Assessment of cooperativity in self-assembly

A method has been proposed to assess cooperativity in self-assembly processes. The method is based on a clear distinction between intermolecular and intramolecular processes which are compared with the corresponding reference reactions. It has been applied to two classical cases, namely the self-assembly of helicates and of porphyrin ladders, by using data previously published by the groups of Lehn and Anderson, respectively. Contrarily to the conclusions of the authors, pointing out self-assembly processes driven by positive cooperativity, the method here presented indicates in both cases the absence of cooperative effects. The methods previously used to assess cooperativity, in particular Scatchard plot and/or Hill plot, are criticized as being inappropriate for self-assembly, because they are pertinent to a specific case only, namely the intermolecular binding of a monovalent ligand L to a multivalent receptor M, a case very different from self-assembly which involves both inter- and intramolecular interactions. The present method underscores the fact that positive cooperativity in artificial self-assembling systems is probably much more rare than it was previously thought.