Development of improved empirical models for estimating the binding constant of a beta-cyclodextrin inclusion complex

Abstract

Purpose: To develop empirical models for predicting the binding between a drug and beta-cyclodextrin. Specifically, the logarithm of the 1:1 binding constant is expressed as the function of various molecular descriptors of the drug. Many potential drugs exhibit poor aqueous solubility. Also, the amount available for solubility studies is limited early in drug development. Thus, models that show which excipients can increase a drug's solubility are useful because formulation scientists can focus on them experimentally.

Methods: Twenty-five descriptors were considered based on molecular characteristics governing complexation. These include the drug's size and/or shape, the dispersion of its electron cloud, its lipophilicity, and its flexibility. The training set contains 258 ligands, ranging from drug-like molecules to small polar organic compounds.

Results: Two models were developed. The first is derived by partial least squares regression and consists of all 25 descriptors. The r2 determined by cross-validation is 0.79. The second contains four variables and was constructed by multiple linear regression. Its cross-validated r2 is 0.65.

Conclusions: Due to its simplicity, the second model is recommended over the first. The most important descriptor in both models is the calculated log P, indicating that drugs with greater lipophilicity form stronger complexes with beta-cyclodextrin.