Modeling of Growth Kinetics
309
b.
Lee and Bailey (1984d) also modeled the lac-operon, but they included binding of the repressor to a
nonspecific binding site in the chromosome (Ad). Again we neglect binding of inducer to the
repressor-operator complex, and the equilibria are therefore
X r + nSlac <r+ X rnSlac
(2a)
<5
(2b)
X 0X rSiac
(2c)
X d + X r
<-»
X dX r
(2d)
X d + X rSlac£ X dX rSlac
(2e)
By assuming that
[Xd]t
*
[Xd],
show that
Q
[x0]
1
[ x 0 \
i+xskJ,+A:,[s,„I(i+x6[^],)+^2[^l
c.
Lee and Bailey (1984d) specified the parameters in Eq. (3) to be
A ^ IO 'M -1,
K2 = 2
1012
M'1,
Ka = 2
109 M"1
K5=
103M ' ,
Ks=
L5 109M‘'
Furthermore, they state that
[Xd]t- 4
10"2 M
and
[XT]t= 2
10'® M
Plot the value of
Qi
using both eq. (3) and Eq. (7,52) as a function of the inducer concentration
[5/flj,. Comment on the result.
The parameters given by Lee and Bailey are for IPTG (isopropyl-P-D-thiogalactosidase), a
frequently used inducer in studies of the lac-operon. Assume that the parameters are the same for
lactose as inducer and calculate the concentration of lactose (in mg L'1) to give
Q, =
0.5. Discuss
why even this low concentration of lactose leads to induction of the lac-operon.
d.
Show that for an antiinducer (neglect binding of the repressor to nonspecific sites)
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