RMSD and TM-score

Purpose

The RMSD and the TM-score [1] are two distinct metrics used to evaluate the structural similarity between protein models or conformations. RMSD measures the average distance between the backbone atoms of superimposed structures; a lower RMSD indicates greater similarity. The TM-score is instead designed to be sensitive to the global topology of the protein, and is normalised by the chain length.

Only the RMSD contributes to the benchmark score. The TM-score normalises distances by \(d_0 = 1.24 (L - 15)^{1/3} - 1.8\), which is undefined below \(L = 15\) and is floored at 0.5 Å by TM-align, so it is not perfectly calibrated for chains as short as the ones in this benchmark (\(L = 10\) to \(36\)). Its absolute values should therefore not be read against the customary “above 0.5 indicates a similar fold” cutoff, which was established on domain-sized proteins. It remains informative for comparing models against each other on the same system, and for following how a single trajectory evolves over time.

The results are presented as the average values over the trajectory. Evolution of the metrics over time is additionally plotted.

Description

The implementation works as follows:

  • The trajectory is loaded as an mdtraj.Trajectory object (see mdtraj) and the solvent is removed.

  • Carbon alpha atoms are extracted from the trajectory and from the experimental reference structure.

  • The RMSD is computed in Å with mdtraj.rmsd, using the known 1:1 atom correspondence between the trajectory and the reference under an RMSD-optimal (Kabsch) superposition. A sequence aligner is deliberately not used here: both structures are the same molecule, so there is no correspondence to infer, and an aligner is free to drop badly displaced residues as gaps, which makes the result non-monotonic in the actual structural deviation.

  • The TM-score is computed on the same carbon alpha atoms with the tm_align function of tmtools.

Interpretation

A RMSD closer to 0 indicates a better match to the reference structure. The score threshold is 2.0 Å, which is the conventional definition of the folded state for miniproteins of this size [2].

The TM-score ranges from 0 to 1, where 1 indicates a perfect match, subject to the normalisation caveat described under Purpose above.

References