Origin of non-linearity in phase solubility: solubilisation by cyclodextrin beyond stoichiometric complexation

The low solubility of drugs, which poses a serious problem in drug development, can in part be overcome by the use of cyclodextrins (CDs) and their derivatives. Here, the key to solubilisation is identified as the formation of inclusion complexes with the drug molecule. If inclusion complexation were the only contribution to drug solubility, it would increase linearly with CD concentration (as per the Higuchi-Connors model); this is because inclusion complexation is a 1 : 1 stoichiometric process. However, solubility curves often deviate from this linearity, whose mechanism is yet to be understood. Here we aim to clarify the origin of such non-linearity, based on the Kirkwood-Buff and the McMillan-Mayer theories of solutions. The rigorous statistical thermodynamic theory shows that non-linearity of solubilisation can be rationalised by two contributions: CD-drug interaction and the drug-induced change of CD-CD interaction.