Multivalence cooperativity leading to "all-or-nothing" assembly: the case of nucleation-growth in supramolecular polymers.

All-or-nothing molecular assembly events, essential for the efficient regulation of living systems at the molecular level, are emerging properties of complex chemical systems that are largely attributed to the cooperativity of weak interactions. The link between the self-assembly and the interactions responsible for the assembly is however often poorly defined. In this work we demonstrate how the chelate effect (multivalence cooperativity) can play a central role in the regulation of the all-or-nothing assembly of structures (supramolecular polymers here), even if the building blocks are not multivalent. We have studied the formation of double-stranded supramolecular polymers formed from Co-metalloporphyrin and bi-pyridine building blocks. Their cooperative nucleation-elongation assembly can be summarized as a thermodynamic cycle, where the monomer weakly oligomerizes linearly or weakly dimerizes laterally. But thanks to the chelate effect, the lateral dimer readily oligomerizes linearly and the oligomer readily dimerizes laterally, leading to long double stranded polymers. A model based on this simple thermodynamic cycle can be applied to the assembly of polymers with any number of strands, and allows for the determination of the length of the polymer and the all-or-nothing switching concentration from the pairwise binding constants. The model, which is consistent with the behaviour of supramolecular polymers such as microtubules and gelators, clearly shows that all-or-nothing assembly is triggered by a change in the mode of assembly, from non-multivalent to multivalent, when a critical concentration is reached. We believe this model is applicable to many molecular assembly processes, ranging from the formation of cell-cell focal adhesion points to crystallization.