Modeling of Growth Kinetics
279
7.5.1
Genetically Structured Models
Gene transcription models aim at quantifying gene transcription based on knowledge of the
promoter function. Among the best-studied promoters is the so-called lac-promoter of
E. coli
,
which takes part in regulating expression of genes that are involved in lactose uptake, i.e., lactose
permease and P-galactosidase. Understanding the regulation of this promoter represented a major
breakthrough in molecular biology, and the history of how the mechanisms were unraveled is an
excellent introduction to modem molecular biology (Muller-Hill, 1996). The lac-promoter is also
of substantial industrial interest as it is often used to drive expression of heterologous genes
encoding recombinant proteins in
E. coli.
The three genes coding for enzymes necessary for lactose metabolism in
E. coli
are coordinated in a
so-called operon, and gene expression is coordinately controlled by two regulatory sites positioned
upstream of the genes (see Fig. 7.16):
Control at the operator by a repressor protein.
*
Carbon catabolite repression at the promotor.
The repressor protein
XT
has two binding sites - one site that specifically ensures binding to the
operator (A'o) and one site which may bind lactose (S’
,*.). When lactose binds to the repressor protein,
its conformation changes so that its affinity for binding to the operator is significantly reduced.
Thus lactose prevents the repressor protein from binding to the operator, and transcription of the
genes by RNA polymerase is therefore allowed. Consequently, lactose serves as an inducer of
transcription; i.e., expression of the three genes
lacZ, lacY,
and
lacA
is not possible unless lactose
(or another inducer, e.g. isopropyl-P-D-thiogalactoside, abbreviated IPTG) is present.1
The binding
of the repressor protein to lactose and the operator may be described by reactions (7.44), where
n =
4 is the number of binding sites for lactose on the repressor protein.
+ nSlac
X rnStac
(7.44a)
X 0 + X r <r> X oX r
(7.44b)
X 0X r + nSlac£ X oX rnSlac
(7.44c)
X a + X rnSlac<-> X 0X rnSlac
(7.44d)
1
More precisely, the regulatory molecule is a lactose isomer, allolactose, that acts as an inducer. This species is
formed
in situ
by P-galactosidase, which transforms lactose to allolactose. Thus, P-galactosidase, which is actually
under the control of the
lac
operon, also has to be expressed constitutively at a basal level as a primer o f the
induction sequence.
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