Contingency and entrenchment in protein evolution under purifying selection

Abstract

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.

Keywords: coevolution; intragenic epistasis; near neutrality; protein stability.

Fig. 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 ($\mathrm{\Delta }\text{G}$) 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.

Fig. 2.

(A) Substitutions that accrue under purifying selection are typically epistatic: They exhibit both contingency with earlier substitutions and entrenchment by later substitutions. A indicates the fitness effects of the mutations that fix at step $i=16$ if they were introduced into earlier (contingency $j<16$) or later (entrenchment $j>16$) genetic backgrounds. Under purifying selection, the epistatic coefficients $E_{\left(16,j\right)}$ are significantly less than zero, on average, for all $j<16$ and significantly greater than zero for all $j>16$. Thus, the substitutions under purifying selection, which are nearly neutral when they fix, are contingent on earlier substitutions, and they become more deleterious to revert as later substitutions accrue. Vertical bars indicate ±2 SE around the ensemble mean of 100 replicate simulated populations. (B) Distribution of scaled selection coefficients ($N_{e}s$) for all substitutions that fix along evolutionary trajectories. The gray histogram shows the distribution of selection coefficients of these mutations at the time that they fix (“near-neutrality”), the blue histogram shows the distribution of selection coefficients for the same mutations i if they were introduced in earlier backgrounds $j=0,\dots ,i-1$ (“contingency”), and the red histogram shows the distribution of selection coefficients for the same mutations i if they are removed from later backgrounds $j=i+1,\dots ,30$ (“entrenchment”).

Fig. 3.

Epistasis constrains paths available to evolution. The figure shows the relative probability of fixing two consecutive substitutions (B and C) in their observed order in simulated evolution ($A\to AB\to ABC$) compared with the reversed order ($A\to AC\to ACB$). Under purifying selection for stability, the distribution of relative fixation probabilities is distinctly bimodal. A large proportion of substitutions have almost equal probability of taking either path, producing a mode near 0.5. For another large portion (>26%) of pairs, the observed path is more than 30 times as likely as the alternate path (producing a mode near 1), indicating that many substitutions are highly contingent on the immediately preceding substitution.

Fig. 4.

Additivity of stability effects. (A) The effects of random mutations on protein stability as calculated by FoldX. The $\mathrm{\Delta }\mathrm{\Delta }\text{G}$ of double mutants in the wild-type argT sequence are highly correlated with the summed effects of their corresponding single mutations. (B) Starting from an evolved argT sequence, which differs from the wild type by 16 substitutions, the $\mathrm{\Delta }\mathrm{\Delta }\text{G}$ of double mutants are, again, highly correlated with the summed effects of their corresponding single mutations. (C) The stability effects of all point mutations around the wild-type argT sequence are highly correlated with their effects in the evolved argT sequence. (D) By contrast, the stability effects of consecutive substitutions along evolutionary trajectories simulated under purifying selection are only weakly additive: the effects of double mutants correlate weakly with the summed effects of single mutants. The line $y=x$ is represented in black and the best-fit regression line with zero intercept ($y=\beta x$) is represented in red in each panel.