SCORING FUNCTION FOR MOLECULAR ALIGNMENT J. Chem. Inf. Model., Vol. 50, No. 9, 2010 1733 Figure 11. The eight rhinovirus ligands bind in two modes. The carbons are in magenta for one mode (2RM2, 2RR1, 2RS1, and 2RS3) and in cyan for the other mode (2R04, 2R06, 2R07, and 2RS5). the ﬂexible alignments. Of the 57 ligands in the system, only 7 ligands have more than 33 or less than 17 heavy atoms, and 1P5E, 1PKD, 1PXI, 1PXJ, and 1WCC are among them, with 13, 36, 14, 14, and 8 heavy atoms, respectively. Since the pharmacophore model is complex,31 it seems that volumetric overlap is an important factor for alignment. Hence ligands that are much smaller or much larger than average would be difﬁcult to align. Moreover, an important pharmacophore element is the set of two hydrogen-bond donors and one acceptor interacting with the hinge region of the protein. These correspond to pharmacophore features D1, D2, and A1 mentioned in Zou et al.31 and are shown in Figure 4. Out of the 57 ligands, only 4 do not have at least 2 out of these 3 features, and ligands 1DI8, 1P5E, and 1WCC are among them. The HIV ligands are big. All but one have 35 or more heavy atoms. The fact that they are relatively comparable in size (all but three have between 39 and 61 atoms), do not have a homogeneous (spherical) shape, and have rich feature sets might have helped the rigid-body alignment result, because there are not that many possibilities for the molecules to align well. One possibility for our superior results is that we have trained our scoring function using a signiﬁcantly larger data set from the PDB than the version of FLEXS or ROCS that were used. Of all six test systems, the drop in performance in going from the rigid-body to the ﬂexible mode is most pronounced for the HIV system. This is because the HIV ligands are particularly big and ﬂexible. Of the 28 HIV ligands, 5 have 10 rotatable bonds. 7 have between 12 and 16 rotatable bonds. The other 16 have 18 or more rotatable bonds. In comparison, no molecules in the other 5 systems have more than 11 rotatable bonds. For the 13 ligands of the p38 system, our scoring function produced an overall correct rate of 43% and 30% for the rigid-body and ﬂexible alignments, respectively (Table 5). It is worth noting that one of the ligands, 1WBO, is signiﬁcantly smaller than the others (Figure 5). The crystal- lographic alignment of the remaining 12 ligands is given in Figure 6. It can be seen that the ligand 1DI9 (magenta in Figure 6) binds in a mode different from the others. The four ligands 1M7Q, 1OUK, 1OUY, and 1OVE (yellow in Figure 6) also bind in a mode somewhat different from the others. For the remaining 7 ligands, our scoring function actually got 73% of the pairwise cross-alignments correct in the rigid-body mode, and 53% correct in the ﬂexible mode. And for the 16 pairwise cross-alignments of the four ligands 1M7Q, 1OUK, 1OUY, and 1OVE, our scoring function got them all, 100%, correct in the rigid-body mode and 94% (all but one of the 16) correct in the ﬂexible mode. The 13 ligands of the estrogen receptor system can be divided into two groups. Ligands within each group have comparable sizes and can be considered to bind in a similar mode, as can be seen in Figure 7. For the pairwise cross- alignments of all 13 ligands, our scoring function got 59% and 41% correct in the rigid-body and ﬂexible modes, respectively. However, for the group of 6 smaller ligands, we got 94% of the 36 rigid-body cross-alignments correct and 72% of the ﬂexible alignments correct. For the group of 7 larger ligands, we got 92% of the 49 rigid-body cross- alignments correct and 65% of the ﬂexible alignments correct. The crystallographic alignment of the 7 trypsin ligands is given in Figure 8. Ligand 1PPH (dark blue in Figure 8) is signiﬁcantly larger than the others. Ligand 1TNI (cyan in Figure 8) assumes a binding mode different from the others. For the remaining 5 ligands, our scoring function got all 25 cross-alignments correct in both the ﬂexible and rigid-body modes. Figure 9 gives our result for ﬂexibly aligning 1TNJ onto the much larger ligand 1PPH. Our second best scoring solution (Figure 9, bottom) yielded the correct alignment mode. As for our best scoring solution (Figure 9, top), it involves a perfect atom to atom matching for all atoms of 1TNJ. The aromatic ring is mapped to an aromatic ring of 1PPH, all aliphatic carbons are mapped to aliphatic carbons on 1PPH, and the nitrogen atom is mapped to a nitrogen on 1PPH. Figure 10 gives our result for ﬂexibly aligning 1TNL onto 1PPH. Our third best scoring solution (Figure 10, bottom) roughly yielded the correct binding mode. Our best scoring solution (Figure 10, top) involves a matching of atoms similar to that of the best scoring solution of aligning 1TNJ onto 1PPH (Figure 9, top). Our second best scoring solution (Figure 10, middle) also involves a good matching of atoms, with the phenyl ring of 1TNL aligned to a six- membered ring of 1PPH. For the 8 rhinovirus ligands, our scoring function got 50% of the pairwise cross-alignments correct in both the rigid- body and ﬂexible modes. As shown in Figure 11, all eight ligands have a long shape and are almost symmetric. There is a heterocyclic ring on either end of each ligand, connected by a long, ﬂexible linker chain. As noted in the original publication for the X-ray structures,32 the ligands have two binding modes, one being the inverse of the other, as shown in Figure 11. It is easy for the alignment algorithm to