Superimposition of protein structures with dynamically weighted RMSD

In protein modeling, one often needs to superimpose a group of structures for a protein. A common way to do this is to translate and rotate the structures so that the square root of the sum of squares of coordinate differences of the atoms in the structures, called the root-mean-square deviation (RMSD) of the structures, is minimized. While it has provided a general way of aligning a group of structures, this approach has not taken into account the fact that different atoms may have different properties and they should be compared differently. For this reason, when superimposed with RMSD, the coordinate differences of different atoms should be evaluated with different weights. The resulting RMSD is called the weighted RMSD (wRMSD). Here we investigate the use of a special wRMSD for superimposing a group of structures with weights assigned to the atoms according to certain thermal motions of the atoms. We call such an RMSD the dynamically weighted RMSD (dRMSD). We show that the thermal motions of the atoms can be obtained from several sources such as the mean-square fluctuations that can be estimated by Gaussian network model analysis. We show that the superimposition of structures with dRMSD can successfully identify protein domains and protein motions, and that it has important implications in practice, e.g., in aligning the ensemble of structures determined by nuclear magnetic resonance.