LoCoHD: a metric for comparing local environments of proteins

Protein folds and the local environments they create can be compared using a variety of differently designed measures, such as the root mean squared deviation, the global distance test, the template modeling score or the local distance difference test. Although these measures have proven to be useful for a variety of tasks, each fails to fully incorporate the valuable chemical information inherent to atoms and residues, and considers these only partially and indirectly. Here, we develop the highly flexible local composition Hellinger distance (LoCoHD) metric, which is based on the chemical composition of local residue environments. Using LoCoHD, we analyze the chemical heterogeneity of amino acid environments and identify valines having the most conserved-, and arginines having the most variable chemical environments. We use LoCoHD to investigate structural ensembles, to evaluate critical assessment of structure prediction (CASP) competitors, to compare the results with the local distance difference test (lDDT) scoring system, and to evaluate a molecular dynamics simulation. We show that LoCoHD measurements provide unique information about protein structures that is distinct from, for example, those derived using the alignment-based RMSD metric, or the similarly distance matrix-based but alignment-free lDDT metric.