Fig. 1. Constructing a local coordinate frame about a tetrahedral C<sub>α</sub> coordinate centre. The C<sub>α</sub> atom is placed at the origin, the.

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Fig. 1. Constructing a local coordinate frame about a tetrahedral C<sub>α</sub> coordinate centre. The C<sub>α</sub> atom is placed at the origin, the C atom on the negative z axis, and the N atom in the positive x region of the xz plane From: Fast protein structure alignment using Gaussian overlap scoring of backbone peptide fragment similarity Bioinformatics. 2012;28(24):3274-3281. doi:10.1093/bioinformatics/bts618 Bioinformatics | © The Author 2012. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Fig. 2. Calculating local pair-wise similarity scores Fig. 2. Calculating local pair-wise similarity scores. The local-frame distribution of all C<sub>α</sub> coordinates from the CATH database (left) is used to calculate the Gaussian width, σ<sub>k</sub>, for each up-stream and down-stream residue position. For a given pair of residues, i and j, the ‘K-score’ is calculated as a product of Gaussian overlap integrals (Equation 6) using the local frame pair-wise C<sub>α</sub> distances (right) From: Fast protein structure alignment using Gaussian overlap scoring of backbone peptide fragment similarity Bioinformatics. 2012;28(24):3274-3281. doi:10.1093/bioinformatics/bts618 Bioinformatics | © The Author 2012. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Fig. 3. An illustration of the principle behind structural alignment using local coordinate frame COM vectors. If two similar proteins are superposed, the COM vectors from equivalent aligned pairs of residues will often be co-linear, as shown here for PDB codes 1cew and 1 mol. Conversely, a pair of similar proteins may be superposed by aligning their COM vectors From: Fast protein structure alignment using Gaussian overlap scoring of backbone peptide fragment similarity Bioinformatics. 2012;28(24):3274-3281. doi:10.1093/bioinformatics/bts618 Bioinformatics | © The Author 2012. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Fig. 4. Cartoon representations of the SSE assignments calculated by Stride, DSSP and Kpax for ubiquitin (PDB code: 1ubq). Supplementary Figure S1 shows nine further examples From: Fast protein structure alignment using Gaussian overlap scoring of backbone peptide fragment similarity Bioinformatics. 2012;28(24):3274-3281. doi:10.1093/bioinformatics/bts618 Bioinformatics | © The Author 2012. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Fig. 5. The structural alignments calculated by TM-Align and Kpax for the pair 1fxiA/1ubqA. Arrows highlight particularly tight regions of the Kpax alignment compared with the TM-Align alignment. SSEs are drawn using Stride assignments. See Supplementary Figure S3 for a large colour version From: Fast protein structure alignment using Gaussian overlap scoring of backbone peptide fragment similarity Bioinformatics. 2012;28(24):3274-3281. doi:10.1093/bioinformatics/bts618 Bioinformatics | © The Author 2012. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Fig. 6. The structural alignments calculated by TM-Align and Kpax for the pair d4aaha_/d1gofa3. Arrows mark especially tight regions of the Kpax alignment. See Supplementary Figure S6 for a large colour version From: Fast protein structure alignment using Gaussian overlap scoring of backbone peptide fragment similarity Bioinformatics. 2012;28(24):3274-3281. doi:10.1093/bioinformatics/bts618 Bioinformatics | © The Author 2012. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Fig. 7. Aggregate ROC comparison of Kpax, TM-Align and Yakusa using 213 structural queries against the CATH database (version 3.4, comprising 11 330 domains at the 35% sequence identity level) From: Fast protein structure alignment using Gaussian overlap scoring of backbone peptide fragment similarity Bioinformatics. 2012;28(24):3274-3281. doi:10.1093/bioinformatics/bts618 Bioinformatics | © The Author 2012. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com