Characterizing molecular flexibility by combining lRMSD measures

The root mean square deviation (RMSD) and the least RMSD are two widely used similarity measures in structural bioinformatics. Yet, they stem from global comparisons, possibly obliterating locally conserved motifs. We correct these limitations with the so-called combined RMSD , which mixes independent lRMSD measures, each computed with its own rigid motion. The combined RMSD can be used to compare (quaternary) structures based on motifs defined from the sequence (domains, SSE), or to compare structures based on structural motifs yielded by local structural alignment methods. We illustrate the benefits of combined RMSD over the usual RMSD on three problems, namely (i) the analysis of conformational changes based on combined RMSD of rigid structural motifs (case study: a class II fusion protein), (ii) the calculation of structural phylogenies (case study: class II fusion proteins), and (iii) the assignment of quaternary structures for hemoglobin. Using these, we argue that the combined RMSD is a tool a choice to perform positive and negative discrimination of degree of freedom, with applications to the design of move sets and collective coordinates. Combined RMSD are available within the Structural Bioinformatics Library ( http://sbl.inria.fr ).