Cell Metabolism - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 495

With these simplifications, the fraction of repressor-free operators is found to be

½ E O ½ E O

E O T ¼ ½ ½ E O þ½ E O $ E R þ½ E O $ E R $ð S L Þ 4

½

E O

¼

S L 4

E O þK 2 ½ E R þK 4 K 1 ½

½ E O ½ E O ½ E R ½

(10.18)

1

¼

S L 4 1 þ K 2 ½ E R þK 4 K 1 ½ E R ½

1
1 þ K 2 K 1 þ K 4 ½

z

S L T

½ E R T

S L T K 1 þ½

Since the total number of operators of a given type in the cell is very small, it does not make
much sense to talk about the fraction of repressor-free operators. However, in a description of
enzyme synthesis, one may use Eqn (10.18) as an expression for the probability that the oper-
ator is repressor free.
Since the transcription of the three genes in the operon is likely to be determined by the
fraction of repressor-free operators, Eqn (10.18) is valuable for description of the synthesis
of the enzymes necessary for lactose metabolism that aims at describing diauxic growth on
glucose and lactose. The inducer concentration [S L ] likely to be correlated with the extracel-
lular lactose concentration, whereas the total content of repressor protein can be assumed to
be constant.
Small molecules that influence the transcription of genes are called effectors, and in the
lac-operon, the effector (lactose) is an inducer. In other operons, there may, however, be a nega-
tive type of control, and here the effector is called an antiinducer. With an inducer, the binding
affinity to the operator of the tree repressor is much larger than that of the inducer-repressor
complex. i.e. K 2 >> K 4 , whereas with antiinducer it is the other way round. For an anti-

inducer, the action of repressor-free operators can be found from an expression similar to
Eqn (10.18) .
The other control mechanism in the lac-operon is the so-called carbon catabolite repres-
sion, which ensures that no enzymes necessary for lactose metabolism are synthesized as
long as a preferred substrate is available, e.g. glucose. When E. coli senses the presence of
a carbon-energy source preferred to lactose, it will not use the lactose until the preferred
substrate (e.g. glucose) is fully consumed. This control mechanism is exercised through
a protein called CAP (cyclic-AMP-activating protein). Cyclic-AMP (cAMP, the single phos-
phate residue is bound on both C3 and C5 positions of the ribose residue) levels increase
as the amount of energy available to the cell decreases. Thus, if glucose or a preferred
substrate is depleted, the level of cAMP will increase. Under these conditions, cAMP will
readily bind to CAP to form a complex that binds near the lac promoter. This complex greatly
enhances RNA polymerase binding to the lac promoter. Enhancer regions exist in both
prokaryotes and eukaryotes.
The site of the binding of the cAMP-CAP complex has been located in several operons that
are under carbon catabolite repression, and binding of the complex to DNA has been found