A biophysical protein folding model accounts for most mutational fitness effects in viruses

Fitness effects of mutations fall on a continuum ranging from lethal to deleterious to beneficial. The distribution of fitness effects (DFE) among random mutations is an essential component of every evolutionary model and a mathematical portrait of robustness. Recent experiments on five viral species all revealed a characteristic bimodal-shaped DFE featuring peaks at neutrality and lethality. However, the phenotypic causes underlying observed fitness effects are still unknown and presumably, are thought to vary unpredictably from one mutation to another. By combining population genetics simulations with a simple biophysical protein folding model, we show that protein thermodynamic stability accounts for a large fraction of observed mutational effects. We assume that moderately destabilizing mutations inflict a fitness penalty proportional to the reduction in folded protein, which depends continuously on folding free energy (ΔG). Most mutations in our model affect fitness by altering ΔG, whereas based on simple estimates, ∼10% abolish activity and are unconditionally lethal. Mutations pushing ΔG > 0 are also considered lethal. Contrary to neutral network theory, we find that, in mutation/selection/drift steady state, high mutation rates (m) lead to less stable proteins and a more dispersed DFE (i.e., less mutational robustness). Small population size (N) also decreases stability and robustness. In our model, a continuum of nonlethal mutations reduces fitness by ∼2% on average, whereas ∼10–35% of mutations are lethal depending on N and m. Compensatory mutations are common in small populations with high mutation rates. More broadly, we conclude that interplay between biophysical and population genetic forces shapes the DFE.