantly different
experimental conditions. Simple structured models are, in one sense or the other, improvements on
the unstructured models since some basic mechanisms of the cellular behavior are at least
qualitatively incorporated. Thus, the structured model may have some predictive strength. It may
describe the growth process at different operating conditions with the same set of parameters, and it
can therefore be applied for, e.g. optimization of the process.
In simple structured models, biomass components are lumped into a few key variables - the vector
X of Section 7.2 - that, hopefully, are representative of the cell behavior. Hereby the microbial
activity becomes not only a function of the abiotic variables, which may change with very small
time constants, but also of the cellular composition. The microbial activity therefore depends of the
history of the cells, i.e., on the environmental conditions that the culture has experienced in the past.
In simple structured models the cellular components included in the model represent pools of
different enzymes, metabolites, or other cellular components. The cellular reactions considered in
these models are therefore empirical since they do not represent the conversion between true
components. Similarly, the kinetics for the individual reactions is normally described with
empirical expressions, of a form that appears to fit the experimental data with a small number of
parameters. Thus, Monod-type expressions are often used since they summarize some fundamental
features of most cellular reactions, i.e., being first order at low substrate concentration and zero
order at high substrate concentration. Despite their empirical nature, simple structured models are
normally based on well-established cell mechanisms, and they are able to simulate certain features
of experiments quite well. In the following we will consider two different types of simple structured
models: Compartment Models and Cybernetic Models.
7.4.1 Compartment Models
In compartment models the biomass is divided into a few compartments or macromolecular pools.
These compartments must be chosen with care, and cell components with similar function should
be placed in the same compartment (e.g., all membrane material and otherwise rather inactive
components in one compartment, and all active material in another compartment). If some thought
is put into this crude structuring process one may regard individual, true cell components, which are
not accounted for in the model, as being either in a frozen state or in pseudo steady state (very long
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