Rigorous nonlinear regression analysis of phase solubility diagrams to obtain complex stoichiometry and true thermodynamic drug-cyclodextrin complexation parameters

This work reports rigorous nonlinear regression procedures aimed at analyzing various types of phase solubility diagrams (PSDs) corresponding to the different soluble and insoluble complex stoichiometries, which are generally encountered in drug-cyclodextrin (CD) complexation studies. These are depicted in final equations that can be modeled to fit experimental data of measured drug solubility against CD concentration utilizing simple spreadsheet software available for all PCs (i.e., the Solver Add-in in Microsoft Excel). They cover all types of guest/host phase solubility diagrams (A-, B_S-and B_I-types) allowing accurate estimation of soluble and insoluble complex stoichiometries generally encountered in drug/CD complexes (1:1, 2:1, 1:2, 2:2, 2:3, 3:2), the corresponding thermodynamic complex formation constants (K₁₁, K₂₁, K₁₂, K₂₂, K₂₃, K₃₂) and solubility product constants (K_sp) of saturated complexes.