Atomistic simulation of protein evolution reveals sequence covariation and time-dependent fluctuations of site-specific substitution rates

Thermodynamic stability is a crucial fitness constraint in protein evolution and is a central factor in shaping the sequence landscapes of proteins. The correlation between stability and molecular fitness depends on the mechanism that relates the biophysical property with biological function. In the simplest case, stability and fitness are related by the amount of folded protein. However, when proteins are toxic in the unfolded state, the fitness function shifts, resulting in higher stability under mutation-selection balance. Likewise, a higher population size results in a similar change in protein stability, as it magnifies the effect of the selection pressure in evolutionary dynamics. This study investigates how such factors affect the evolution of protein stability, site-specific mutation rates, and residue-residue covariation. To simulate evolutionary trajectories with realistic modeling of protein energetics, we develop an all-atom simulator of protein evolution, RosettaEvolve. By evolving proteins under different fitness functions, we can study how the fitness function affects the distribution of proposed and accepted mutations, site-specific rates, and the prevalence of correlated amino acid substitutions. We demonstrate that fitness pressure affects the proposal distribution of mutational effects, that changes in stability can largely explain variations in site-specific substitution rates in evolutionary trajectories, and that increased fitness pressure results in a stronger covariation signal. Our results give mechanistic insight into the evolutionary consequences of variation in protein stability and provide a basis to rationalize the strong covariation signal observed in natural sequence alignments.Author summary: Modern-day proteins are the result of the process of evolution. The fate of random substitutions at the nucleotide level is dependent on the fitness of the new gene variant. One of the strongest fitness pressures shaping the sequences of protein is thermodynamic stability; proteins must typically be stable to carry out its function and misfolded proteins can be toxic. To understand the importance of thermodynamic stability in protein evolution and to what extent it can explain natural sequence variation we have developed a method for simulating protein evolution using a three-dimensional structure and structure-based stability calculations. In the simulations, the strength of selection can be varied, and complete phylogenetic trees of a protein family can be generated. Using these simulations, we demonstrate how mutation rates at individual sites in a protein are coupled to the overall stability of the protein, and how the spectrum of accepted mutations is shaped by stability, and how strong interactions between residues in a protein can result in sequence covariation.