Amino acid positions subject to multiple coevolutionary constraints can be robustly identified by their eigenvector network centrality scores.

As proteins evolve, amino acid positions key to protein structure or function are subject to mutational constraints. These positions can be detected by analyzing sequence families for amino acid conservation or for coevolution between pairs of positions. Coevolutionary scores are usually rank-ordered and thresholded to reveal the top pairwise scores, but they also can be treated as weighted networks. Here, we used network analyses to bypass a major complication of coevolution studies: For a given sequence alignment, alternative algorithms usually identify different, top pairwise scores. We reconciled results from five commonly-used, mathematically divergent algorithms (ELSC, McBASC, OMES, SCA, and ZNMI), using the LacI/GalR and 1,6-bisphosphate aldolase protein families as models. Calculations used unthresholded coevolution scores from which column-specific properties such as sequence entropy and random noise were subtracted; "central" positions were identified by calculating various network centrality scores. When compared among algorithms, network centrality methods, particularly eigenvector centrality, showed markedly better agreement than comparisons of the top pairwise scores. Positions with large centrality scores occurred at key structural locations and/or were functionally sensitive to mutations. Further, the top central positions often differed from those with top pairwise coevolution scores: instead of a few strong scores, central positions often had multiple, moderate scores. We conclude that eigenvector centrality calculations reveal a robust evolutionary pattern of constraints-detectable by divergent algorithms--that occur at key protein locations. Finally, we discuss the fact that multiple patterns coexist in evolutionary data that, together, give rise to emergent protein functions.