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Visualization of structure-activity relationships (SARs) in compound data sets substantially contributes to their systematic analysis. For SAR visualization, different types of activity landscape (AL) representations have been introduced. Three-dimensional (3D) AL models in which an activity hypersurface is constructed in chemical space are particularly intuitive because these 3D ALs are reminiscent of "true" (geographical) landscapes. Accordingly, the topologies of 3D AL representations can be immediately associated with different SAR characteristics of compound data sets. However, the comparison of 3D ALs has thus far been confined to visual inspection and qualitative analysis. We have focused on image analysis as a possible approach to facilitate a quantitative comparison of 3D ALs, which would further increase their utility for SAR exploration. Herein, we introduce a new computational methodology for quantifying topological relationships between 3D ALs. Images of color-coded 3D ALs were converted into top-down views of these ALs. From transformed images, different categories of shape features were systematically extracted, and multilevel shape correspondence was determined as a measure of AL similarity. This made it possible to differentiate between 3D ALs in quantitative terms.

Quantitative Comparison of Three-Dimensional Activity Landscapes of Compound Data Sets Based upon Topological Features