How root-mean-square distance (r.m.s.d.) values depend on the resolution of protein structures that are compared

The most popular estimator of structural similarity is the root-mean-square distance (r.m.s.d.) between equivalent atoms, computed after optimal superposition of the two structures that are compared. It is known that r.m.s.d. values do not depend only on conformational differences but also on other features, for example the dimensions of the structures that are compared. An open question is how they might depend on the accuracy of the experimentally determined protein structures. Given that the accuracy of the protein crystal structures is generally estimated through the crystallographic resolution, it is important to know the dependence of the r.m.s.d. on the crystallographic resolution of the two structures that are compared. 14458 protein structure pairs of identical sequence were compared and the resulting r.m.s.d. values were normalized to 100-residue length to avoid the bias introduced by the dependence of the r.m.s.d. values on the protein-pair dimensions. On average, smaller r.m.s.d. values are associated with protein structure pairs at better resolution and the r.m.s.d. values tend to increase if the two proteins that are compared have been refined at different resolutions. For crystallographic resolutions ranging between 1.6 and 2.9 Angstrom, both relationships appear to be linear: r.m.s.d. = -0.73 + 0.48 resolution and delta_r.m.s.d. = 0.20 + 0.30 delta_resolution ('delta' indicating difference). Although the linearity of these relationships is not expected to hold outside the 1.6-2.9 Angstrom resolution range, they are useful in making the r.m.s.d. values more reliable.