Multi-way PLS modeling of structure–activity data by incorporating electrostatic and lipophilic potentials on molecular surface

We devised and elaborated a surface-based three-dimensional-quantitative structure–activity relationship (3D-QSAR) method, which had been proposed in the previous study. This approach can be applied to more general case where both the electrostatic and lipophilic potentials on molecular surface simultaneously change. The 3D coordinates of all sampling points on molecular surface are projected into a 2D map by Kohonen neural network (KNN). Each node in the map is coded by the associated molecular electrostatic potential (MEP) or molecular lipophilic potential (MLP) values. The electrostatic and lipophilic KNN maps are generated for each compound and the four-way array is constructed by collecting two KNN maps of all samples. The correlation between four-way array and biological activity is examined by four-way partial least-squares (PLS). For validation, the structure–activity data of estrogen receptor antagonists was investigated. The four-way PLS model gave the high statistics at calibration and validation stages. The coefficients of the four-way PLS model back-projected on molecular surface had a reasonable 3D distribution and it was nicely consistent with active site of the estrogen receptor which was recently made clear by X-ray crystallography.