The Relationship Between Epistasis and Clustering of Amino Acid Substitutions Under Simulated Purifying Selection

Abstract

The rate and predictability of protein evolution are determined in part by the availability of viable evolutionary paths from a starting sequence. These paths are limited in part due to dependent interactions between amino acids (epistasis), although how much epistasis constrains evolutionary outcomes remains a topic of debate. Previous reports indicating that amino acid substitutions tend to cluster in a lineage-specific manner suggest that epistasis may play a larger role than previously appreciated in shaping the the distribution of amino acid substitutions. To test this hypothesis, I performed simulations of protein evolution under purifying selection to test for clustering of substitution due to epistasis. No clustering was observed in 30-step evolutionary trajectories despite prevalent observed epistasis between substitutions.In two-step evolutionary trajectories, substitutions do not appear closer together than would be expected by chance, and if anything appear to appear further apart spatially than random substitutions in the absence of selection. However, constraining the evolutionary landscape further by only allowing mutations at sites with low weighted contact number produces clustering of 20% above baseline, albeit none that can be attributed to epistasis. Conversely, disallowing substitutions with nearly-additive effects on stability produces substantial clustering due to epistasis, up to 40% above baseline. The magnitude of clustering observed under these conditions suggests an upper bound for clustering of substitutions due to purifying selection of just 150% relative to the asymptotic value. The inability of purifying selection to explain most clustering potentially implicates positive selection as a stronger contributor.