Contingency and entrenchment in protein evolution under purifying selection

The phenotypic effect of an allele at one genetic site may depend on alleles at other sites, a phenomenon known as epistasis. Epistasis can profoundly influence the process of evolution in populations and shape the patterns of protein divergence across species. Whereas epistasis between adaptive substitutions has been studied extensively, relatively little is known about epistasis under purifying selection. Here we use computational models of thermodynamic stability in a ligand-binding protein to explore the structure of epistasis in simulations of protein sequence evolution. Even though the predicted effects on stability of random mutations are almost completely additive, the mutations that fix under purifying selection are enriched for epistasis. In particular, the mutations that fix are contingent on previous substitutions: Although nearly neutral at their time of fixation, these mutations would be deleterious in the absence of preceding substitutions. Conversely, substitutions under purifying selection are subsequently entrenched by epistasis with later substitutions: They become increasingly deleterious to revert over time. Our results imply that, even under purifying selection, protein sequence evolution is often contingent on history and so it cannot be predicted by the phenotypic effects of mutations assayed in the ancestral background.Whether a heritable mutation is advantageous or deleterious to an organism often depends on the evolutionary history of the population. A mutation that is beneficial at the time of its introduction may confer its beneficial effect only in the presence of other potentiating or permissive mutations (1–9). Thus, the fate of a mutation arising in a population may be contingent on previous mutations (10–13). Conversely, once a mutation has fixed in a population, the mutation becomes part of the genetic background onto which subsequent modifications are introduced. Because the beneficial effects of the subsequent modifications may depend on the focal mutation, as time passes reversion of the focal mutation may become increasingly deleterious, leading to a type of evolutionary conservatism, or entrenchment (14–18).In the context of protein evolution, the effects of contingency and entrenchment are most easily studied by considering a sequence of single amino acid changes (19) that extends both forward and backward in time from some focal substitution. To assess the roles of contingency and entrenchment we can study the degree to which each focal substitution was facilitated by previous substitutions, and the degree to which the focal substitution influences the subsequent course of evolution (Fig. 1A).Open in a separate windowFig. 1.(A) A schematic model indicating how a focal substitution may be contingent on prior substitutions and may constrain future substitutions along an evolutionary trajectory, owing to epistasis. (B) A model of protein evolution under weak mutation and purifying selection for thermodynamic stability. Starting from the wild-type sequence of argT we propose 10 random 1-aa point mutations. For each of the proposed mutants we compute its predicted stability (ΔG) using FoldX, and its associated fitness. The fitness function is assumed to be either Gaussian or semi-Gaussian, with a maximum at the wild-type stability. One of the proposed mutants fixes in the population, based on its relative fixation probability under the Moran model with effective population size N_e. This process is iterated for 30 consecutive substitutions to produce an evolutionary trajectory. We simulate 100 replicate trajectories, each initiated at the wild-type argT sequence.Dependencies within a sequence of substitutions are closely connected to the concept of epistasis—that is, the idea that the phenotypic effect of a mutation at a particular genetic site may depend on the genetic background in which it arises (20–24). In the absence of epistasis, a mutation has the same effect regardless of its context and therefore regardless of any prior history or subsequent evolution. By contrast, in the presence of epistasis, each substitution may be contingent on the entire prior history of the protein, and it may constrain all subsequent evolution.The potential for epistasis to play an important role in evolution, including protein evolution, has not been overlooked by researchers (1, 8, 25–34), nor have the concepts of contingency (3, 4, 9, 12, 35–38) and, more recently, entrenchment (18, 39, 40). However, most studies have addressed the role of epistasis in the context of adaptive evolution (1–9, 27, 30, 31, 36, 38), whereas the consequences of epistasis under purifying selection have received less attention (18, 41–44). Indeed, although some more sophisticated models have been proposed (e.g., refs. 45–50), all commonly used phylogenetic models of long-term protein evolution assume that epistasis is absent so that sites evolve independently (51–56).Here we explore the relationships between epistasis, contingency, and entrenchment under long-term purifying selection on protein stability. Our analysis combines computational models for protein structures with population-genetic models for evolutionary dynamics. We use a force-field-based model, FoldX (57), to characterize the effects of point mutations on a protein’s stability and fitness. This approach allows us to simulate evolutionary trajectories of protein sequences under purifying selection, by the sequential fixation of nearly neutral mutations. We can then dissect the epistatic relationships between these substitutions by systematically inserting or reverting particular substitutions at various time points along the evolutionary trajectory.Our analysis considers epistasis both at the level of protein stability and at the level of fitness. Whereas empirical studies in diverse proteins have demonstrated that the stability effects of point mutations are typically additive across sites (58, 59), in this study we are specifically interested in epistasis for stability among the mutations that fix during evolution. Even if most random mutations are virtually additive in their effects on stability, the mutations that fix under purifying selection are highly nonrandom, and so there is reason to suspect that epistasis for stability may be enriched among such mutations. Moreover, because the mapping from stability to fitness is itself nonlinear (18, 26, 60, 61) and because selection is sensitive to selection coefficients as small as the inverse of the population size (62), even slight variation in the stability effects of mutations across different genetic backgrounds may be sufficient to influence the course of evolution.Using the computational approach summarized above, we will demonstrate that the nearly neutral mutations that fix under purifying selection are, indeed, often epistatic with each other for both stability and fitness. In particular, we find that each mutation that fixes is typically permitted to fix by the presence of preceding substitutions—that is, most substitutions would be too deleterious to fix were it not for epistasis with preceding substitutions. Conversely, we also find that mutations that fix typically become entrenched over time by epistasis—so that a substitution that was nearly neutral when it fixed becomes increasingly deleterious to revert as subsequent substitutions accumulate (18, 39). These results imply an important role for epistasis in shaping the course of sequence evolution in a protein under selection to maintain thermodynamic stability.