SCORING FUNCTION FOR MOLECULAR ALIGNMENT J. Chem. Inf. Model., Vol. 50, No. 9, 2010 1731 Figure 6. Different binding modes of the p38 ligands. 1DI9 is in magenta. 1M7Q, 1OUK, 1OUY, and 1OVE are in yellow. Figure 7. Two binding modes of the ESR1 ligands. The 6 smaller ligands (1A52, 1GWQ, 1L2I, 1X7E, 1X7R, and 3ERD) are in cyan. The 7 larger ligands (1R5K, 1SJ0, 1UOM, 1XP1, 1XP9, 1XQC, and 2BJ4) are in magenta. Figure 8. Crystallographic alignment of the 7 trypsin ligands. Carbon atoms of 1PPH are in dark blue. Those of 1TNI are in cyan. The remaining ligands are 1TNH, 1TNJ, 1TNK, 1TNL, 3PTB. To summarize, it was found that a good scoring function is of the form given by the terms of Table 1, except terms T6 and T7, with the values of the various coefﬁcients given in Table 3. Uncertainty Considerations. For each of the parameters considered, only one run was performed. However, there was a considerable number of ligand-pocket systems, and in each system, there was a considerable number (at least 25, but often much more) of pairs of source-target ligands. There- fore random noise can be expected to have averaged out. More importantly, the fact that there are smooth trends in the numbers in Tables 2a-2h, as the parameters were varied, serves to conﬁrm that the numbers are accurate enough for our purpose of locating the optimal values for the parameters. Validation Runs: The Procedure. MOE’s ﬂexible align- ment (FlexAlign) functionality22 was used for the validation runs. For rigid-body alignments, conformers from the PDB were used as the input. FlexAlign generated random poses of the source molecule superposed onto the target molecule and optimized the alignment score S, while keeping the molecules rigid. For the ﬂexible alignments, for each source molecule, one randomized conformation was used as input. FlexAlign generated a random conformer from this input, randomly superposed it onto the target molecule, and then optimized this pose under the inﬂuence of the alignment score between the source and target molecules. The target molecule remained ﬁxed throughout the process. In order to avoid unrealistic conformations, the internal energy U of the source molecule must also be considered alongside the alignment score S. For the internal energy, we used the MMFF94 force ﬁeld22,30 with a distance-dependent dielectric. Pose optimiza- tion was carried out by minimizing the effective energy, E, which was deﬁned by E ) U - kS Alignment solutions were also ranked according to their E values. A value of 4 kcal/mol was used for k. This value seemed to give a good balance between the internal energy U and the alignment score S. The difference in the force ﬁeld energy U between the conformation of the source molecule in the top scoring (i.e., the one with the lowest E value) solution and its corresponding local energy minimum was generally small. The average of this difference (over the n × n cross-alignments for each system) for the CDK2, HIV, p38, ESR1, trypsin, and rhinovirus systems were, respectively, 0.32, 0.76, 0.25, 0.33, 0.25, 0.25 kcal/mol per heavy atom. In contrast, the average of the difference in the internal energy U between the ligand conformer in the crystal structure and its corresponding local energy minimum is over 1 kcal/mol per heavy atom for all the six systems. We also investigated whether the value of the alignment score S or the effective energy E gives an indication of the goodness of the alignment. Unfortunately there did not seem to be any correlation (unpublished results). Validation Runs: The Results. Our results were ﬁrst compared with those in Table 4 of Proschak et al.6 This involved pairwise rigid-body alignments on a system of eight thermolysin ligands. For each ligand pair, one ligand was used as the target, while the other was used as the source. Self-alignments were not performed. Therefore there was a total of 28 cross-alignments. An alignment was considered successful if the top scoring pose had a heavy atom rmsd of under 2 Å from the correct answer. Our results, together with those obtained by Proshak et al.,6 are tabulated in Table 4.