Inference of the fitness landscape from Evolutionary interplay between structure, energy and epistasis in the coat protein of the <i>ϕX</i>174 phage family

Viral capsids are structurally constrained by interactions among the amino acids (AAs) of their constituent proteins. Therefore, epistasis is expected to evolve among physically interacting sites and to influence the rates of substitution. To study the evolution of epistasis, we focused on the major structural protein of the <i>ϕ</i>X174 phage family by, first, reconstructing the ancestral protein sequences of 18 species using a Bayesian statistical framework. The inferred ancestral reconstruction differed at eight AAs, for a total of 256 possible ancestral haplotypes. For each ancestral haplotype and the extant species, we estimated, <i>in silico</i>, the distribution of free energies and epistasis of the capsid structure. We found that free energy has not significantly increased but epistasis has. We decomposed epistasis up to fifth order and found that higher-order epistasis sometimes compensates pairwise interactions making the free energy seem additive. The d<i>N</i>/d<i>S</i> ratio is low, suggesting strong purifying selection, and that structure is under stabilizing selection. We synthesized phages carrying ancestral haplotypes of the coat protein gene and measured their fitness experimentally. Our findings indicate that stabilizing mutations can have higher fitness, and that fitness optima do not necessarily coincide with energy minima.