TM-score

Unlike RMSD, which increases with protein size, TM-score is normalized by a length-dependent scale factor. This ensures that a score of 0.5 means the same degree of structural similarity regardless of whether the protein has 50 or 500 residues.

• d0 normalization: The metric uses a distance scale d0 = 1.24 * ∛(N - 15) - 1.8 to normalize residue pair distances
• Statistical robustness: Random structure pairs converge to a TM-score of ~0.17, while scores >0.5 indicate the same fold
• Size-independent comparison: Enables fair benchmarking across diverse protein families and domains

TM-score maps structural similarity to a bounded range where 0 represents completely dissimilar structures and 1 represents identical structures. This linear scale provides immediate interpretability for assessing model quality.

• Fold discrimination threshold: A TM-score ≥ 0.5 reliably indicates that two proteins share the same global fold topology
• CASP benchmark standard: Adopted as an official metric in the Critical Assessment of Structure Prediction experiments
• Complementary to RMSD: While RMSD measures absolute deviation in Ångströms, TM-score captures topological agreement

TM-score applies a sigmoidal weighting function to each aligned residue pair, down-weighting distant residue pairs that would otherwise dominate the score. This focuses the metric on the core structural alignment.

• Weighting formula: Each residue pair contributes 1 / (1 + (dᵢ/d₀)²) to the final score
• Outlier suppression: Large local deviations from distant domains or flexible loops are naturally penalized less
• Global topology focus: The weighting emphasizes overall fold agreement over local fluctuations

TM-score is computed after an optimal structural alignment that maximizes the metric itself, not a separate objective like minimum RMSD. This self-consistent approach ensures the superposition is optimized for topological similarity.

• TM-align algorithm: Uses dynamic programming and iterative refinement to find the rotation matrix and residue correspondence that maximize TM-score
• Sequence-order dependent: Unlike GDT-TS, TM-score respects sequential residue ordering, making it sensitive to circular permutations
• Heuristic search: Employs gapless threading and secondary structure matching for initial alignment seeding

TM-score belongs to a family of topology-focused metrics that evaluate structural similarity by rewarding correctly aligned core regions rather than penalizing flexible loops or disordered termini.

• GDT-TS comparison: Global Distance Test–Total Score uses fixed distance thresholds (1, 2, 4, 8 Å) while TM-score uses a continuous weighting function
• MaxSub similarity: Both metrics emphasize the largest well-aligned substructure, but TM-score normalizes by protein size
• Complementary usage: CASP reports both GDT-TS and TM-score to provide a multi-faceted assessment of prediction quality

The expected TM-score for random unrelated protein pairs is approximately 0.17, with a standard deviation that decreases as protein length increases. This well-characterized null distribution enables rigorous statistical assessment.

• P-value estimation: The probability of observing a given TM-score by chance can be estimated from the extreme value distribution
• Fold space coverage: TM-score distributions across the PDB reveal clustering patterns corresponding to known fold classifications
• Normalization validation: The d0 parameter was empirically calibrated to produce length-independent random scores across the protein size range