Inconsistent Distances in Substitution Matrices can be Avoided by Properly Handling Hydrophobic Residues

The adequacy of substitution matrices to model evolutionary relationships between amino acid sequences can be numerically evaluated by checking the mathematical property of triangle inequality for all triplets of residues. By converting substitution scores into distances, one can verify that a direct path between two amino acids is shorter than a path passing through a third amino acid in the amino acid space modeled by the matrix. If the triangle inequality is not verified, the intuition is that the evolutionary signal is not well modeled by the matrix, that the space is locally inconsistent and that the matrix construction was probably based on insufficient biological data. Previous analysis on several substitution matrices revealed that the number of triplets violating the triangle inequality increases with sequence divergence. Here, we compare matrices which are dedicated to the alignment of highly divergent proteins. The triangle inequality is tested on several classical substitution matrices as well as in a pair of “complementary” substitution matrices recording the evolutionary pressures inside and outside hydrophobic blocks in protein sequences. The analysis proves the crucial role of hydrophobic residues in substitution matrices dedicated to the alignment of distantly related proteins

Prevalence of Epistasis in the Evolution of Influenza A Surface Proteins

The surface proteins of human influenza A viruses experience positive selection to escape both human immunity and, more recently, antiviral drug treatments. In bacteria and viruses, immune-escape and drug-resistant phenotypes often appear through a combination of several mutations that have epistatic effects on pathogen fitness. However, the extent and structure of epistasis in influenza viral proteins have not been systematically investigated. Here, we develop a novel statistical method to detect positive epistasis between pairs of sites in a protein, based on the observed temporal patterns of sequence evolution. The method rests on the simple idea that a substitution at one site should rapidly follow a substitution at another site if the sites are positively epistatic. We apply this method to the surface proteins hemagglutinin and neuraminidase of influenza A virus subtypes H3N2 and H1N1. Compared to a non-epistatic null distribution, we detect substantial amounts of epistasis and determine the identities of putatively epistatic pairs of sites. In particular, using sequence data alone, our method identifies epistatic interactions between specific sites in neuraminidase that have recently been demonstrated, in vitro, to confer resistance to the drug oseltamivir; these epistatic interactions are responsible for widespread drug resistance among H1N1 viruses circulating today. This experimental validation demonstrates the predictive power of our method to identify epistatic sites of importance for viral adaptation and public health. We conclude that epistasis plays a large role in shaping the molecular evolution of influenza viruses. In particular, sites with , which would normally not be identified as positively selected, can facilitate viral adaptation through epistatic interactions with their partner sites. The knowledge of specific interactions among sites in influenza proteins may help us to predict the course of antigenic evolution and, consequently, to select more appropriate vaccines and drugs