Modeling of Growth Kinetics
289
growth rate is reduced synthesis of the repressor protein. In Lee and Bailey (1984d,e) the gene
transcription efficiency "H
is examined for the recombinant protein when the lac promotor is
included in the plasmids (often the promotors of operons for which the control mechanisms are well
known are used in plasmids, since thereby the transcription of the gene can be controlled). A
similar model describes the lac-operon in the chromosome, but the binding of RNA polymerase to
the promotor is included. This is important since in the recombinant strain the promotors in the
plasmids and in the chromosome compete for the available RNA polymerases. The overall
transcription efficiency is given as the product of
Q{, Q2,
and
Q3
(see Equation 7.60). In a study of
the effects of multicopy plasmids containing the lac promotor, Lee and Bailey (1984d,e) found that
Qi
increases with the plasmid copy number and that both
Q2
and
Q3
decrease with the plasmid copy
number. The overall effect is a decreasing gene-expression efficiency with increasing plasmid copy
number, and the overall transcription rate of the cloned gene is therefore not increasing linearly
with the plasmid copy number, as has also been experimentally verified (Seo and Bailey, 1985).
The decrease in
Q3
with the plasmid copy number is explained by an increasing competition for the
available RNA polymerases. Lee and Bailey (1984e) suggest that the empirical expression in Eq.
(7.64) may be used in simple structured models to account for this effect:
r
Q3
=
l -
v
X .
X .
' p,
max
J
(7.64)
The modeling work of Lee and Bailey has been used to study host-plasmid interactions and to
explain experimental observations, which are seldom obvious due to the many interactions present
in recombinant microorganisms.
7.5.2 Single Cell Models
In single-cell models, characteristic features of the individual cells are considered (e.g., the cell
geometry) and particular events during the cell cycle may be studied. All the models that we have
described so far are based on the assumption of an equal distribution of cellular material to the
daughter cells upon cell division, and the intracellular concentration of a component is therefore not
affected by cell division. Furthermore, no special events in the cell cycle have been included in the
model, and cell age is consequently of no importance. Therefore the overall kinetics is completely
defined by the composition of each cell (the state vector X). The single-cell models are used to
study microbial behavior at the cellular level. The advantages of single-cell models are (Shuler and
Domach, 1982): 1
2
3
4
1.
It is possible to account explicitly for cell geometry and thereby examine its potential
effects on nutrient transport.
2.
Temporal events during the cell cycle can be included in the model.
3.
Spatial arrangements of intracellular components can be considered.
4.
Biochemical pathway models and metabolic control models can be included with ease.
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