Self-Assembly Principles of Helicates - Metallofoldamers: Supramolecular Architectures from Helicates to Biomimetics - page 107

is also in line with a slow formation kinetics observed for complicated assemblies of pen-
tanuclear helicates [35,40], whose completion at stoichiometric conditions requires a long
equilibration time. The kinetics and reaction intermediates can then be conveniently
examined with NMR or ESMS.

3.5 Understanding Self-Assembly Processes

3.5.1 Assessment of Cooperativity

3.5.1.1 Cooperativity Tests for Intermolecular Interactions

To reveal cooperativity interactions in metallo-organic compounds, chemists borrowed
established tests valid for biological systems, and the formal aspects of these methods
were reviewed by Permutter-Hayman [27]. Cooperativity is usually evaluated with graph-
ical tests such as the binding curve and Scatchard and Hill plots, which are based on the
calculation of the occupancy r (Equation 3.8), in other words, the average number of lig-
ands bound per receptor.

½ PL þ 2 ½ PL 2 þþ n ½ PL n

r ¼ ð 3 : 8 Þ

½ P þ½ PL þ½ PL 2 þþ½ PL n

According to the curve shape, one can detect deviations from the statistically governed
intermolecular binding of ligands (or metal ions) to a receptor and eventually detect posi-
tive or negative cooperativity. These methods are strictly limited and give a correct indi-
cation of allosteric cooperativity only for systems with intermolecular interactions (see
Section 3.3). As an illustrative example, the Scatchard plot for NH 3 binding to a Ni(II)
receptor is shown in Figure 3.12. The concave upward curve for this simple mononuclear

Figure 3.12 Scatchard plot for the formation of [Ni(NH 3 ) x ] 2þ , which shows a negative allo-
steric cooperativity indicated by a concave upward curve shape [41].