Estimating the contribution of folding stability to nonspecific epistasis in protein evolution

The extent of nonadditive interaction among mutations or epistasis reflects the ruggedness of the fitness landscape, the mapping of genotype to reproductive fitness. In protein evolution, there is strong support for the importance and prevalence of epistasis but the quantitative and relative contribution of various factors to epistasis are poorly known. Here, we determine the contribution of selection for folding stability to epistasis in protein evolution. By combining theoretical estimates of the rates of molecular evolution and the nonlinear mapping between protein folding thermodynamics and fitness, we show that the simple selection for folding stability imposes at least ~30% to ~40% epistasis in long-term protein evolution. Estimating the contribution of governing factors in molecular evolution such as protein folding stability to epistasis will provide a better understanding of epistasis that could improve methods in molecular evolution.