SCORING FUNCTION FOR MOLECULAR ALIGNMENT any heavy atom of the source must exceed 0.5, and the fraction of heavy atoms in the source that lie within 2 Å of any heavy atom of the target must exceed 0.75. This excluded ligands with different binding modes and ensured that no source ligand was substantially larger than the target. Conformers of the source ligand were systematically generated by assigning favorable torsion angles. If this resulted in more than 5000 conformers, a random subset of the systematically generated conformers would be used. Only conformers with severe atomic overlaps were discarded. This is because we envisioned that when the scoring function is used to distinguish poses with the correct binding mode, any poses that are ﬁshed out can be reﬁned to improve the pose geometry and any atomic overlap within the molecule will be relieved. For each source-target pair, 15 000 dummy alignment poses were generated, one at a time. Each time, a random set of three heavy atoms on the target ligand was chosen, together with a random conformer of the source ligand. Triplets of heavy atoms on the source ligand, which formed a triangle similar to that formed by the three chosen target atoms, were used to align the source ligand onto the target ligand. Poses whose root-mean-square deviation (rmsd) for the heavy atoms was under 1.5 Å were considered duplicated, and only one copy was kept. RESULTS AND DISCUSSION Scoring Function Training. For each scoring function, the scores for all dummy poses were calculated. For each set of alignments involving a particular pair of source and target ligands, we counted the number of “good” poses, n25, among the top 25 scoring poses. As for whether a pose is “good” or not, we used fuzzy logic. Poses with an rmsd (heavy atoms only) from the correct pose of under 2.0 Å were considered good. Poses with an rmsd of over 3.0 Å were considered not good. Poses with an rmsd between 2.0 and 3.0 Å were considered partial good poses, with the “partiality” decreasing linearly from 1 to 0. For each system (i.e., same pocket), we averaged the number of good poses for all source-target pairs in the system. We then averaged these averaged numbers over all 89 training systems. The higher this ﬁnal averaged number was, the better the scoring function was. The receiver operating characteristic (ROC) curve is often used to measure the success of scoring functions for virtual screening.29 In short, the ROC curve plots the fraction of true positives recovered (out of all active compounds) against the fraction of false positives obtained (out of all inactive compounds), as the cutoff value varies. It is generally considered that the bigger the area under the curve, the better is the scoring function. We felt that, for our purpose, using the area under the ROC curve was not as suitable as using “the number of good poses amongst the top 25”, since we generally can only afford to consider a limited number of top scoring poses. Hence all but the very beginning part of the ROC curve would be of signiﬁcance to us. As for why 25? We think that human inspection can typically handle 10 or so poses. On the other hand, if a thorough reﬁnement is desired as part of an automatic process, then it would be reasonable to intensively process up to about 100 poses per ligand. Hence here we used the “top 25 poses”. As a precaution, we repeated all the J. Chem. Inf. Model., Vol. 50, No. 9, 2010 1727 Table 2a. Parameter Optimization for Raa Ra (Å-2) n25 0.06 3.10 0.125 4.11 0.175 4.44 0.25 4.67 0.35 4.79 0.5 4.83 0.7 4.76 a The scoring function at this stage is T0, the volume overlap term. Refer to Table 1 for details of T0. This table gives the average number of good poses, n25, within the top 25 scoring poses for various values of Ra. Figure 2. How the scoring function is controlled by the parameter R, for the case of a target molecule consisting of two atoms, located at positions -0.75 and 0.75. For a source atom to be superimposed onto the target molecule, the scoring function is exp(-Rr12) + exp(-Rr22), where r1 and r2 are the distances from the source atom to the two target atoms. The scoring functions corresponding to R values of 2.0, 1.5, and 1.2 are plotted in blue, red, and black, respectively. Table 2b. Parameter Optimization for wDAa wDA n25 0 4.83 0.5 5.28 1 5.61 2 5.98 4 6.10 8 5.85 16 5.40 32 4.99 a The scoring function at this stage is (T0 + T1 + T2). The new terms are T1 and T2, which correspond to the attraction between hydrogen-bond donor/acceptor atoms. Refer to Table 1 for the details of these terms. This table gives the average number of good poses, n25, within the top 25 scoring poses for various values of wDA. calculations and validation runs using the “top 100 poses” instead of the “top 25”. It turned out that only one out of the six optimized parameters for the scoring function would come out different, and the quality of the of validation runs remained very similar. The details are given in Section A of the Supporting Information. As mentioned previously, the constituent terms of the scoring function are given in Table 1. The scoring function was built up term by term. At each stage, only one (or two) parameter was introduced. This parameter was varied, and the most favorable value for it was picked. We then proceeded to optimize the next parameter. The optimization procedure is captured in Tables 2a-2h. Each table corre- sponds to one stage of optimization where one (or two) parameter was optimized. The resulting numbers of good poses among the top 25, n25, corresponding to the various values of the parameter being optimized are given in the tables. The optimal value of the parameter and its corre- sponding value of n25 are highlighted in bold. We started by including only the volume overlap term (T0 in Table 1) in the scoring function. In other words, to a ﬁrst approximation, the bigger the volume overlap between two molecules, the better was the score. In order to make the scoring function quick to calculate, hydrogen atoms were