Predicting skin permeability from complex chemical mixtures: incorporation of an expanded QSAR model

Quantitative structure–activity relationship (QSAR) models have been widely used to study the permeability of chemicals or solutes through skin. Among the various QSAR models, Abraham’s linear free-energy relationship (LFER) model is often employed. However, when the experimental conditions are complex, it is not always appropriate to use Abraham’s LFER model with a single set of regression coefficients. In this paper, we propose an expanded model in which one set of partial slopes is defined for each experimental condition, where conditions are defined according to solvent: water, synthetic oil, semi-synthetic oil, or soluble oil. This model not only accounts for experimental conditions but also improves the ability to conduct rigorous hypothesis testing. To more adequately evaluate the predictive power of the QSAR model, we modified the usual leave-one-out internal validation strategy to employ a leave-one-solute-out strategy and accordingly adjust the Q² _LOO statistic. Skin permeability was shown to have the rank order: water > synthetic > semi-synthetic > soluble oil. In addition, fitted relationships between permeability and solute characteristics differ according to solvents. We demonstrated that the expanded model (r² = 0.70) improved both the model fit and the predictive power when compared with the simple model (r² = 0.21).