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.     

Identifying quantitative trait locus by genetic background interactions in association studies

Association studies are designed to identify main effects of alleles across a potentially wide range of genetic backgrounds. To control for spurious associations, effects of the genetic background itself are often incorporated into the linear model, either in the form of subpopulation effects in the case of structure or in the form of genetic relationship matrices in the case of complex pedigrees. In this context epistatic interactions between loci can be captured as an interaction effect between the associated locus and the genetic background. In this study I developed genetic and statistical models to tie the locus by genetic background interaction idea back to more standard concepts of epistasis when genetic background is modeled using an additive relationship matrix. I also simulated epistatic interactions in four-generation randomly mating pedigrees and evaluated the ability of the statistical models to identify when a biallelic associated locus was epistatic to other loci. Under additive-by-additive epistasis, when interaction effects of the associated locus were quite large (explaining 20% of the phenotypic variance), epistasis was detected in 79% of pedigrees containing 320 individuals. The epistatic model also predicted the genotypic value of progeny better than a standard additive model in 78% of simulations. When interaction effects were smaller (although still fairly large, explaining 5% of the phenotypic variance), epistasis was detected in only 9% of pedigrees containing 320 individuals and the epistatic and additive models were equally effective at predicting the genotypic values of progeny. Epistasis was detected with the same power whether the overall epistatic effect was the result of a single pairwise interaction or the sum of nine pairwise interactions, each generating one ninth of the epistatic variance. The power to detect epistasis was highest (94%) at low QTL minor allele frequency, fell to a minimum (60%) at minor allele frequency of about 0.2, and then plateaued at about 80% as alleles reached intermediate frequencies. The power to detect epistasis declined when the linkage disequilibrium between the DNA marker and the functional polymorphism was not complete.     

The Consistency of Beneficial Fitness Effects of Mutations across Diverse Genetic Backgrounds

Parallel and convergent evolution have been remarkably common observations in molecular adaptation but primarily in the context of the same genotype adapting to the same conditions. These phenomena therefore tell us about the stochasticity and limitations of adaptation. The limited data on convergence and parallelism in the adaptation of different genotypes conflict as to the importance of such events. If the effects of beneficial mutations are highly context dependent (i.e., if they are epistatic), different genotypes should adapt through different mutations. Epistasis for beneficial mutations has been investigated but mainly through measurement of interactions between individually beneficial mutations for the same genotype. We examine epistasis for beneficial mutations at a broader genetic scale by measuring the fitness effects of two mutations beneficial for the ssDNA bacteriophage ID11 in eight different, related genotypes showing 0.3-3.7% nucleotide divergence from ID11. We found no evidence for sign epistasis, but the mutations tended to have much smaller or no effects on fitness in the new genotypes. We found evidence for diminishing-returns epistasis; the effects were more beneficial for lower-fitness genotypes. The patterns of epistasis were not determined by phylogenetic relationships to the original genotype. To improve our understanding of the patterns of epistasis, we fit the data to a model in which each mutation had a constant, nonepistatic phenotypic effect across genotypes and the phenotype-fitness map had a single optimum. This model fit the data well, suggesting that epistasis for these mutations was due to nonlinearity in the phenotype-fitness mapping and that the likelihood of parallel evolution depends more on phenotype than on genotype.     

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.     

Dynamic Epistasis under Varying Environmental Perturbations

Epistasis describes the phenomenon that mutations at different loci do not have independent effects with regard to certain phenotypes. Understanding the global epistatic landscape is vital for many genetic and evolutionary theories. Current knowledge for epistatic dynamics under multiple conditions is limited by the technological difficulties in experimentally screening epistatic relations among genes. We explored this issue by applying flux balance analysis to simulate epistatic landscapes under various environmental perturbations. Specifically, we looked at gene-gene epistatic interactions, where the mutations were assumed to occur in different genes. We predicted that epistasis tends to become more positive from glucose-abundant to nutrient-limiting conditions, indicating that selection might be less effective in removing deleterious mutations in the latter. We also observed a stable core of epistatic interactions in all tested conditions, as well as many epistatic interactions unique to each condition. Interestingly, genes in the stable epistatic interaction network are directly linked to most other genes whereas genes with condition-specific epistasis form a scale-free network. Furthermore, genes with stable epistasis tend to have similar evolutionary rates, whereas this co-evolving relationship does not hold for genes with condition-specific epistasis. Our findings provide a novel genome-wide picture about epistatic dynamics under environmental perturbations.     

Epistasis among Deleterious Mutations in the HIV-1 Protease

A central goal in molecular evolution is to understand how genetic interactions between protein mutations shape protein function and fitness. While intergenic epistasis has been extensively explored in eukaryotes, bacteria, and viruses, intragenic epistatic interactions have been insufficiently studied. Here, we employ a model system in which lambda phage fitness correlates with the enzymatic activity of human immunodeficiency virus type 1 (HIV-1) protease to systematically determine the epistatic interactions between intragenic pairs of deleterious protein substitutions. We generated 114 genotypes of the HIV-1 protease, each carrying pairs of nucleotide substitution mutations whose separated and combined deleterious effects on fitness were then determined. A high proportion (39%) of pairs displayed lethality. Several pairs exhibited significant interactions for fitness, including positive and negative epistasis. Significant negative epistatic interactions predominated (15%) over positive interactions (2%). However, the average ± SD epistatic effect, ē = 0.0025 ± 0.1334, was not significantly different from zero (p = 0.8368). Notably, epistatic interactions, regardless of epistatic direction, tend to be more frequent in the context of less deleterious mutations. In the present study, the high frequencies of lethality and negative epistasis indicate that the HIV-1 protease is highly sensitive to the effects of deleterious mutations. Therefore, proteins may not be as robust to mutational change as is usually expected.     

Interaction between directional epistasis and average mutational effects.

We investigate the relationship between the average fitness decay due to single mutations and the strength of epistatic interactions in genetic sequences. We observe that epistatic interactions between mutations are correlated to the average fitness decay, both in RNA secondary structure prediction as well as in digital organisms replicating in silico. This correlation implies that, during adaptation, epistasis and average mutational effect cannot be optimized independently. In experiments with RNA sequences evolving on a neutral network, the selective pressure to decrease the mutational load then leads to a reduction in the amount of sequences with strong antagonistic interactions between deleterious mutations in the population.     

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.     

Magnitude and sign epistasis among deleterious mutations in a positive-sense plant RNA virus

How epistatic interactions between mutations determine the genetic architecture of fitness is of central importance in evolution. The study of epistasis is particularly interesting for RNA viruses because of their genomic compactness, lack of genetic redundancy, and apparent low complexity. Moreover, interactions between mutations in viral genomes determine traits such as resistance to antiviral drugs, virulence and host range. In this study we generated 53 Tobacco etch potyvirus genotypes carrying pairs of single-nucleotide substitutions and measured their separated and combined deleterious fitness effects. We found that up to 38% of pairs had significant epistasis for fitness, including both positive and negative deviations from the null hypothesis of multiplicative effects. Interestingly, the sign of epistasis was correlated with viral protein-protein interactions in a model network, being predominantly positive between linked pairs of proteins and negative between unlinked ones. Furthermore, 55% of significant interactions were cases of reciprocal sign epistasis (RSE), indicating that adaptive landscapes for RNA viruses maybe highly rugged. Finally, we found that the magnitude of epistasis correlated negatively with the average effect of mutations. Overall, our results are in good agreement to those previously reported for other viruses and further consolidate the view that positive epistasis is the norm for small and compact genomes that lack genetic robustness.     

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.     

Epistasis in Measured Genotypes: Drosophila P-Element Insertions

Transposon tagging provides an opportunity to construct large numbers of strains of organisms that differ by single insertional mutations. By scoring the phenotypes of these ``measured genotypes,' powerful tests of effects of mutations on phenotypic expression have been performed. Here we extend this approach by constructing with simple crosses all possible two-locus genotypes for each of eight pairs of P-element insertions. Analysis of metabolic phenotypes (fat and glycogen contents, enzyme activities, total protein, and body weight) of the resulting nine genotypes provides direct estimates of additive, dominance, and epistatic effects of the mutations. Nested two-way analysis of variance identified significant epistatic effects in 27% of the tests (35/128 of the trait X P-element combinations). Posterior contrasts were performed to partition the epistatic variance into the four orthogonal components of COCKERHAM, and the data exhibit a tendency toward additive X dominance and dominance X dominance epistasis. Mutations in this study have epistatic effects on metabolic traits that are on the same order of magnitude as main (additive and dominance) effects. Measured genotypes have been used in other contexts to quantify epistatic effects on phenotypic expression, and these results are also briefly reviewed.     

Coalescent under the evolution of coadaptation

Adaptation to novel environments arises either from new beneficial mutations or by utilizing pre‐existing genetic variation. When standing variation is used as the source of new adaptation, fitness effects of alleles may be altered through an environmental change. Alternatively, changes in epistatic genetic backgrounds may convert formerly neutral mutations into beneficial alleles in the new genetic background. By extending the coalescent theory to describe the genealogical histories of two interacting loci, I here investigated the hitchhiking effect of epistatic selection on the amount and pattern of sequence diversity at the linked neutral regions. Assuming a specific form of epistasis between two new mutations that are independently neutral, but together form a coadapted haplotype, I demonstrate that the footprints of epistatic selection differ markedly between the interacting loci depending on the order and relative timing of the two mutational events, even though both mutations are equally essential for the formation of an adaptive gene combination. Our results imply that even when neutrality tests could detect just a single instance of adaptive substitution, there may, in fact, be numerous other hidden mutations that are left undetected, but still play indispensable roles in the evolution of a new adaptation. We expect that the integration of the coalescent framework into the general theory of polygenic inheritance would clarify the connection between factors driving phenotypic evolution and their consequences on underlying DNA sequence changes, which should further illuminate the evolutionary foundation of coadapted systems.     

Pervasive Pairwise Intragenic Epistasis among Sequential Mutations in TEM-1 β-Lactamase

Interactions between mutations play a central role in shaping the fitness landscape, but a clear picture of intragenic epistasis has yet to emerge. To further reveal the prevalence and patterns of intragenic epistasis, we present a survey of epistatic interactions between sequential mutations in TEM-1 β-lactamase. We measured the fitness effect of ~ 12,000 pairs of consecutive amino acid substitutions and used our previous study of the fitness effects of single amino acid substitutions to calculate epistasis for over 8000 mutation pairs. Since sequential mutations are prone to physically interact, we postulated that our study would be surveying specific epistasis instead of nonspecific epistasis. We found widespread negative epistasis, especially in beta-strands, and a high frequency of negative sign epistasis among individually beneficial mutations. Negative epistasis (52%) occurred 7.6 times as frequently as positive epistasis (6.8%). Buried residues experienced more negative epistasis that surface-exposed residues. However, TEM-1 exhibited a couple of hotspots for positive epistasis, most notably L221/ R222 at which many combinations of mutations positively interacted. This study is the first to systematically examine pairwise epistasis throughout an entire protein performing its native function in its native host.     

Positive Epistasis Drives the Acquisition of Multidrug Resistance

The evolution of multiple antibiotic resistance is an increasing global problem. Resistance mutations are known to impair fitness, and the evolution of resistance to multiple drugs depends both on their costs individually and on how they interact—epistasis. Information on the level of epistasis between antibiotic resistance mutations is of key importance to understanding epistasis amongst deleterious alleles, a key theoretical question, and to improving public health measures. Here we show that in an antibiotic-free environment the cost of multiple resistance is smaller than expected, a signature of pervasive positive epistasis among alleles that confer resistance to antibiotics. Competition assays reveal that the cost of resistance to a given antibiotic is dependent on the presence of resistance alleles for other antibiotics. Surprisingly we find that a significant fraction of resistant mutations can be beneficial in certain resistant genetic backgrounds, that some double resistances entail no measurable cost, and that some allelic combinations are hotspots for rapid compensation. These results provide additional insight as to why multi-resistant bacteria are so prevalent and reveal an extra layer of complexity on epistatic patterns previously unrecognized, since it is hidden in genome-wide studies of genetic interactions using gene knockouts.     

Pervasive cryptic epistasis in molecular evolution

The functional effects of most amino acid replacements accumulated during molecular evolution are unknown, because most are not observed naturally and the possible combinations are too numerous. We created 168 single mutations in wild-type Escherichia coli isopropymalate dehydrogenase (IMDH) that match the differences found in wild-type Pseudomonas aeruginosa IMDH. 104 mutant enzymes performed similarly to E. coli wild-type IMDH, one was functionally enhanced, and 63 were functionally compromised. The transition from E. coli IMDH, or an ancestral form, to the functional wild-type P. aeruginosa IMDH requires extensive epistasis to ameliorate the combined effects of the deleterious mutations. This result stands in marked contrast with a basic assumption of molecular phylogenetics, that sites in sequences evolve independently of each other. Residues that affect function are scattered haphazardly throughout the IMDH structure. We screened for compensatory mutations at three sites, all of which lie near the active site and all of which are among the least active mutants. No compensatory mutations were found at two sites indicating that a single site may engage in compound epistatic interactions. One complete and three partial compensatory mutations of the third site are remote and lie in a different domain. This demonstrates that epistatic interactions can occur between distant (>20Å) sites. Phylogenetic analysis shows that incompatible mutations were fixed in different lineages.     

The role of deleterious mutations in allopatric speciation

Allopatric speciation is often assumed to occur as a consequence of adaptive divergence between two isolated populations. However, there are some scenarios in which reproductive isolation can be favored due to accumulated unconditionally deleterious mutations. If deleterious mutations have synergistic epistatic effects, it is shown here that the average fitness of recombinants between two parental lines with a given number of fixed mutations is lower than that of the parents in both the F1 and F2 generations. If individual mutations are only slightly deleterious, then they will tend to fixation at a high enough rate to cause lower hybrid fitness. If the fitness effects of mutation give rise to antagonistic epistasis, the hybrids tend to have a higher average fitness than the parental lines, suggesting a possible scenario for the origin of hybrid vigor. The other model of deleterious mutations investigated is the accumulation of knockout mutants in a duplicated gene family. While neutral in the parental lines, upon contact the F1 and later generations have a significant probability of carrying double knockouts. Under this scenario, selection may also favor reproductive isolation between the two lines. Even when the selection coefficients generated are too low to drive speciation, epistatic interactions between deleterious mutations offer a possible explanation for both outbreeding depression and hybrid vigor.     

The Environment Affects Epistatic Interactions to Alter the Topology of an Empirical Fitness Landscape

The fitness effect of mutations can be influenced by their interactions with the environment, other mutations, or both. Previously, we constructed 32 ( = 2⁵) genotypes that comprise all possible combinations of the first five beneficial mutations to fix in a laboratory-evolved population of Escherichia coli. We found that (i) all five mutations were beneficial for the background on which they occurred; (ii) interactions between mutations drove a diminishing returns type epistasis, whereby epistasis became increasingly antagonistic as the expected fitness of a genotype increased; and (iii) the adaptive landscape revealed by the mutation combinations was smooth, having a single global fitness peak. Here we examine how the environment influences epistasis by determining the interactions between the same mutations in two alternative environments, selected from among 1,920 screened environments, that produced the largest increase or decrease in fitness of the most derived genotype. Some general features of the interactions were consistent: mutations tended to remain beneficial and the overall pattern of epistasis was of diminishing returns. Other features depended on the environment; in particular, several mutations were deleterious when added to specific genotypes, indicating the presence of antagonistic interactions that were absent in the original selection environment. Antagonism was not caused by consistent pleiotropic effects of individual mutations but rather by changing interactions between mutations. Our results demonstrate that understanding adaptation in changing environments will require consideration of the combined effect of epistasis and pleiotropy across environments.     

Loss of least-loaded class in asexual populations due to drift and epistasis

We consider the dynamics of a nonrecombining haploid population of finite size that accumulates deleterious mutations irreversibly. This ratchet-like process occurs at a finite speed in the absence of epistasis, but it has been suggested that synergistic epistasis can halt the ratchet. Using a diffusion theory, we find explicit analytical expressions for the typical time between successive clicks of the ratchet for both nonepistatic and epistatic fitness functions. Our calculations show that the interclick time is of a scaling form that in the absence of epistasis gives a speed that is determined by size of the least-loaded class and the selection coefficient. With synergistic interactions, the ratchet speed is found to approach zero rapidly for arbitrary epistasis. Our analytical results are in good agreement with the numerical simulations.     

Perspective: Sign epistasis and genetic constraint on evolutionary trajectories

Epistasis for fitness means that the selective effect of a mutation is conditional on the genetic background in which it appears. Although epistasis is widely observed in nature, our understanding of its consequences for evolution by natural selection remains incomplete. In particular, much attention focuses only on its influence on the instantaneous rate of changes in frequency of selected alleles via epistatic contribution to the additive genetic variance for fitness. Thus, in this framework epistasis only has evolutionary importance if the interacting loci are simultaneously segregating in the population. However, the selective accessibility of mutational trajectories to high fitness genotypes may depend on the genetic background in which novel mutations appear, and this effect is independent of population polymorphism at other loci. Here we explore this second influence of epistasis on evolution by natural selection. We show that it is the consequence of a particular form of epistasis, which we designate sign epistasis. Sign epistasis means that the sign of the fitness effect of a mutation is under epistatic control; thus, such a mutation is beneficial on some genetic backgrounds and deleterious on others. Recent experimental innovations in microbial systems now permit assessment of the fitness effects of individual mutations on multiple genetic backgrounds. We review this literature and identify many examples of sign epistasis, and we suggest that the implications of these results may generalize to other organisms. These theoretical and empirical considerations imply that strong genetic constraint on the selective accessibility of trajectories to high fitness genotypes may exist and suggest specific areas of investigation for future research.     

A SHIFT FROM MAGNITUDE TO SIGN EPISTASIS DURING ADAPTIVE EVOLUTION OF A BACTERIAL SOCIAL TRAIT

Although the importance of epistasis in evolution has long been recognized, remarkably little is known about the processes by which epistatic interactions evolve in real time in specific biological systems. Here, we have characterized how the epistatic fitness relationship between a social gene and an adapting genome changes radically over a short evolutionary time frame in the social bacterium Myxococcus xanthus. We show that a highly beneficial effect of this social gene in the ancestral genome is gradually reduced—and ultimately reversed into a deleterious effect—over the course of an experimental adaptive trajectory in which a primitive form of novel cooperation evolved. This reduction and reversal of a positive social allelic effect is driven solely by changes in the genetic context in which the gene is expressed as new mutations are sequentially fixed during adaptive evolution, and explicitly demonstrates a significant evolutionary change in the genetic architecture of an ecologically important social trait.