Correlation between the stability constant and pH for β-cyclodextrin complexes

In drug formulations, cyclodextrins are used to increase aqueous solubility and chemical stability of drugs via formation of inclusion complexes. For ionizable drug molecules, the complexation strength depends on pH. Increased ionization leads to a more soluble drug, but also results in destabilization of cyclodextrin complexes. Therefore, formulation scientists aim to find a balance between increased drug solubility and high complexation strength. In this work, a theoretical expression for the dependency between the stability constant and pH is presented, allowing the accurate prediction of the stability constant at any pH. The theoretical expression requires three out of four input parameters; the pK_a of the free guest molecule, the pK_a of the complex, and the stability constants for the neutral and fully ionized complex. Stability constants for β-cyclodextrin and ibuprofen complexes were determined by isothermal titration calorimetry at seven pH values (2.5-5.5) and four temperatures (15-55 °C). All these measured stability constants complied with the theoretical expression. Ten additional data sets from the literature comprising eight different drug molecules and three different cyclodextrins confirmed the ability of the theoretical expression to account for the observed pH-dependence of stability constants.