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 additionally consider the functional relationship between passive permeation and acidity. To discover easily interpretable equations that explain the data well, we use the recently proposed sure-independence screening and sparsifying operator (SISSO), an artificial-intelligence technique that combines symbolic regression with compressed sensing. Our study is based on a large in silico dataset of 0.4 million small molecules extracted from coarse-grained simulations. We rationalize the equation suggested by SISSO via 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, but surprisingly contributes stepwise rather than proportionally. Our results are in line with previously observed changes in permeability, suggesting the distinction between liquid-disordered (Ld) and liquid-ordered (Lo) 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.
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