44 J. Chem. Inf. Model., Vol. 50, No. 1, 2010 CLARK Figure 10. Portion of a dendrogram fragment display, with selected leaf nodes indicated. Figure 11. Selected core fragments of COX2 inhibitors. patterns, the ﬁnal spatial orientation using 2D structures reveals the alignment shown. Figure 12 shows a portion of a radial dendrogram, composed from the hierarchy of COX-2 inhibitors, using the same algorithm as described in the previous section. One sub-branch is shown in its entirety, and the structures of six of these compounds are shown. All of these compounds are based on the same 1,2-diphenylimidazole core, with a triﬂuoromethyl substituent in the 4-position. The activity values vary from 68 to 0.03 µ M. Compounds a and b, as well as all of the compounds that are arranged in between them in the linear cluster, feature a sulfonamide substituent in the same position on the phenyl ring at the 1-position, and all of them exhibit high activity, as can be seen by the bright green color coding. The remainder of the compounds in this sub-branch have a methylsulfonyl substituent in place of sulfonamide, and their activity is much more varied and is determined by the substitution pattern on the phenyl ring at the 2-position. For example, compounds c and d, which have a small substituent in the meta position, exhibit strong activity, while compounds e and f, which have larger substituents, exhibit weaker activity. Each of the compounds shown has a meta-substituted phenyl ring at the 2-position, and in each case, one of the meta substituents is depicted so that it is oriented at approximately the 2 o’clock position. While an unconstrained depiction algorithm will be likely to make these layout choices on the grounds of congestion, the symmetrical phenyl substituents are explicitly mapped to each other on an atom- by-atom basis, in order to maximize the topological similarity of the interstructure mapping. A single depiction is chosen for the precursor fragment, and applied to all descendents, which ensures that the most similar substituents are placed at a consistent position.