290
Chapter 7
To set up a single-cell model one must have a detailed knowledge of the microorganism, and good
single-cell models are therefore developed only for well examined microorganisms:
E. coli,
Bacillus subtilis,
and
S. cerevisiae.
Among the most comprehensive single-cell models constructed
is the so-called Cornell model for
E. coli
, which was developed by Mike Shuler and co-workers at
Cornell University. The original model by Shuler
et a l
(1979) contained 14 components, and it
formed the basis for all later versions of this model - particularly a more detailed model with 20
intracellular components (Shuler and Domach, 1982). The additional components were introduced
in order to describe the incorporation of ammonium ions into amino acids, to allow more accurate
estimates of cellular energy expenditures, and to allow a more complete simulation of the systems
which control transcription and translation of the genes (Shuler and Domach, 1982). The model
correctly predicts an increase in cell volume with increasing specific growth rate during both
glucose- and ammonia-limited growth (Domach
et al.,
1984), a decrease in the glycogen content
with increasing specific growth rate during ammonia-limited growth (Shuler and Domach, 1982),
and many other observations made with
E, coli.
Peretti and Bailey (1986) revised the Cornell model by introducing a more refined description of
the protein and RNA synthesis, including initiation of translation and distribution of RNA
polymerase along with initiation of DNA and chromosomal replication. Changes and additions to
the Cornell model are motivated by a desire to expand the range of applications of single-cell
models. In particular it is desired to study the effect of plasmid insertion into a host cell and the
expression of any plasmid genes, as in Peretti and Bailey (1987), who describe host-plasmid
interactions in
E. coli.
Their extension of the model can be applied to study the effect of copy
number, promoter strength, and ribosome-binding-site strength on the metabolic activity of the host
cell and on the plasmid gene expression.
With the rapid development in experimental techniques it becomes feasible to extend the rather
empirical single cell model described above to “complete” models of living cells. In these
models all known molecular mechanisms are incorporated, and the interaction between the
different components in the system can be analyzed at the quantitative level (Endy and Brent,
2000). This approach is currently referred to as systems biology, and even though the ultimate
goal is to describe all processes in the cell, it is currently only possible to describe a few of the
key processes.
However,
eventually
models
of different
cellular processes,
e.g.,
gene
transcription, specific biochemical pathways, cell cycle control, mating type shifts, may be
assembled into an overall model that may reveal the relative importance of the many different
processes operating in a living cell. In the quest for a complete mathematical description of
cellular function interaction between model construction and evaluation is important, since a
final model will be the result of several iterations where the model is continuously revised as
soon as new biological data become available.
7.6 Morphologically Structured Models
In sections 7.3-7.5 we specified the growth kinetics assuming that all the cells in a culture have the
same metabolism; i.e., the cell population is assumed to be completely homogeneous, and a non-
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