1728 J. Chem. Inf. Model., Vol. 50, No. 9, 2010 Table 2c. Parameter Optimization for wHH using the MOE Deﬁnition for Hydrophobic Atomsa wHH n25 0 6.10 0.5 6.33 1 6.36 2 6.23 4 5.90 8 5.44 a The scoring function at this stage is (T0 + T1 + T2 + T3). The new term is T3 and corresponds to the attraction between hydrophobic atoms. Refer to Table 1 for the details of this term. This table gives the average number of good poses, n25, within the top 25 scoring poses for various values of wHH. Table 2d. Parameter Optimization for wHH, where Hydrophobic Atoms Are Deﬁned as Atoms That Are at Least Two Bonds Away from any Hydrogen-Bonding Atoma wHH n25 0 6.10 0.5 6.30 1 6.32 2 6.17 4 5.81 8 5.29 a The scoring function at this stage is (T0 + T1 + T2 + T3). The new term is T3 and corresponds to the attraction between hydrophobic atoms. Refer to Table 1 for the details of this term. This table gives the average number of good poses, n25, within the top 25 scoring poses for various values of wHH. Table 2e. Parameter Optimization for wR1 using the MOE Deﬁnition for Hydrophobic Atomsa wR1 n25 0 6.36 -0.125 6.38 -0.25 6.40 -0.5 6.44 -1 6.45 -2 6.36 -4 5.92 -8 4.56 a The scoring function at this stage is (T0 + T1 + T2 + T3 + T4 + T5). The new terms T4 and T5 correspond to the repulsion between hydrophobic and hydrogen-bonding 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 wR1. Table 2f. Parameter Optimization for wR1, where Hydrophobic Atoms Are Deﬁned as Atoms That Are at Least Two Bonds Away from any Hydrogen-Bonding Atoma wR1 n25 0 6.32 -0.125 6.33 -0.25 6.34 -0.5 6.35 -1 6.34 -2 6.23 -4 5.89 -8 5.22 a The scoring function at this stage is (T0 + T1 + T2 + T3 + T4 + T5). The new terms T4 and T5 correspond to the repulsion between hydrophobic and hydrogen-bonding 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 wR1. ignored. The only parameter to be optimized was R. Obviously a smaller value for R would result in a more diffuse Gaussian function. Consider the simple case to align one atom (the source) onto a diatomic molecule (the target). This is similar to trying to align methane, with one heavy atom, onto ethane, with two heavy atoms. Suppose the internuclear distance of the diatomic molecule is 1.5 Å (for comparison, a C-C bond in a benzene ring is about 1.40 Å, and a C-C bond in an ethane is about 1.54 Å). The shapes of the scoring function for three different values of R are plotted in Figure 2. For large values of R, the source atom will see a score with two distinct peaks located very close to the two target atoms. It will have a strong tendency to align with either one of the target atoms. For example, if R is 2.0 Å-2 (the blue curve of Figure 2), then the distance between the peaks will be 1.46 Å. The value of the score at the trough midway between the peaks will be 64% of the CHAN AND LABUTE Table 2g. Parameter Optimization for wR2a wR2 n25 0 6.45 -0.125 6.45 -0.25 6.45 -0.5 6.44 -1 6.43 -2 6.40 a The scoring function at this stage is (T0 + T1 + T2 + T3 + T4 + T5 + T6 + T7). The new terms T6 and T7 correspond to the repulsion between hydrogen-bond donor atoms that are not acceptors and hydrogen-bond acceptor atoms that are not donors. 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 wR2. Table 2h. Parameter Optimization for wPF and Rpa wPF n25 n25 n25 n25 0 6.45 6.45 6.45 6.45 0.25 6.48 6.51 6.54 6.57 0.5 1 For Rp ) 0.5 Å-2 6.50 6.52 For Rp ) 0.25 Å-2 6.54 6.60 For Rp ) 0.125 Å-2 6.61 6.68 For Rp ) 0.0625 Å-2 6.64 6.69 2 6.48 6.61 6.71 6.66 4 6.35 6.52 6.60 6.44 8 6.01 6.22 6.28 5.98 a The scoring function at this stage is (T0 + T1 + T2 + T3 + T4 + T5 + T8 + T9). The new terms T8 and T9 correspond to the attraction between hydrogen-bond donor/acceptor projected features. 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 wPF and Rp. Table 3. Optimal Parameters for the Scoring Functiona Ra 0.5 Å-2 Rp 0.125 Å-2 wDA 4 wHH 1 wR1 -1 wPF 2 a The optimal scoring function consists of the terms T0-T5, T8, and T9, as given in Table 1, with the various parameters as given by this table. Table 4. Success Rates of the 28 Rigid-Body Cross-Alignments of 8 Thermolysin Ligands Using Various Methodsa SURFCOMP,24 electrostatic potential SURFCOMP,24 lipophilic potential Cosgrove et al.25 Shapelets6 current work 75% 71% 50% 71% 93% a The eight thermolysin ligands have PDB ID’s 1THL, 1TLP, 1TMN, 3TMN, 4TMN, 5TLN, 5TMN, and 6TMN. For each pair of nonidentical ligands, one ligand was chosen as the template, and the other ligand was aligned onto the template. If the top scoring solution yielded an rmsd of under 2 Å with the crystallographic pose for the heavy atoms, then it was considered successful. This table gives the success rates for the 28 cases, as reported on Table 4 of Proschak et al.6 height of the peaks. When R decreases to 1.2 Å-2 (the black curve of Figure 2), the peaks will move toward each other, away from the atomic positions. The distance between the peaks will drop to 1.18 Å, and the trough to peak height ratio of the score will increase to 94%. In other words, the score has already very much smoothed out the atomic positions. The source atom can settle for any position between the two atoms with little change on the score. Given a scoring scheme and an initial aligned pose between two rigid ligands, one can reﬁne the alignment