On the (un)predictability of a large intragenic fitness landscape

Abstract

The study of fitness landscapes, which aims at mapping genotypes to fitness, is receiving ever-increasing attention. Novel experimental approaches combined with next-generation sequencing (NGS) methods enable accurate and extensive studies of the fitness effects of mutations, allowing us to test theoretical predictions and improve our understanding of the shape of the true underlying fitness landscape and its implications for the predictability and repeatability of evolution. Here, we present a uniquely large multiallelic fitness landscape comprising 640 engineered mutants that represent all possible combinations of 13 amino acid-changing mutations at 6 sites in the heat-shock protein Hsp90 in Saccharomyces cerevisiae under elevated salinity. Despite a prevalent pattern of negative epistasis in the landscape, we find that the global fitness peak is reached via four positively epistatic mutations. Combining traditional and extending recently proposed theoretical and statistical approaches, we quantify features of the global multiallelic fitness landscape. Using subsets of the data, we demonstrate that extrapolation beyond a known part of the landscape is difficult owing to both local ruggedness and amino acid-specific epistatic hotspots and that inference is additionally confounded by the nonrandom choice of mutations for experimental fitness landscapes.

Keywords: adaptation; epistasis; evolution; fitness landscape; mutagenesis.

Fig. 1.

Individual amino acid substitutions and their effect on the parental background in elevated salinity, obtained from 1,000 samples from the posterior distribution of growth rates. Boxes represent the interquartile range [i.e., the 50% confidence interval (CI)], whiskers extend to the highest/lowest data point within the box $\pm$1.5 times the interquartile range, and circles represent outliers; gray and white background shading alternates by amino acid position. The box below indicates with colored dots which mutations are involved in the focal landscapes discussed throughout the main text: the four mutations leading from the parental type to the global optimum (“opt”), the four individually most beneficial mutations on the parental background (“best”), and the four mutations with the individually lowest growth rates on the parental background (“worst”). (Inset) Parental sequence at positions 582–590 and assessed amino acids by position.

Fig. 2.

(A) Empirical fitness landscape by mutational distance to parental type. Each line represents a single substitution. Vertical lines appear when multiple alleles have been screened at the same position. There is a global pattern of negative epistasis. The three focal landscapes are highlighted. (B) Close-up on the beneficial portion of the landscape. (C) Expected (“Exp.”) versus observed (“Obs.”) fitness for the focal landscapes, obtained from 1,000 posterior samples. We observe strong positive epistasis in the landscape that contains the global optimum, whereas the other two are dominated by negative epistasis. In A–C, the y axis depicts growth rate as a proxy for fitness.

Fig. 3.

(A) Distribution of average lengths of adaptive walks starting from any type in the full landscape (i.e., absorbing times of the Markov chain). The red line indicates mean path length for adaptive walks from the parental genotype. (B and C) Distribution of absorbing probabilities, that is, the probability to reach a specific optimum starting from a given genotype computed for all genotypes in the dataset. The red line corresponds to the respective probability when starting from the parental sequence. The global optimum (B) is, in general, reached with a very high probability, but there are starting points from which it is poorly accessible.

Fig. 4.

(A) Expected pattern of landscape-wide epistasis measure ${\gamma }_d$ (SI Appendix, Eq. S1_15) with mutational distance for theoretical fitness landscapes with 6 loci from ref. . (B) Observed decay of ${\gamma }_d$ with mutational distance under the drop-one approach is quite homogenous, except when hot spot mutation 588P is removed; 95% CIs are contained within the lines for the global landscape. (C) Observed decay of ${\gamma }_d$ for all diallelic six-locus sublandscapes. Depending on the underlying mutations, ${\gamma }_d$ is vastly different, suggesting qualitative differences in the topography of the underlying fitness landscape and in the extent of additivity in the landscape. Three focal landscapes representative of different types and ${\gamma }_d$ for the full landscape have been highlighted. (D) Observed decay of ${\gamma }_d$ for all diallelic four-locus sublandscapes containing the parental type, indicative of locally different landscape topographies. Highlighted are the three focal landscapes. (Insets) Histograms of the roughness-to-slope ratio $r\mathrm{/}s$ for the respective subset, with horizontal lines indicating values for highlighted landscapes [$r\mathrm{/}s$ for global landscape (blue) is significantly different from HoC expectation, $p\mathrm{=}\mathrm{0.01}$]. Similar to ${\gamma }_d$, there is a huge variation in $r\mathrm{/}s$ for subparts of the fitness landscape, especially when considering the four-locus subsets.

Fig. 5.

(A) Epistasis measure ${\gamma }_{(A_i,B_i)\to (A_j,B_j)}$ (SI Appendix, Eq. S1_8; $(A_i,B_i)$ on the x axis) between any two substitutions, averaged across the entire landscape. The majority of interactions are small to moderate (blue). Parts of the fitness landscape show highly localized and mutation-specific epistasis, ranging from strong magnitude epistasis (white) to sign and reciprocal sign epistasis (yellow). (B) The average epistatic effect ${\gamma }_{A_i\to }$ (SI Appendix, Eq. S1_10) of a mutation occurring on any background is always small. (C) The average epistatic effect ${\gamma }_{\to A_j}$ (SI Appendix, Eq. S1_13) of a background on any new mutation is usually small, except for mutations to *588P, which shows a strong magnitude effect. (D) Locus-specific gamma for the four mutations leading to the global optimum (Top), the four largest single-effect mutations (Middle), and the single-effect mutations with the lowest fitness (Bottom). The opt landscape exhibits strong sign epistasis between loci 587 and 588 and between loci 588 and 589. Also, the best landscape exhibits pervasive epistasis with sign epistasis between locus 588 and loci 585 and 586, respectively. We observe almost no epistasis in the worst landscape.