Distance-based metrics for comparing conformational ensembles of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) are proteins whose native functional states represent ensembles of highly diverse conformations. Such ensembles are a challenge for quantitative structure comparisons as their conformational diversity precludes optimal superimposition of the atomic coordinates, necessary for deriving common similarity measures such as the root-mean-square deviation (RMSD) of these coordinates. Here we introduce superimposition-free metrics, which are based on computing matrices of C-C distance distributions within ensembles and comparing these matrices between ensembles. Differences between two matrices yield information on the similarity between specific regions of the polypeptide, whereas the global structural similarity is captured by the ens_dRMS, defined as the root-mean-square difference between the medians of the C-C distance distributions of two ensembles. Together, our metrics enable rigorous investigations of structure-function relationships in conformational ensembles of IDPs derived using experimental restraints or by molecular simulations, and for proteins containing both structured and disordered regions.