1726 J. Chem. Inf. Model., Vol. 50, No. 9, 2010 compared their result with two previous alignment meth- ods.24,25 We performed validation runs on these thermolysin ligands to see how our scoring function fared. Chen et al.23 studied the geometric accuracy of aligning small molecules using ROCS26 and FLEXS.27 They used eight protein targets as test sets: HIV protease, cyclin- dependent kinase 2 (CDK2), estrogen receptor 1 (ESR1), mitogen-activated protein kinase 14 (p38), thermolysin, human rhinovirus capsid, elastase, and trypsin. Six of these (all but thermolysin and elastase) consist exclusively of structures from the publicly accessible PDB.17 We used these six systems for validation runs. Both rigid-body alignments and ﬂexible alignments were compared. For training a scoring function for the validation runs, all systems that contain any PDB entries involved in the test sets were naturally excluded. Compiling the Training Set. Ligands from identical or almost identical pockets (see below for details) from the PDB were used for training the scoring function. Only PDB entries with a resolution of better than 2.5 Å were used. Ligands were deﬁned as freestanding molecules with no more than 300 heavy atoms and 10 residues. In order to exclude waters and very small molecules, each ligand must have at least one pair of heavy atoms separated by three bonds. Ligands were also required to be reasonably drug-like. Ligands without carbon atoms or with exotic elements (elements other than C, H, N, O, S, P, F, Cl, Br, and I) were discarded. Hemes and sugars were excluded. ATP analogs were excluded because their large population in the PDB would likely skew the data. Ligands without any rings were also excluded so as to remove the lipids without excluding any drug-like compounds. We ﬁrst obtained a list of protein domains from Structural Classiﬁcation of Proteins (SCOP).28 For each domain, all PDB entries containing that domain were superposed using the protein backbone of that domain. Ligands were then detected around the domain. Overlapping ligands were clustered into groups so that each group would correspond to one pocket. For each pocket, a ﬁne superposition was performed based on the R carbons common to all pockets. Since we started from SCOP domains, it was possible that pockets within a group could involve different residues or have different geometries. For our purpose of scoring function training, it may not be very meaningful to study the alignment of ligands in different pockets. Therefore we divided each pocket into subgroups in the following way. We ﬁrst collected all R carbons within 7.5 Å of any ligand. These were then clustered using single linkage clustering with a cutoff of 1.0 Å. Clusters with no R carbon within 6.0 Å of any ligand were discarded. A table was then constructed with each row corresponding to one protein and each column corresponding to one R carbon cluster. A cell of the table has the residue type as the entry if the protein contributes to that cluster. The pocket similarity between a pair of proteins was deﬁned to be the fraction of table columns that are identical (i.e., same residue type, or empty cell, for all cells in the column). After the pocket similarities between all protein pairs were determined, the proteins were clustered, using complete linkage and pocket similarity as the metric, with a cutoff of 0.8. In other words, any two pockets in the same group had at least 80% of the table columns identical. Each original pocket group might thus be divided into CHAN AND LABUTE Figure 1. Aspartate aminotransferase ligands from their aligned PDB structures. multiple groups. For each resulting group, a ﬁne superposi- tion on the 3D structures was performed again using R carbons common to all pockets, since the deﬁnition of the pocket might have changed due to the change in the content of the ligand set. This whole procedure was repeated until there was no new division of the pocket groups. Upon inspection, some systems were found to be unin- teresting in the sense that the aligned ligands only displayed one type of structure at most regions of the pocket. An example is given in Figure 1. Studying this type of system would not give us more information than studying self- alignments. Hence they were discarded from the training set. It is desirable to have the conformational space reasonably covered when dummy poses were generated. Therefore the training ligands were restricted to those having no more than 12 rotatable bonds. Finally, to ensure diversity, a set of representative ligands was chosen for each system such that no pair of representatives had a Tanimoto similarity of over 0.8 on their MACCS ﬁngerprints. Systems with fewer than ﬁve representatives were discarded. Only 100 systems remained after these ﬁnal ﬁlters, and 85 systems had no more than 20 representative ligands. The highest number of representatives in a system was 53. This is our comprehensive aligned small molecules data set. For training a scoring function for the validation runs, 11 of the 100 systems in the comprehensive data set were excluded because they contained entries that would be used in the runs. This was more than the number of test systems (7) because some test systems (e.g., the 57 ligands in the CDK2 system) had variations in the pocket residue composi- tion or geometry and were hence subdivided into more than one pocket group when our comprehensive data set was constructed. Dummy Pose Generation. To keep things simple, the training of the scoring function was based on trying to align a ﬂexible source ligand onto a rigid target ligand. The input conformation of the source ligand was randomized from the crystal conformation. Dummy poses were generated by making small adaptations to the MOE docking engine,22 as described below. For each system of n aligned ligands, all n × n pairs of ligands were considered with the following requirement. The fraction of heavy atoms in the target that lie within 2 Å of