Construction of 3D-QSAR Models Using the 4D-QSAR Analysis Formalism

4D-QSAR analysis incorporates conformational and alignment freedom into the development of 3D-QSAR models for training sets of structure−activity data by performing ensemble averaging, the fourth “dimension”. The descriptors in 4D-QSAR analysis are the grid cell (spatial) occupancy measures of the atoms composing each molecule in the training set realized from the sampling of conformation and alignment spaces. Grid cell occupancy descriptors can be generated for any atom type, group, and/or model pharmacophore. A single “active” conformation can be postulated for each compound in the training set and combined with the optimal alignment for use in other molecular design applications including other 3D-QSAR methods. The influence of the conformational entropy of each compound on its activity can be estimated. Serial use of partial least-squares, PLS, regression and a genetic algorithm, GA, is used to perform data reduction and identify the manifold of top 3D-QSAR models for a training set. The unique manifold of 3D-QSAR models is arrived at by computing the extent of orthogonality in the residuals of error among the most significant 3D-QSAR models in the general GA population. Receptor independent (RI) 4D-QSAR analysis has been successfully applied to three training sets: (a) benzylpyrimidine inhibitors of dihydrofolate reductase, (b) prostaglandin PGF2α antinidatory analogs, and, (c) dipyridodiazepinone inhibitors of HIV-1 reverse transcriptase (RT). Two general findings from these applications are that grid cell occupancy descriptors associated with the “constant” chemical structure of an analog series can be significant in the 3D-QSAR models and that there is an enormous data reduction in constructing 3D-QSAR models. The resultant 3D-QSAR models can be graphically represented by plotting the significant 3D-QSAR grid cells in space along with their descriptor attributes.