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.evolution | adaptation | epistasis | fitness landscape | mutagenesis S ince first proposed by Sewall Wright in 1932 (1), the idea of a fitness landscape relating genotype (or phenotype) to the reproductive success of an individual has inspired evolutionary biologists and mathematicians alike (2-4). With the advancement of molecular and systems biology toward large and accurate datasets, the fitness landscape concept has received increasing attention across other subfields of biology (5-9). The shape of the fitness landscape carries information on the repeatability and predictability of evolution, the potential for adaptation, the importance of genetic drift, the likelihood of convergent and parallel evolution, and the degree of optimization that is (theoretically) achievable (4). Unfortunately, the dimensionality of a complete fitness landscape of an organism-that is, a mapping of all possible combinations of mutations to their respective fitness effects-is much too high to be assessed experimentally. With the development of experimental approaches that allow for the assessment of full fitness landscapes of tens to hundreds of mutations, there is growing interest in statistics that capture the features of the landscape and that relate an experimental landscape to theoretical landscapes of similar architecture, which have been studied extensively (10). It is, however, unclear whether this categorization allows for an extrapolation to unknown parts of the landscape, which would be the first step toward quantifying predictability-an advancement that would yield impacts far beyond the field of evolutionary biology, in particular for the clinical study of drug-resistan...

Minimum epistasis interpolation for sequence-function relationships

“…in partial factorial designs where higher-order interactions are purposefully confounded with main effects and lower-order interactions 73 ). However, there is a growing consensus that such higher-order interactions are not only common in genotype-phenotype maps 10,18,29,32,38 but are expected even for very simple, smooth genotype-phenotype relationships, such as where the observed phenotype is just an additive trait that has been run through a nonlinear transformation 31,32,40,[74][75][76] . Our results contribute to this view by showing that the incorporation of higher-order interactions in fact allows substantially less epistatic fits than standard pairwise models.…”

“…Besides viewing genotype-phenotype maps as being defined by sums of interactions between sites as in regression models 26,29,77 , there are a rich variety of other formalisms for describing genetic interaction that are related to the techniques we have developed here [78][79][80][81][82] . Probably the most relevant of these is the correlation between the effects of mutations measured in mutationally adjacent genetic backgrounds, γ 10,81 . Conceptually, maximizing γ would be quite similar to our method except that γ depends on both ϵ 2 and the variance in the phenotypic effects of mutations 81 , so that maximizing γ would tend to inflate the magnitude of mutational effects, in essence minimizing the relative rather than absolute amount of epistasis.…”

“…ecent advances in quantification via next-generation sequencing have allowed the proliferation of high-throughput combinatorial mutagenesis assays that measure molecular function for tens of thousands to millions of sequences simultaneously 1 . These assays have been applied to many different classes of functional elements, including protein-coding sequences [2][3][4][5][6][7][8][9][10][11][12][13] , RNAs [14][15][16][17][18] , and regulatory or splicing elements [19][20][21][22] . However, in practice, due to both the vastness of sequence space and the limitations of techniques for library preparation, such experiments typically result in missing measurements for a subset of possible genotypes.…”

“…In the special case where such interactions are limited to occuring between pairs of sites, the prediction problem can be solved using regularized regression 26 -a technique that has sometimes performed quite well 27,28 . However, there is now abundant evidence that adding pairwise interaction terms to an otherwise additive model is not sufficient to capture the complex interdependencies between mutations observed in the empirical data 10,24,[29][30][31][32][33][34][35][36][37][38][39] .…”

Analysis of statistical correlations between properties of adaptive walks in fitness landscapes

“…Massive parallel evolution experiments and advances in the next-generation sequencing has allowed the assessment of a large amount of evolutionary information on empirical landscapes [13][14][15], though their analyses have been restricted to small parts of the landscapes and their inferred topography may not be truly representative [16]. Another limitation of those empirical analyses relies on the fact that the topography itself is shaped by the environment, which in turn is likely to change during evolution [17][18][19].…”