Evolutionary interplay between structure, energy and epistasis in the coat protein of the $\phi \chi 174$ phage family

TL;DR

This study investigates how structural constraints influence epistasis and evolution in viral capsids, revealing that high-order epistasis evolves to compensate pairwise interactions, with minimal impact on fitness.

Contribution

It provides a comprehensive in silico and experimental analysis of epistasis evolution in viral capsids, highlighting the role of high-order interactions in structural stability.

Findings

High-order epistasis increases over evolutionary time.

Free energy remains stable despite epistasis evolution.

Predicted free energy deviations do not significantly affect fitness.

Abstract

Viral capsids are structurally constrained by interactions amongst the amino acids of the constituting proteins. Therefore, epistasis is expected to evolve amongst sites engaged in physical interactions, and to influence their substitution rates. In order to study the distribution of structural epistasis, we modeled \emph{in silico} the capsid of 18 species of the \phix \, family, including the wild type. \phix \, is amongst the simplest organisms, making it suitable for experimental evolution and \emph{in silico} modeling. We found nearly 40 variable amino acid sites in the main capsid protein across the 18 species. To study how epistasis evolved in this group, we reconstructed the ancestral sequences using a Bayesian phylogenetic framework. The ancestral states include 8 variable amino acids, for a total of 256 possible haplotypes. The $dN/dS$ ratio is low, suggesting strong purifying selection, consistent with the idea that the structure is constrained by some form of stabilizing selection. For each haplotype in the ancestral node and for the extant species we estimated \emph{in silico} the distribution of free energies and of epistasis. We found that free energy has not significantly increased but epistasis has. We decomposed epistasis up to fifth order and found that high-order epistasis can sometimes compensate pairwise interactions, often making the free energy seem additive. By synthesizing some of the ancestral haplotypes of the capsid gene, we measured their fitness experimentally, and found that the predicted deviations in the coat protein free energy do not significantly affect fitness, which is consistent with the stabilizing selection hypothesis.