Distance-Based Metrics for Comparing Conformational Ensembles of Intrinsically Disordered Proteins

Intrinsically disordered proteins are proteins whose native functional states represent ensembles of highly diverse conformations. Such ensembles are a challenge for quantitative structure comparisons because their conformational diversity precludes optimal superimposition of the atomic coordinates necessary for deriving common similarity measures such as the root mean-square deviation of these coordinates. Here, we introduce superimposition-free metrics that are based on computing matrices of the C alpha-C alpha 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 root mean-square difference between the medians of the C alpha-C alpha distance distributions of two ensembles. Together, our metrics enable rigorous investigations of structure-function relationships in conformational ensembles of intrinsically disordered proteins derived using experimental restraints or by molecular simulations and for proteins containing both structured and disordered regions.