Template modeling score

TM-score between two protein structures (e.g., a template structure and a target structure) is defined by

${\displaystyle {\text{TM-score}}=\max \left[{\frac {1}{L_{\text{target}}}}\sum _{i}^{L_{\text{common}}}{\frac {1}{1+\left({\frac {d_{i}}{d_{0}(L_{\text{target}})}}\right)^{2}}}\right]}$

where ${\displaystyle L_{\text{target}}}$ is the length of the amino acid sequence of the target protein, and ${\displaystyle L_{\text{common}}}$ is the number of residues that appear in both the template and target structures. ${\displaystyle d_{i}}$ is the distance between the ${\displaystyle i}$th pair of residues in the template and target structures, and ${\displaystyle d_{0}(L_{\text{target}})=1.24{\sqrt[{3}]{L_{\text{target}}-15}}-1.8}$ is a distance scale that normalizes distances.

When comparing two protein structures that have the same residue order, ${\displaystyle L_{\text{common}}}$ reads from the C-alpha order number of the structure files (i.e., Column 23-26 in Protein Data Bank (file format)). When comparing two protein structures that have different sequences and/or different residue orders, a structural alignment is usually performed first, and TM-score is then calculated on the commonly aligned residues from the structural alignment.

An often used structural similarity measure is root-mean-square deviation (RMSD). Because RMSD ${\displaystyle ={\sqrt {\sum _{i=1}^{L}d_{i}^{2}/{L}}}}$ is calculated as an average of distance error (${\displaystyle d_{i}}$) with equal weight over all residue pairs, a large local error on a few residue pairs can result in a quite large RMSD. On the other hand, by putting ${\displaystyle d_{i}}$ in the denominator, TM-score naturally weights smaller distance errors more strongly than larger distance errors. Therefore, TM-score value is more sensitive to the global structural similarity rather than to the local structural errors, compared to RMSD. Another advantage of TM-score is the introduction of the scale ${\displaystyle d_{0}(L_{\text{target}})=1.24{\sqrt[{3}]{L_{\text{target}}-15}}-1.8}$ which makes the magnitude of TM-score length-independent for random structure pairs, while RMSD and most other measures are length-dependent metrics.

The Global Distance Test (GDT) algorithm, and its GDT TS score to represent "total score", is another measure of similarity between two protein structures with known amino acid correspondences (e.g. identical amino acid sequences) but different tertiary structures.[4] GDT score has the same length-dependence issue as RMSD, because the average GDT score for random structure pairs has a power-law dependence on the protein size.[1]

• RMSD — a different structure comparison measure
• GDT — a different structure comparison measure
• Longest continuous segment (LCS) — A different structure comparison measure
• Global distance calculation (GDC_sc, GDC_all) — Structure comparison measures that use full-model information (not just α-carbon) to assess similarity
• Local global alignment (LGA) — Protein structure alignment program and structure comparison measure

• TM-score webserver — by the Yang Zhang research group. Calculates TM-score and supplies source code.
• GDT and LGA description services and documentation on structure comparison and similarity measures.