Data-driven equation for drug-membrane permeability across drugs and membranes.

Drug efficacy depends on its capacity to permeate across the cell membrane. We consider the prediction of passive drug-membrane permeability coefficients. Beyond the widely recognized correlation with hydrophobicity, we apply sure-independence screening and sparsifying operator (SISSO), a data-driven compressed-sensing technique, to a large (0.4 million compounds) database of coarse-grained computer simulations as a way to also incorporate the role of acidity. We rationalize our derived equation by means of an analysis of the inhomogeneous solubility-diffusion model in several asymptotic acidity regimes. We further extend our analysis to the dependence on lipid-membrane composition. Lipid-tail unsaturation plays a key role: we report a permeability ratio between liquid-disordered (Ld) and liquid-ordered (Lo) domains of roughly 25, largely independent of the chemistry of the drug. They confirm the role of membrane surface-density fluctuations in passive permeation. Together, compressed sensing with analytically derived asymptotes establish and validate an accurate, broadly applicable, and interpretable equation for passive permeability across both drug and lipid-tail chemistry.