How to adapt Scatchard plot for graphically addressing cooperativity in multicomponent self-assemblies.

A graphical method has been developed for the reliable detection of cooperativity in polymetallic complexes involving intra- and intermolecular complexation processes. The method relies on the determination of the partial occupancy r(AL)n, which represents the average number of metals bound per preassembled receptor AL(n) made up of n ligands bound to a linker A. We observe nonlinear, i.e., nonstatistical, Scatchard-like plots (r(AL)n/[M] vs r(AL)n) for metal-binding in double-stranded helicates. The present concept is extended to a virtual, pre-organized receptor L(n), in which no specific linker is involved. Applications to several polymetallic helicates reveal the presence of negatively cooperative processes attributed mainly to intermetallic repulsions, in agreement with recent thermodynamic models.