Theoretical Calculation of the Solubility and Other Parameters for Poorly Water-Soluble Compounds from Binding Constants of Inclusion Complexes: The Examples of Betulin Derivatives with Cyclodextrins

Experimental determination of solubility is a time-consuming procedure with relatively high reagent consumption. The solubility of poorly water-soluble compounds in solubilizer solutions can be calculated from the values of their binding constants (also called stability, formation, or association constants) determined by other methods that require less time and reagents for research. For the case of the formation of both 1:1 and 1:2 complexes, comparison of solubility based on binding constant values is impossible without calculations. The paper considers the theoretical relationship of the solubility to the binding constants for this situation, as well as to the intrinsic solubility in the absence of solubilizer in solution. In addition, equations are presented for calculating the solubilizer concentration to obtain the desired solubility. Assumptions and limitations for such calculations are discussed. Demonstrative calculations were carried out using literature data on binding constants, previously determined by the authors using affinity capillary electrophoresis, for betulin 3,28-diphthalate and 3,28-disuccinate with six cyclodextrins: β-cyclodextrin (β-CD), hydroxypropyl-β-CD, randomly methylated β-CD, dimethyl-β-CD, γ-CD, and hydroxypropyl-γ-CD. It was shown that for calculating solubility at high values of binding constants it is important to use not the total concentration of the solubilizer in solution, but its equilibrium concentration. Higher values of the binding constants were found to do not always provide higher solubility. It turned out that the difference in solubilizing capacity between solubilizers may not be too significant at relatively high values of solubility in the absence of a solubilizer.