Figure 2. Performance of various alignment methods and similarity measures in identifying common homologs and/or DS-related homologs.

The binary classification performance of several conventional alignment methods in distinguishing homologous from non-homologous structures is shown in (a), while their performances in distinguishing DS homologs from non-homologs and common homologs are shown in (b) and (c), respectively. The results of the binary classification tests for several similarity measures to distinguish homologs from non-homologs are summarized in (d). The results of distinguishing DS from non-homologs and common homologs by those measures are shown in (e) and (f), respectively. In these experiments, which involve Dataset L, a number of known DS-related homologous pairs (L_ds), common homologous pairs (L_ch) and non-homologous pairs (L_nh) of protein structures were used as positive or negative data for different purposes. In (a) and (d) both L_ds and L_ch were used as positive data, and L_nh served as the negative data, in (b) and (e) L_ds was the positive and L_nh was the negative data, whereas in (c) and (f) L_ds and L_ch were respectively viewed as the positive and negative data. The x-axes indicate that proteins pairs with globally superimposable structures are gradually filtered out as the alignment ratio cutoff decreases; meanwhile, the average MCC obtained by five-fold cross-validations is plotted on the y-axes. TM-align [31], CE [33] and FAST [30] are order-dependent structural alignment methods. FASE [58] and SHEBA [59] can perform order-independent alignments. SARST acquires a more flexible nature than conventional methods by using a structure linear-encoding methodology [34]. BLAST [42] is a widely-used sequence alignment method. The MCCs of various alignment methods shown in (a)–(c) were determined based on a structural similarity measure known as structural diversity (S-div) [41] except those for BLAST, which were based on a normalized sequence similarity score (refer to Table S2). See the RESULTS and DISCUSSION Sections for explanations of these results. The structural similarity measures assessed in (d)–(f) include the Q-score [43], S-div, qCOPS [56], [60], MI [61], SI [61], S-score [44], RMSD, RMSD over the alignment size and the Z-score of TM-align.