Population characteristics of cyclodextrin complex stabilities in aqueous solution.

Binding constants (K11) of 1:1 complexes of alpha-cyclodextrin, beta-cyclodextrin, and gamma-cyclodextrin with many substrates (guests) were collected from published sources and subjected to statistical analysis. All systems refer to 25 +/- 5 degrees C and aqueous solution. The frequency distributions of log K11 are satisfactorily described by normal distributions with the following parameters (n = number of complexes, mu = population mean, sigma = population standard deviation): alpha-cyclodextrin, n = 663, mu = 2.11, sigma = 0.90; beta-cyclodextrin, n = 721, mu = 2.69, sigma = 0.89; gamma-cyclodextrin, n = 166, mu = 2.55, sigma = 0.93. Stabilities of pairs of cyclodextrin complexes with a common substrate are not precisely correlated, but they do not appear to be wholly independent quantities. The stabilities of alpha-cyclodextrin complexes are consistent with a recent interpretation of solvent effects on alpha-cyclodextrin complex stabilities.