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2
EM
1
2
EM
2
8
κ
κ
+ 2
+
M
2
L
L
c
-M
2
L
2
L
c
-M
2
L
3
Figure 3.8 Schematic illustration of interannular cooperativity in self-assembly processes.
Adapted with permission from [11]. Copyright 2011 Wiley-VCH Verlag GmbH & Co. KGaA,
Weinheim.
3.3.3
Interannular Cooperativity
In order to describe the interplay of two or more intramolecular binding processes, inter-
annular cooperativity has been recently introduced by Ercolani [11,12]. Let us consider
the ligand binding event and the intramolecular ring closure with
EM
1
, which suppress an
internal rotational freedom by the freezing of torsional motion, for instance. Conse-
quently, the binding of the second ligand molecule and the closure of the virtual second
ring can be facilitated or hindered. The origin of this behaviour is attributed to the varia-
tion of
EM
2
accompanying the second ring closure with respect to the first one (
EM
1
) and
not to an increase in site binding affinity. The reference value of
EM
can be evaluated
independently for a model receptor undergoing the same interactions. The interannular
cooperativity factor can be quantitatively expressed as the ratio
EM
2
.
This situation is shown in Figure 3.8 for a tetravalent receptor and its binding with a
divalent ligand. Interannular cooperativity is clearly evidenced for porphyrin-type com-
pounds [31], but it can likely be detected in self-assemblies of triple- or more stranded
helicates.
g ¼
EM
1
EM
2
=
3.4 Kinetic Aspects of Multicomponent Organization
With the increasing complexity of supramolecular systems (the number of interacting
components, ligand branching, etc.), the probability of “good” coordination interactions
decreases, and the number of possible products increases. Consequently, more complex-
ation and decomplexation events (reversibility) are necessary for convergence to thermo-
dynamic products. The reaction path to the final assembly can be theoretically predicted
as the sequence of coordination steps within the assembly tree, which also includes
unfruitful sequences [2]. Nevertheless, kinetic studies are required for identifying the role
of real reaction intermediates that are preferentially formed through self-organization.
This knowledge significantly contributes to a better understanding of metallosupramolec-
ular assembly processes. However, compared with the structural characterization of
supramolecular compounds, the measuring of kinetic parameters for self-assembly pro-
cesses has been somewhat retarded. This is probably related to the high complexity of the
systems, where the simultaneous formation of different complexes makes the interpreta-
tion of kinetic data difficult. Moreover, the instrumentation for measuring fast reactions
was limited to stopped-flow techniques with spectrophotometric or fluorimetric detection.
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