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

Abstract

Epistatic interactions between residues determine a protein’s adaptability and shape its evolutionary trajectory. When a protein experiences a changed environment, it is under strong selection to find a peak in the new fitness landscape. It has been shown that strong selection increases epistatic interactions as well as the ruggedness of the fitness landscape, but little is known about how the epistatic interactions change under selection in the long-term evolution of a protein. Here we analyze the evolution of epistasis in the protease of the human immunodeficiency virus type 1 (HIV-1) using protease sequences collected for almost a decade from both treated and untreated patients, to understand how epistasis changes and how those changes impact the long-term evolvability of a protein. We use an information-theoretic proxy for epistasis that quantifies the co-variation between sites, and show that positive information is a necessary (but not sufficient) condition that detects epistasis in most cases. We analyze the “fossils” of the evolutionary trajectories of the protein contained in the sequence data, and show that epistasis continues to enrich under strong selection, but not for proteins whose environment is unchanged. The increase in epistasis compensates for the information loss due to sequence variability brought about by treatment, and facilitates adaptation in the increasingly rugged fitness landscape of treatment. While epistasis is thought to enhance evolvability via valley-crossing early-on in adaptation, it can hinder adaptation later when the landscape has turned rugged. However, we find no evidence that the HIV-1 protease has reached its potential for evolution after 9 years of adapting to a drug environment that itself is constantly changing. We suggest that the mechanism of encoding new information into pairwise interactions is central to protein evolution not just in HIV-1 protease, but for any protein adapting to a changing environment.

Inference of epistatic effects leading to entrenchment and drug resistance in HIV-1 protease

“…Phylogenetic trees of drug-naive and drugtreated HIV-1-infected patients have been shown to exhibit star-like phylogenies (Keele et al 2008;Gupta and Adami 2016), and thus phylogenetic corrections are not needed. Further, phylogenetic corrections based on pairwise sequence similarity cut-offs of 40% of sequence length or more which are common in studies utilizing direct coupling analysis (DCA) (Weigt et al 2009;Morcos et al 2011Morcos et al , 2014 of protein families would drastically reduce the number of effective sequences in our MSA and would lead to mischaracterization of the true underlying mutational landscape.…”

Epistasis and Entropy

“…For instance, if two mutations tend to co-occur, then they will have nonzero shared entropy. Gupta and Adami [2] consider entropy for HIV drug resistance mutations and interpret shared entropy for a pair of mutations as evidence for pairwise epistasis. However, the authors’ conclusion is not valid under realistic assumptions.…”

“…However, the starting point in Gupta and Adami [2] is sound. If there is no epistasis at all in a system, then one would measure little or no shared entropy for mutations under ideal circumstances.…”

“…Nevertheless, it is possible that some approach of the type proposed in Gupta and Adami [2] could work as a rule of thumb. However, that would require a statistical argument.…”

“…Applications of information theory to human genetics depends on the ability to compare genetic information to health conditions. No similar information that directly relates genotype and phenotype is available for the HIV data analyzed in Gupta and Adami [2]. In that sense, the authors considered a more difficult problem.…”