288
Chapter 7
1 protein molecule Y
1200 amino acids
Y 1 active ribosome
y
ribonucleotides
active ribosomes *
min Jv 264 ribonucleotides
(
3vdeoxyribonucleotidesl
—------------------------------- =13.8 protems per mRNA per min
V
mRNA
)
In Eq. (8) for each amino acid incorporated in the protein three ribonucleotides on the mRNA have to be
translated. The transcription and translation constants calculated above can be used to estimate reasonable
values of the parameters in other, less mechanistic models. Furthermore, it is illustrated how the parameters
in a very mechanistic model can be calculated from information in the biochemistry literature.
The rate of degradation of mRNA
is on the order of 0.53 min'1
and fairly constant for different
mRNAs. The rate of degradation of protein, A*e is different from protein to protein but it is a much slower
process—for most proteins the rate constant is below 0.1 h'1._______________________________________
For recombinant microorganisms the cellular content of the gene to be expressed (normally called
the
gene dosage)
is not necessarily constant. If the gene is inserted directly in the chromosome the
gene dosage is approximately independent of the operating conditions. However, in bacteria and
yeast the inserted gene is often present in so-called plasmids, which are circular non-chromosomal
DNA. The plasmids are replicated independently of the chromosomal DNA, and the ratio of the
plasmid number to the chromosome number (often called the
plasmid copy , number)
may therefore
vary with the operating conditions. The concentration of the gene
Xg
in Eq. (7.60) should therefore
be replaced with the concentration of plasmid copy number when recombinant bacteria are
considered. The plasmid is normally designed with a certain replication control mechanism, and in
some cases one uses a replication control mechanism that permits induction of rapid plasmid
replication, e.g., by the addition of chemical components or changing the temperature.
With the detailed knowledge of recombinant
E. coli
, it has been possible to set up truly mechanistic
models for this organism. The largest contribution to the modeling of recombinant
E. coli
has been
made in a series of papers from the group of Jay Bailey. Thus Lee and Bailey (1984a-e) describe
very detailed modeling of both plasmid replication and protein synthesis. In Lee and Bailey (1984a-
c) a mechanistic model for replication of the plasmid in
E. coli
is described. The plasmid copy
number was found to vary with the specific growth rate. Replication control o f the plasmid involves
both a repressor and an initiator (which are both proteins). In their model formation of the repressor
and the initiator is described by transcription of the genes followed by translation of the mRNA
using kinetic expressions similar to Eqs. (7.60) and (7.62). The repressor affects the transcription
efficiency of the genes coding for both the repressor and the initiator, whereas the initiator is
necessary for formation of a so-called replication complex. The plasmid replication is initiated
when the replication complex increases above a certain threshold value, and once plasmid
replication is initiated it is assumed that the replication is almost instantaneous, a reasonable
assumption considering the small size of the plasmid. The influence of the specific growth rate is
included through the overall transcription and translation constants, as discussed in Note 7.6. The
model correctly describes a decreasing plasmid content with increasing specific growth rate, and
model simulations reveal that the primary reason for the higher copy number at the lower specific
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