Chemistry Reference
In-Depth Information
O
N
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O
O
HO
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HN
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HO
HO
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O
O
N
N
N
H
N
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HO
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HN
HO
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H
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(a)
(b)
Figure 3.7 Examples of ditopic organic receptors: (a) for K
þ
[29] and (b) for Fe
3þ
[30], show-
ing allosteric cooperativity upon metal binding.
way, we must consider two related but distinct chelate cooperativity factors which are
associated with intermolecular binding processes [11]. Access to these parameters can be
illustrated for the binding of a ditopic ligand L to a divalent receptor M (Figure 3.2).
While the first binding event provides the opened complex
o
-ML via intermolecular bind-
ing, the second binding may occur in intramolecular or intermolecular fashion to provide
c
-ML or ML
2
, respectively. Considering these equilibria, the apparent constant
K
app
for
the second binding is expressedwithEquation3.5,whereby
K
is the reference micro-
scopic constant for intermolecular binding.
K
app
¼
½
ML
2
þ½
c
ML
EM
2
¼
K
1
þ
ð
3
:
5
Þ
½
o
ML
:½
L
½
L
K
app
in the presence of
chelate cooperativity, which may compare with the overall constant 4
K
2
in the absence of
cooperativity. The ratio of these constants provides the chelate cooperativity factor b
0
,
which is always positive (
The overall equilibrium constant for the binding process is 4
K
b
0
>
1), and depends on both
EM
and the ligand concentration
and thus satisfies all the requirements for a chelate cooperativity factor.
The term
EM
/2[L] indeed properly compares intramolecular reactions with respect
to intermolecular binding. The deviation of the factor
b¼
from unity is thus a measure of
chelate cooperativity. Non-cooperative behaviour occurs for
EM
/2
b
¼
[L] (
b¼
1), while
positive and negative cooperativity occur for
b>
1and
b<
1, respectively. The expres-
can be generalized for the case of
x
-valent ligand B to an
x
-valent receptor
x
A
(Equation 3.6) [11].
sion for
b
x
1
2
x
x
EM
2
b ¼
ð
3
:
6
Þ
½
L
The effective molarity and the ligand concentration represent two important parameters
which play a key role in tuning chelate cooperativity. Moreover, since the effective molar-
ity, and mainly its enthalpy part, depends on the ligand structure, chelate cooperativity
can be manipulated via ligand design (see above).
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