# Template modeling score

In bioinformatics, the template modeling score or TM-score is a measure of similarity between two protein structures with different tertiary structures. The TM-score is intended as a more accurate measure of the quality of full-length protein structures than the often used RMSD and GDT measures. The TM-score indicates the difference between two structures by a score between ${\displaystyle (0,1]}$, where 1 indicates a perfect match between two structures.[1] Generally scores below 0.20 corresponds to randomly chosen unrelated proteins whereas structures with a score higher than 0.5 assume roughly the same fold.[2] A quantitative study [3] shows that proteins of TM-score = 0.5 have a posterior probability of 37% in the same CATH topology family and of 13% in the same SCOP fold family. The probabilities increase rapidly when TM-score > 0.5. The TM-score is designed to be independent of protein lengths.

## The equation

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

where ${\displaystyle L_{\text{target}}}$ and {\displaystyle L_{\text{aligned}}} are the lengths of the target protein and the aligned region respectively. ${\displaystyle d_{i}}$ is the distance between the ${\displaystyle i}$th pair of residues and

${\displaystyle d_{0}(L_{\text{target}})=1.24{\sqrt[{3}]{L_{\text{target}}-15}}-1.8}$

is a distance scale that normalizes distances.