The Impact of Macroscopic Epistasis on Long-Term Evolutionary Dynamics

Genetic interactions can strongly influence the fitness effects of individual mutations, yet the impact of these epistatic interactions on evolutionary dynamics remains poorly understood. Here we investigate the evolutionary role of epistasis over 50,000 generations in a well-studied laboratory evolution experiment in Escherichia coli. The extensive duration of this experiment provides a unique window into the effects of epistasis during long-term adaptation to a constant environment. Guided by analytical results in the weak-mutation limit, we develop a computational framework to assess the compatibility of a given epistatic model with the observed patterns of fitness gain and mutation accumulation through time. We find that a decelerating fitness trajectory alone provides little power to distinguish between competing models, including those that lack any direct epistatic interactions between mutations. However, when combined with the mutation trajectory, these observables place strong constraints on the set of possible models of epistasis, ruling out many existing explanations of the data. Instead, we find that the data are consistent with a “two-epoch” model of adaptation, in which an initial burst of diminishing-returns epistasis is followed by a steady accumulation of mutations under a constant distribution of fitness effects. Our results highlight the need for additional DNA sequencing of these populations, as well as for more sophisticated models of epistasis that are compatible with all of the experimental data.     

Long-term adaptation of epistatic genetic networks

Gene networks are likely to govern most traits in nature. Mutations at these genes often show functional epistatic interactions that lead to complex genetic architectures and variable fitness effects in different genetic backgrounds. Understanding how epistatic genetic systems evolve in nature remains one of the great challenges in evolutionary biology. Here we combine an analytical framework with individual-based simulations to generate novel predictions about long-term adaptation of epistatic networks. We find that relative to traits governed by independently evolving genes, adaptation with epistatic gene networks is often characterized by longer waiting times to selective sweeps, lower standing genetic variation, and larger fitness effects of adaptive mutations. This may cause epistatic networks to either adapt more slowly or more quickly relative to a nonepistatic system. Interestingly, epistatic networks may adapt faster even when epistatic effects of mutations are on average deleterious. Further, we study the evolution of epistatic properties of adaptive mutations in gene networks. Our results show that adaptive mutations with small fitness effects typically evolve positive synergistic interactions, whereas adaptive mutations with large fitness effects evolve positive synergistic and negative antagonistic interactions at approximately equal frequencies. These results provide testable predictions for adaptation of traits governed by epistatic networks and the evolution of epistasis within networks.     

Epistatic interaction maps relative to multiple metabolic phenotypes

An epistatic interaction between two genes occurs when the phenotypic impact of one gene depends on another gene, often exposing a functional association between them. Due to experimental scalability and to evolutionary significance, abundant work has been focused on studying how epistasis affects cellular growth rate, most notably in yeast. However, epistasis likely influences many different phenotypes, affecting our capacity to understand cellular functions, biochemical networks adaptation, and genetic diseases. Despite its broad significance, the extent and nature of epistasis relative to different phenotypes remain fundamentally unexplored. Here we use genome-scale metabolic network modeling to investigate the extent and properties of epistatic interactions relative to multiple phenotypes. Specifically, using an experimentally refined stoichiometric model for Saccharomyces cerevisiae, we computed a three-dimensional matrix of epistatic interactions between any two enzyme gene deletions, with respect to all metabolic flux phenotypes. We found that the total number of epistatic interactions between enzymes increases rapidly as phenotypes are added, plateauing at approximately 80 phenotypes, to an overall connectivity that is roughly 8-fold larger than the one observed relative to growth alone. Looking at interactions across all phenotypes, we found that gene pairs interact incoherently relative to different phenotypes, i.e. antagonistically relative to some phenotypes and synergistically relative to others. Specific deletion-deletion-phenotype triplets can be explained metabolically, suggesting a highly informative role of multi-phenotype epistasis in mapping cellular functions. Finally, we found that genes involved in many interactions across multiple phenotypes are more highly expressed, evolve slower, and tend to be associated with diseases, indicating that the importance of genes is hidden in their total phenotypic impact. Our predictions indicate a pervasiveness of nonlinear effects in how genetic perturbations affect multiple metabolic phenotypes. The approaches and results reported could influence future efforts in understanding metabolic diseases and the role of biochemical regulation in the cell.     

A phylogenetic method for detecting positive epistasis in gene sequences and its application to RNA virus evolution

RNA virus genomes are compact, often containing multiple overlapping reading frames and functional secondary structure. Consequently, it is thought that evolutionary interactions between nucleotide sites are commonplace in the genomes of these infectious agents. However, the role of epistasis in natural populations of RNA viruses remains unclear. To investigate the pervasiveness of epistasis in RNA viruses, we used a parsimony-based computational method to identify pairs of co-occurring mutations along phylogenies of 177 RNA virus genes. This analysis revealed widespread evidence for positive epistatic interactions at both synonymous and nonsynonymous nucleotide sites and in both clonal and recombining viruses, with the majority of these interactions spanning very short sequence regions. These findings have important implications for understanding the key aspects of RNA virus evolution, including the dynamics of adaptation. Additionally, many comparative analyses that utilize the phylogenetic relationships among gene sequences assume that mutations represent independent, uncorrelated events. Our results show that this assumption may often be invalid.     

Epistasis between beneficial mutations and the phenotype-to-fitness Map for a ssDNA virus

Epistatic interactions between genes and individual mutations are major determinants of the evolutionary properties of genetic systems and have therefore been well documented, but few quantitative data exist on epistatic interactions between beneficial mutations, presumably because such mutations are so much rarer than deleterious ones. We explored epistasis for beneficial mutations by constructing genotypes with pairs of mutations that had been previously identified as beneficial to the ssDNA bacteriophage ID11 and by measuring the effects of these mutations alone and in combination. We constructed 18 of the 36 possible double mutants for the nine available beneficial mutations. We found that epistatic interactions between beneficial mutations were all antagonistic-the effects of the double mutations were less than the sums of the effects of their component single mutations. We found a number of cases of decompensatory interactions, an extreme form of antagonistic epistasis in which the second mutation is actually deleterious in the presence of the first. In the vast majority of cases, recombination uniting two beneficial mutations into the same genome would not be favored by selection, as the recombinant could not outcompete its constituent single mutations. In an attempt to understand these results, we developed a simple model in which the phenotypic effects of mutations are completely additive and epistatic interactions arise as a result of the form of the phenotype-to-fitness mapping. We found that a model with an intermediate phenotypic optimum and additive phenotypic effects provided a good explanation for our data and the observed patterns of epistatic interactions.     

Environmental Dependence of Genetic Constraint

The epistatic interactions that underlie evolutionary constraint have mainly been studied for constant external conditions. However, environmental changes may modulate epistasis and hence affect genetic constraints. Here we investigate genetic constraints in the adaptive evolution of a novel regulatory function in variable environments, using the lac repressor, LacI, as a model system. We have systematically reconstructed mutational trajectories from wild type LacI to three different variants that each exhibit an inverse response to the inducing ligand IPTG, and analyzed the higher-order interactions between genetic and environmental changes. We find epistasis to depend strongly on the environment. As a result, mutational steps essential to inversion but inaccessible by positive selection in one environment, become accessible in another. We present a graphical method to analyze the observed complex higher-order interactions between multiple mutations and environmental change, and show how the interactions can be explained by a combination of mutational effects on allostery and thermodynamic stability. This dependency of genetic constraint on the environment should fundamentally affect evolutionary dynamics and affects the interpretation of phylogenetic data.     

Synergistic epistasis of the deleterious effects of transposable elements

The replicative nature and generally deleterious effects of transposable elements (TEs) raise an outstanding question about how TE copy number is stably contained in host populations. Classic theoretical analyses predict that, when the decline in fitness due to each additional TE insertion is greater than linear, or when there is synergistic epistasis, selection against TEs can result in a stable equilibrium of TE copy number. While several mechanisms are predicted to yield synergistic deleterious effects of TEs, we lack empirical investigations of the presence of such epistatic interactions. Purifying selection with synergistic epistasis generates repulsion linkage between deleterious alleles. We investigated this population genetic signal in the likely ancestral Drosophila melanogaster population and found evidence supporting the presence of synergistic epistasis among TE insertions, especially TEs expected to exert large fitness impacts. Even though synergistic epistasis of TEs has been predicted to arise through ectopic recombination and TE-mediated epigenetic silencing mechanisms, we only found mixed support for the associated predictions. We observed signals of synergistic epistasis for a large number of TE families, which is consistent with the expectation that such epistatic interaction mainly happens among copies of the same family. Curiously, significant repulsion linkage was also found among TE insertions from different families, suggesting the possibility that synergism of TEs’ deleterious fitness effects could arise above the family level and through mechanisms similar to those of simple mutations. Our findings set the stage for investigating the prevalence and importance of epistatic interactions in the evolutionary dynamics of TEs.     

Dynamic genetic interactions determine odor-guided behavior in Drosophila melanogaster

Understanding the genetic architecture of complex traits requires identification of the underlying genes and characterization of gene-by-gene and genotype-by-environment interactions. Behaviors that mediate interactions between organisms and their environment are complex traits expected to be especially sensitive to environmental conditions. Previous studies on the olfactory avoidance response of Drosophila melanogaster showed that the genetic architecture of this model behavior depends on epistatic networks of pleiotropic genes. We performed a screen of 1339 co-isogenic p[GT1]-element insertion lines to identify novel genes that contribute to odor-guided behavior and identified 55 candidate genes with known p[GT1]-element insertion sites. Characterization of the expression profiles of 10 p[GT1]-element insertion lines showed that the effects of the transposon insertions are often dependent on developmental stage and that hypomorphic mutations in developmental genes can elicit profound adult behavioral deficits. We assessed epistasis among these genes by constructing all possible double heterozygotes and measuring avoidance responses under two stimulus conditions. We observed enhancer and suppressor effects among subsets of these P-element-tagged genes, and surprisingly, epistatic interactions shifted with changes in the concentration of the olfactory stimulus. Our results show that the manifestation of epistatic networks dynamically changes with alterations in the environment.     

Molecular basis of adaptive convergence in experimental populations of RNA viruses

Characterizing the molecular basis of adaptation is one of the most important goals in modern evolutionary genetics. Here, we report a full-genome sequence analysis of 21 independent populations of vesicular stomatitis ribovirus evolved on the same cell type but under different demographic regimes. Each demographic regime differed in the effective viral population size. Evolutionary convergences are widespread both at synonymous and nonsynonymous replacements as well as in an intergenic region. We also found evidence for epistasis among sites of the same and different loci. We explain convergences as the consequence of four factors: (1) environmental homogeneity that supposes an identical challenge for each population, (2) structural constraints within the genome, (3) epistatic interactions among sites that create the observed pattern of covariation, and (4) the phenomenon of clonal interference among competing genotypes carrying different beneficial mutations. Using these convergences, we have been able to estimate the fitness contribution of the identified mutations and epistatic groups. Keeping in mind statistical uncertainties, these estimates suggest that along with several beneficial mutations of major effect, many other mutations got fixed as part of a group of epistatic mutations.     

Variable epistatic effects between mutations at host recognition sites in phiX174 bacteriophage

Epistatic interactions between mutations are widespread. Theoretical investigations have shown that variability in epistatic effects influences fundamental evolutionary processes, yet few empirical studies have identified causes or the extent of this variation. We examined variation in epistatic effects of mutations at two host recognition sites in phiX174 bacteriophage. We calculated epistatic effects from the sum of fitness effects (log scale) of two single mutants and their corresponding double mutant for five combinations of mutations in six conditions. We found that epistatic effects differed in sign, degree, and variability across conditions. The data highlight that even between single mutations at the same two sites the sign and variability of epistatic effects are affected by environment. We discuss these findings in the context of studying the role of epistasis in evolution.     

The strength of genetic interactions scales weakly with mutational effects

Background

Genetic interactions pervade every aspect of biology, from evolutionary theory, where they determine the accessibility of evolutionary paths, to medicine, where they can contribute to complex genetic diseases. Until very recently, studies on epistatic interactions have been based on a handful of mutations, providing at best anecdotal evidence about the frequency and the typical strength of genetic interactions. In this study, we analyze a publicly available dataset that contains the growth rates of over five million double knockout mutants of the yeast Saccharomyces cerevisiae.

Results

We discuss a geometric definition of epistasis that reveals a simple and surprisingly weak scaling law for the characteristic strength of genetic interactions as a function of the effects of the mutations being combined. We then utilized this scaling to quantify the roughness of naturally occurring fitness landscapes. Finally, we show how the observed roughness differs from what is predicted by Fisher''s geometric model of epistasis, and discuss the consequences for evolutionary dynamics.

Conclusions

Although epistatic interactions between specific genes remain largely unpredictable, the statistical properties of an ensemble of interactions can display conspicuous regularities and be described by simple mathematical laws. By exploiting the amount of data produced by modern high-throughput techniques, it is now possible to thoroughly test the predictions of theoretical models of genetic interactions and to build informed computational models of evolution on realistic fitness landscapes.     

Epistasis for fitness-related quantitative traits in Arabidopsis thaliana grown in the field and in the greenhouse

The extent to which epistasis contributes to adaptation, population differentiation, and speciation is a long-standing and important problem in evolutionary genetics. Using recombinant inbred (RI) lines of Arabidopsis thaliana grown under natural field conditions, we have examined the genetic architecture of fitness-correlated traits with respect to epistasis; we identified both single-locus additive and two-locus epistatic QTL for natural variation in fruit number, germination, and seed length and width. For fruit number, we found seven significant epistatic interactions, but only two additive QTL. For seed germination, length, and width, there were from two to four additive QTL and from five to eight epistatic interactions. The epistatic interactions were both positive and negative. In each case, the magnitude of the epistatic effects was roughly double that of the effects of the additive QTL, varying from -41% to +29% for fruit number and from -5% to +4% for seed germination, length, and width. A number of the QTL that we describe participate in more than one epistatic interaction, and some loci identified as additive also may participate in an epistatic interaction; the genetic architecture for fitness traits may be a network of additive and epistatic effects. We compared the map positions of the additive and epistatic QTL for germination, seed width, and seed length from plants grown in both the field and the greenhouse. While the total number of significant additive and epistatic QTL was similar under the two growth conditions, the map locations were largely different. We found a small number of significant epistatic QTL x environment effects when we tested directly for them. Our results support the idea that epistatic interactions are an important part of natural genetic variation and reinforce the need for caution in comparing results from greenhouse-grown and field-grown plants.     

Environment Determines Epistatic Patterns for a ssDNA Virus

Despite the accumulation of substantial quantities of information about epistatic interactions among both deleterious and beneficial mutations in a wide array of experimental systems, neither consistent patterns nor causal explanations for these interactions have yet emerged. Furthermore, the effects of mutations depend on the environment in which they are characterized, implying that the environment may also influence epistatic interactions. Recent work with beneficial mutations for the single-stranded DNA bacteriophage ID11 demonstrated that interactions between pairs of mutations could be understood by means of a simple model that assumes that mutations have additive phenotypic effects and that epistasis arises through a nonlinear phenotype–fitness map with a single intermediate optimum. To determine whether such a model could also explain changes in epistatic patterns associated with changes in environment, we measured epistatic interactions for these same mutations under conditions for which we expected to find the wild-type ID11 at different distances from its phenotypic optimum by assaying fitnesses at three different temperatures: 33°, 37°, and 41°. Epistasis was present and negative under all conditions, but became more pronounced as temperature increased. We found that the additive-phenotypes model explained these patterns as changes in the parameters of the phenotype–fitness map, but that a model that additionally allows the phenotypes to vary across temperatures performed significantly better. Our results show that ostensibly complex patterns of fitness effects and epistasis across environments can be explained by assuming a simple structure for the genotype–phenotype relationship.     

Epigenetic epistatic interactions constrain the evolution of gene expression

Reduced activity of two genes in combination often has a more detrimental effect than expected. Such epistatic interactions not only occur when genes are mutated but also due to variation in gene expression, including among isogenic individuals in a controlled environment. We hypothesized that these ‘epigenetic’ epistatic interactions could place important constraints on the evolution of gene expression. Consistent with this, we show here that yeast genes with many epistatic interaction partners typically show low expression variation among isogenic individuals and low variation across different conditions. In addition, their expression tends to remain stable in response to the accumulation of mutations and only diverges slowly between strains and species. Yeast promoter architectures, the retention of gene duplicates, and the divergence of expression between humans and chimps are also consistent with selective pressure to reduce the likelihood of harmful epigenetic epistatic interactions. Based on these and previous analyses, we propose that the tight regulation of epistatic interaction network hubs makes an important contribution to the maintenance of a robust, ‘canalized’ phenotype. Moreover, that epigenetic epistatic interactions may contribute substantially to fitness defects when single genes are deleted.     

Evolution of genetic architecture under directional selection

We investigate the multilinear epistatic model under mutation-limited directional selection. We confirm previous results that only directional epistasis, in which genes on average reinforce or diminish each other's effects, contribute to the initial evolution of mutational effects. Thus, either canalization or decanalization can occur under directional selection, depending on whether positive or negative epistasis is prevalent. We then focus on the evolution of the epistatic coefficients themselves. In the absence of higher-order epistasis, positive pairwise epistasis will tend to weaken relative to additive effects, while negative pairwise epistasis will tend to become strengthened. Positive third-order epistasis will counteract these effects, while negative third-order epistasis will reinforce them. More generally, gene interactions of all orders have an inherent tendency for negative changes under directional selection, which can only be modified by higher-order directional epistasis. We identify three types of nonadditive quasi-equilibrium architectures that, although not strictly stable, can be maintained for an extended time: (1) nondirectional epistatic architectures; (2) canalized architectures with strong epistasis; and (3) near-additive architectures in which additive effects keep increasing relative to epistasis.     

Fitness ranking of individual mutants drives patterns of epistatic interactions in HIV-1

Fitness interactions between mutations, referred to as epistasis, can strongly impact evolution. For RNA viruses and retroviruses with their high mutation rates, epistasis may be particularly important to overcome fitness losses due to the accumulation of deleterious mutations and thus could influence the frequency of mutants in a viral population. As human immunodeficiency virus type 1 (HIV-1) resistance to azidothymidine (AZT) requires selection of sequential mutations, it is a good system to study the impact of epistasis. Here we present a thorough analysis of a classical AZT-resistance pathway (the 41-215 cluster) of HIV-1 variants by fitness measurements in single round infection assays covering physiological drug concentrations ex vivo. The sign and value of epistasis varied and did not predict the epistatic effect on the mutant frequency. This complex behavior is explained by the fitness ranking of the variants that strongly depends on environmental factors, i.e., the presence and absence of drugs and the host cells used. Although some interactions compensate fitness losses, the observed small effect on the relative mutant frequencies suggests that epistasis might be inefficient as a buffering mechanism for fitness losses in vivo. While the use of epistasis-based hypotheses to make general assumptions on the evolutionary dynamics of viral populations is appealing, our data caution their interpretation without further knowledge on the characteristics of the viral mutant spectrum under different environmental conditions.     

Initial mutations direct alternative pathways of protein evolution

Whether evolution is erratic due to random historical details, or is repeatedly directed along similar paths by certain constraints, remains unclear. Epistasis (i.e. non-additive interaction between mutations that affect fitness) is a mechanism that can contribute to both scenarios. Epistasis can constrain the type and order of selected mutations, but it can also make adaptive trajectories contingent upon the first random substitution. This effect is particularly strong under sign epistasis, when the sign of the fitness effects of a mutation depends on its genetic background. In the current study, we examine how epistatic interactions between mutations determine alternative evolutionary pathways, using in vitro evolution of the antibiotic resistance enzyme TEM-1 β-lactamase. First, we describe the diversity of adaptive pathways among replicate lines during evolution for resistance to a novel antibiotic (cefotaxime). Consistent with the prediction of epistatic constraints, most lines increased resistance by acquiring three mutations in a fixed order. However, a few lines deviated from this pattern. Next, to test whether negative interactions between alternative initial substitutions drive this divergence, alleles containing initial substitutions from the deviating lines were evolved under identical conditions. Indeed, these alternative initial substitutions consistently led to lower adaptive peaks, involving more and other substitutions than those observed in the common pathway. We found that a combination of decreased enzymatic activity and lower folding cooperativity underlies negative sign epistasis in the clash between key mutations in the common and deviating lines (Gly238Ser and Arg164Ser, respectively). Our results demonstrate that epistasis contributes to contingency in protein evolution by amplifying the selective consequences of random mutations.     

The Evolution of Epistasis and Its Links With Genetic Robustness, Complexity and Drift in a Phenotypic Model of Adaptation

The epistatic interactions among mutations have a large effect on the evolution of populations. In this article we provide a formalism under which epistatic interactions among pairs of mutations have a distribution whose mean can be modulated. We find that the mean epistasis is correlated to the effect of mutations or genetic robustness, which suggests that such formalism is in good agreement with most in silico models of evolution where the same pattern is observed. We further show that the evolution of epistasis is highly dependant on the intensity of drift and of how complex the organisms are, and that either positive or negative epistasis could be selected for, depending on the balance between the efficiency of selection and the intensity of drift.     

The role of epistatic gene interactions in the response to selection and the evolution of evolvability

It has been argued that the architecture of the genotype-phenotype map determines evolvability, but few studies have attempted to quantify these effects. In this article we use the multilinear epistatic model to study the effects of different forms of epistasis on the response to directional selection. We derive an analytical prediction for the change in the additive genetic variance, and use individual-based simulations to understand the dynamics of evolvability and the evolution of genetic architecture. This shows that the major determinant for the evolution of the additive variance, and thus the evolvability, is directional epistasis. Positive directional epistasis leads to an acceleration of evolvability, while negative directional epistasis leads to canalization. In contrast, pure non-directional epistasis has little effect on the response to selection. One consequence of this is that the classical epistatic variance components, which do not distinguish directional and non-directional effects, are useless as predictors of evolutionary dynamics. The build-up of linkage disequilibrium also has negligible effects. We argue that directional epistasis is likely to have major effects on evolutionary dynamics and should be the focus of empirical studies of epistasis.     

EPISTASIS BETWEEN NEW MUTATIONS AND GENETIC BACKGROUND AND A TEST OF GENETIC CANALIZATION

Abstract The importance for fitness of epistatic interactions among mutations is poorly known, yet epistasis can exert important effects on the dynamics of evolving populations. We showed previously that epistatic interactions are common between pairs of random insertion mutations in the bacterium Escherichia coli . In this paper, we examine interactions between these mutations and other mutations by transducing each of twelve insertion mutations into two genetic backgrounds, one ancestral and the other having evolved in, and adapted to, a defined laboratory environment for 10,000 generations. To assess the effect of the mutation on fitness, we allowed each mutant to compete against its unmutated counterpart in that same environment. Overall, there was a strong positive correlation between the mutational effects on the two genetic backgrounds. Nonetheless, three of the twelve mutations had significantly different effects on the two backgrounds, indicating epistasis. There was no significant tendency for the mutations to be less harmful on the derived background. Thus, there is no evidence supporting the hypothesis that the derived bacteria had adapted, in part, by becoming buffered against the harmful effects of mutations.