Can small drugs predict the intrinsic aqueous solubility of 'beyond Rule of 5' big drugs?

Abstract

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.

Keywords: Abraham Solvation Equation (ABSOLV); General Solubility Equation (GSE); Partial Least Squares (PLS); Random Forest regression (RFR); Rule of 5 (Ro5), beyond Ro5 (bRo5); Solubility Enhancement–Big Molecules (SEBM); aqueous intrinsic solubility; intramolecular hydrogen bonding (IMHB).

Figure 1.

Distribution of the big-molecule intrinsic aqueous solubility values in Wiki-pS0

Figure 2.

Plot of log S0 versus octanol-water partition coefficient, clogP, calculated using the RDKit software [62]. Squares refer to big molecules; circles refer to small molecules

Figure 3.

Big-molecule property distributions: (a) clogP, (b) molecular weight (M_W), and (c) number of H-bond donors (NHD) and acceptors (NHA). The separation between the groups is greater than that found in small molecules [20].

Figure 4.

The log P in the figure refers to calculated octanol-water partition coefficients, clogP. The solid diagonals are the identity lines, and the dashed lines refer to ±0.5 log deviations. The MPP pie charts refer to percentage of ‘correct’ prediction, based on absolute residuals being ≤ 0.5 log. The prediction of log S0 values of (a) small molecules and (b) big molecules using the classical General Solubility Equation (numeric compound labels are of paclitaxel analogs). (c) When using just the big-molecule data, the three constants in the GSE (Eq. 1) subjected to MLR analysis (cf., Eq. 6b) produce the modified GSE, which is valid only for molecules with MW > 800 Da. There are not enough big molecules in the Wiki pS0 database to test the predictiveness of Eq. (6b).

Figure 5.

The prediction of log S0 values of (a) small molecules and (b) big molecules using the Abraham Solvation Equation (ABSOLV). (c) An additional nonlinear descriptor was added to the ABSOLV equation (cf., Eq. 5), which was then trained with the small-molecule set. This improved the prediction accuracy of the modified ABSOLV equation. The pie chart denotes MPP, the fraction of ‘correctly’ predicted molecules (absolute residuals ≤ 0.5 log unit).

Figure 6.

Random Forest regression analysis. (a) Training set using the small molecules. (b) Internal validation test set, based on 30% of the small molecules randomly selected. (c) External test set prediction of big molecules, not used in the method training.

Figure 7.

Logarithm of the Solubility Enhancement–Big Molecules as a function of the number of rotatable bonds: log SEBM = log S₀^Obs – log S₀^ABSOLV.