RESUMEN

This study describes a novel nonlinear variant of the well-known Yalkowsky general solubility equation (GSE). The modified equation can be trained with small molecules, mostly from the Lipinski Rule of 5 (Ro5) chemical space, to predict the intrinsic aqueous solubility, S0, of large molecules (MW > 800 Da) from beyond the rule of 5 (bRo5) space, to an accuracy almost equal to that of a recently described random forest regression (RFR) machine learning analysis. The new approach replaces the GSE constant factors in the intercept (0.5), the octanol-water log P (-1.0), and melting point, mp (-0.01) terms with simple exponential functions incorporating the sum descriptor, Φ+B (Kier Φ molecular flexibility and Abraham H-bond acceptor potential). The constants in the modified three-variable (log P, mp, Φ+B) equation were determined by partial least-squares (PLS) refinement using a small-molecule log S0 training set (n = 6541) of mostly druglike molecules. In this "flexible-acceptor" GSE(Φ,B) model, the coefficient of log P (normally fixed at -1.0) varies smoothly from -1.1 for rigid nonionizable molecules (Φ+B = 0) to -0.39 for typically flexible (Φ âˆ¼ 20, B ∼ 6) large molecules. The intercept (traditionally fixed at +0.5) varies smoothly from +1.9 for completely inflexible small molecules to -2.2 for typically flexible large molecules. The mp coefficient (-0.007) remains practically constant, near the traditional value (-0.01) for most molecules, which suggests that the small-to-large molecule continuum is mainly solvation responsive, apparently with only minor changes in the crystal lattice contributions. For a test set of 32 large molecules (e.g., cyclosporine A, gramicidin A, leuprolide, nafarelin, oxytocin, vancomycin, and mostly natural-product-derived therapeutics used in infectious/viral diseases, in immunosuppression, and in oncology) the modified equation predicted the intrinsic solubility with a root-mean-square error of 1.10 log unit, compared to 3.0 by the traditional GSE, and 1.07 by RFR.

Asunto(s)

Modelos Químicos , Preparaciones Farmacéuticas/química , Química Farmacéutica , Solubilidad

RESUMEN

The aim of the study was to explore to what extent small molecules (mostly from the Rule of 5 chemical space) can be used to predict the intrinsic aqueous solubility, S0, of big molecules from beyond the Rule of 5 (bRo5) space. It was demonstrated that the General Solubility Equation (GSE) and the Abraham Solvation Equation (ABSOLV) underpredict solubility in systematic but slightly ways. The Random Forest regression (RFR) method predicts solubility more accurately, albeit in the manner of a 'black box.' It was discovered that the GSE improves considerably in the case of big molecules when the coefficient of the log P term (octanol-water partition coefficient) in the equation is set to -0.4 instead of the traditional -1 value. The traditional GSE underpredicts solubility for molecules with experimental S0 < 50 µM. In contrast, the ABSOLV equation (trained with small molecules) underpredicts the solubility of big molecules in all cases tested. It was found that the errors in the ABSOLV-predicted solubilities of big molecules correlate linearly with the number of rotatable bonds, which suggests that flexibility may be an important factor in differentiating solubility of small from big molecules. Notably, most of the 31 big molecules considered have negative enthalpy of solution: these big molecules become less soluble with increasing temperature, which is compatible with 'molecular chameleon' behavior associated with intramolecular hydrogen bonding. The X-ray structures of many of these molecules reveal void spaces in their crystal lattices large enough to accommodate many water molecules when such solids are in contact with aqueous media. The water sorbed into crystals suspended in aqueous solution may enhance solubility by way of intra-lattice solute-water interactions involving the numerous H-bond acceptors in the big molecules studied. A 'Solubility Enhancement-Big Molecules' index was defined, which embodies many of the above findings.