Analysis of protein homology by assessing the (dis)similarity in protein loop regions

Two proteins are considered to have a similar fold if sufficiently many of their secondary structure elements are positioned similarly in space and are connected in the same order. Such a common structural scaffold may arise due to either divergent or convergent evolution. The intervening unaligned regions ("loops") between the superimposable helices and strands can exhibit a wide range of similarity and may offer clues to the structural evolution of folds. One might argue that more closely related proteins differ less in their nonconserved loop regions than distantly related proteins and, at the same time, the degree of variability in the loop regions in structurally similar but unrelated proteins is higher than in homologs. Here we introduce a new measure for structural (dis)similarity in loop regions that is based on the concept of the Hausdorff metric. This measure is used to gauge protein relatedness and is tested on a benchmark of homologous and analogous protein structures. It has been shown that the new measure can distinguish homologous from analogous proteins with the same or higher accuracy than the conventional measures that are based on comparing proteins in structurally aligned regions. We argue that this result can be attributed to the higher sensitivity of the Hausdorff (dis)similarity measure in detecting particularly evident dissimilarities in structures and draw some conclusions about evolutionary relatedness of proteins in the most populated protein folds.