Modeling of Growth Kinetics
287
k m = amk meN p
(1)
k p = a p k peN r
(2)
where
am
and
ap
are conversion factors,
and
represent the mRNA chain elongation rate per active
RNA polymerase and the polypeptide chain elongation rate per active ribosome, respectively.
Nv
and
Nt
are
the number of active RNA polymerase molecules per gene and the number of active ribosomes per mRNA,
respectively. The rate of elongation of mRNA chains per active RNA polymerase
(k^)
is about 2400
nucleotides min', and this value does not vary significantly with the specific growth rate. The polypeptide
chain elongation rate per active ribosome
(k^)
is about 1200 amino acids min'1
when M
» ln(2), whereas it
is proportional to
^
for
fj
« ln(2). Thus
k pe
= 1200a
where
j 1
i
M
> ln(2)
}/r/ln(2) ;
(à <
ln(2)
(3)
(4)
Np
is estimated from the size of the gene and the intermolecular distances between transcribing RNA
polymerase molecules
(d?).
Similarly,
NT
is found from the size of the mRNA and the intermolecular
distance between translating ribosomes
(dt).
The intermolecular distances depend on the cellular activity,
and they are correlated with the specific growth rate (in h'1):
d p
= 233/A2 + 78 nucleotides
(5)
d r
= 82.5//“*
+145 nucleotides
(6)
where the intermolecular distances are specified as the number of nucleotides between each RNA
polymerase and the next (or a translating ribosome).
Assume that there are
z
deoxyribonucleotides in the gene. These are transcribed into
z
ribonucleotides, and
at a specific growth rate P = ln(2) h'1
(corresponding to a doubling time of 1 h) we obtain
1 mRNA molecule Y
2400 ribonucleotides
Y 1 active RNA polymerase
z
ribonucleotides A active RNA polymerase ■
min A 563 deoxyribonucleotides
z
deoxyribonucleotides i
.
,
,
---------
-
---------------------
= 4.26 mRNA molecules per gene per min
gene
}
Similarly, if
y
amino acid molecules are used to synthesize one protein molecule the overall protein
translation rate constant is determined by
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