Strong Selection Significantly Increases Epistatic Interactions in the Long-Term Evolution of a Protein

The human immuno-deficiency virus sub-type 1 (HIV-1) is evolving to keep up with a changing fitness landscape, due to the various drugs introduced to stop the virus’s replication. As the virus adapts, the information the virus encodes about its environment must change, and this change is reflected in the amino-acid composition of proteins, as well as changes in viral RNAs, binding sites, and splice sites. Information can also be encoded in the interaction between residues in a single protein as well as across proteins, leading to a change in the epistatic patterns that can affect how the virus can change in the future. Measuring epistasis usually requires fitness measurements that are difficult to obtain in high-throughput. Here we show that epistasis can be inferred from the pair-wise information between residues, and study how epistasis and information have changed over the long-term. Using HIV-1 protease sequence data from public databases covering the years 1998-2006 (from both treated and untreated subjects), we show that drug treatment has increased the protease’s per-site entropies on average. At the same time, the sum of mutual entropies across all pairs of residues within the protease shows a significant increase over the years, indicating an increase in epistasis in response to treatment, a trend not seen within sequences from untreated subjects. Our findings suggest that information theory can be an important tool to study long-term trends in the evolution of macromolecules.