308
Chapter 7
P i
g L'1)
Z xfaPW x'X
o
0.16
0.16
0.14
0.14
0.14
0.12
0.11
0.10
0.09
7.5
13.0
18.5
21.0
32.0
38.5
45.0
48.5
How can you explain the decrease in the yield coefficient with increasing lactic acid concentration?
e.
Assume that the maintenance coefficient
is 0.05 h"1. Calculate the true yield coefficient
stoichiometric coefficient in eq. (7.26) for
p -
0. Using the model derived in (b), calculate the
maintenance coefficient as a function of
pu.
Explain the results.
Problem 7.3
Modeling of the lac-operon in
E. coli
We will now consider the model for the lac-operon described in Section 7.5.1.
a.
The repressor has four binding sites for the inducer (lactose), but in the derivation of Eq. (7.52) only
the repressor-inducer complex where all four sites are occupied is considered. We now consider
binding at all four sites. Specify all the equilibria and the definitions of the association constants.
The association constant for formation of
XJS-,
is termed
and that for formation of
XoX&
is
termed
K4i.
Binding of the inducer to the repressor operator complex can be neglected (i.e., the
equilibrium in eq. (7.44c) is not considered).
Assume that the affinity for the binding of the repressor to the operator is approximately the same
whether no, one, two or three inducers are bound to the repressor, i.e., /Cn =
Ka
2
= K
A3
= Km.
This
assumption is reasonable since the repressor probably changes its conformation only when the last
inducer is bound to it. With this assumption show that the fraction of repressor-free operators is
given by
where
Ki=K
4
, K
41
K
43
K
44
.
We now assume that the
~
K
l2
~
~
K[4,
i.e., the association constant for the fourth inducer is
much stronger than the corresponding constants for the first three sites. This assumption follows
from our assumption above that the conformation of the repressor changes only when the fourth
inducer is bound and when the conformation changes the repressor-inducer complex becomes very
stable. What other assumptions are required for reducing Eq. (1) to Eq. (7.52)?
(
1
)
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