Human Skin Permeability Prediction by Machine Learning for Transdermal Drug Delivery

Background and Objectives: The dose a transdermal patch delivers is governed by the drug's permeability coefficient (Kp) across skin, and the reference Potts-Guy equation assumes log Kp is linear in lipophilicity and molecular weight. Whether that form holds across the whole of the public human data, and how far such a model generalises to a new therapeutic class, is unknown. Materials and Methods: Two open human skin permeation databases were merged and standardised, yielding 732 permeability records for 327 compounds, 40 of them analgesics. Fifteen two-dimensional descriptors were computed. Linear, ridge, random forest and gradient boosting models were compared by cross-validation, a held-out test set and leave-analgesics-out extrapolation, with every fold and split defined on compounds. Results: Predicted log Kp rose steeply with lipophilicity but plateaued above an octanol-water partition coefficient of about 2.5, a saturation confirmed by accumulated local effects. The apparent decline above a molecular weight of about 220 g mol^-1 spanned only 0.44 log units, lay within its bootstrap interval, and is reported as model-derived. The bilinear Potts-Guy equation could not represent this form (R² = -0.172 pooled). A random forest reached R² = 0.312 on the held-out set (median 0.383 across 200 resplits), outperforming Potts-Guy (p = 0.006). Epidermis-only analysis raised R² from 0.213 to 0.443, a large effect that loses significance once fold dependence is corrected (p = 0.059). With the analgesic class withheld, a two-descriptor linear model beat both ensembles; all 40 lay inside the applicability domain, yet predictions were compressed where fentanyl, sufentanil and morphine sit. Conclusions: Lipophilicity shows a saturating relationship with skin permeability that a linear equation cannot represent. Achievable accuracy is limited at least as much by variability between independent studies of the same compound as by molecular description, and interpolation within the sampled chemical space does not imply generalisation to a new class.