Origins of coevolution between residues distant in protein 3D structures.

Residue pairs that directly coevolve in protein families are generally close in protein 3D structures. Here we study the exceptions to this general trend-directly coevolving residue pairs that are distant in protein structures-to determine the origins of evolutionary pressure on spatially distant residues and to understand the sources of error in contact-based structure prediction. Over a set of 4,000 protein families, we find that 25% of directly coevolving residue pairs are separated by more than 5 Å in protein structures and 3% by more than 15 Å. The majority (91%) of directly coevolving residue pairs in the 5-15 Å range are found to be in contact in at least one homologous structure-these exceptions arise from structural variation in the family in the region containing the residues. Thirty-five percent of the exceptions greater than 15 Å are at homo-oligomeric interfaces, 19% arise from family structural variation, and 27% are in repeat proteins likely reflecting alignment errors. Of the remaining long-range exceptions (<1% of the total number of coupled pairs), many can be attributed to close interactions in an oligomeric state. Overall, the results suggest that directly coevolving residue pairs not in repeat proteins are spatially proximal in at least one biologically relevant protein conformation within the family; we find little evidence for direct coupling between residues at spatially separated allosteric and functional sites or for increased direct coupling between residue pairs on putative allosteric pathways connecting them.