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 buffers the fitness effects of rifampicin- resistance mutations in Pseudomonas aeruginosa

Epistatic interactions between resistance mutations in antibiotic-free environments potentially play a crucial role in the spread of resistance in pathogen populations by determining the fitness cost associated with resistance. We used an experimental evolution approach to test for epistatic interactions between 14 different pairs of rifampicin mutations in the pathogenic bacterium Pseudomonas aeruginosa in 42 different rifampicin-free environments. First, we show that epistasis between rifampicin-resistance mutations tends to be antagonistic: the fitness effect of having two mutations is generally smaller than that predicted from the effects of individual mutations on the wild-type. Second, we show that sign epistasis between resistance mutations is both common and strong; most notably, pairs of deleterious resistance mutations often partially or completely compensate for each others' costs, revealing a novel mechanism for compensatory adaptation. These results suggest that antagonistic epistasis between intragenic resistance mutations may be a key determinant of the cost of antibiotic resistance and compensatory adaptation in pathogen populations.     

Impact of epistasis and pleiotropy on evolutionary adaptation

Evolutionary adaptation is often likened to climbing a hill or peak. While this process is simple for fitness landscapes where mutations are independent, the interaction between mutations (epistasis) as well as mutations at loci that affect more than one trait (pleiotropy) are crucial in complex and realistic fitness landscapes. We investigate the impact of epistasis and pleiotropy on adaptive evolution by studying the evolution of a population of asexual haploid organisms (haplotypes) in a model of N interacting loci, where each locus interacts with K other loci. We use a quantitative measure of the magnitude of epistatic interactions between substitutions, and find that it is an increasing function of K. When haplotypes adapt at high mutation rates, more epistatic pairs of substitutions are observed on the line of descent than expected. The highest fitness is attained in landscapes with an intermediate amount of ruggedness that balance the higher fitness potential of interacting genes with their concomitant decreased evolvability. Our findings imply that the synergism between loci that interact epistatically is crucial for evolving genetic modules with high fitness, while too much ruggedness stalls the adaptive process.     

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 simple model of co-evolutionary dynamics caused by epistatic selection

Epistasis is the dependency of the effect of a mutation on the genetic background in which it occurs. Epistasis has been widely documented and implicated in the evolution of species barriers and the evolution of genetic architecture. Here we propose a simple model to formalize the idea that epistasis can also lead to co-evolutionary patterns in molecular evolution of interacting genes. This model epistasis is represented by the influence of one gene substitution on the fitness rank of the resident allele at another locus. We assume that increasing or decreasing fitness rank occur equally likely. In simulations we show that this form of epistasis leads to co-evolution in the sense that the length of an adaptive walk between interacting loci is highly correlated. This effect is caused by episodes of elevated rate of evolution in both loci simultaneously. We find that the influence of epistasis on these measures of co-evolutionary dynamics is relatively robust to the details of the model. The main factor influencing the correlation in evolutionary rates is the probability that a substitution will have an epistatic effect, but the strength of epistasis or the asymmetry of the initial fitness ranks of the alleles have only a minor effect. We suggest that covariance in rates of evolution among loci could be used to detect epistasis among loci.     

Properties of selected mutations and genotypic landscapes under Fisher's geometric model

The fitness landscape—the mapping between genotypes and fitness—determines properties of the process of adaptation. Several small genotypic fitness landscapes have recently been built by selecting a handful of beneficial mutations and measuring fitness of all combinations of these mutations. Here, we generate several testable predictions for the properties of these small genotypic landscapes under Fisher's geometric model of adaptation. When the ancestral strain is far from the fitness optimum, we analytically compute the fitness effect of selected mutations and their epistatic interactions. Epistasis may be negative or positive on average depending on the distance of the ancestral genotype to the optimum and whether mutations were independently selected, or coselected in an adaptive walk. Simulations show that genotypic landscapes built from Fisher's model are very close to an additive landscape when the ancestral strain is far from the optimum. However, when it is close to the optimum, a large diversity of landscape with substantial roughness and sign epistasis emerged. Strikingly, small genotypic landscapes built from several replicate adaptive walks on the same underlying landscape were highly variable, suggesting that several realizations of small genotypic landscapes are needed to gain information about the underlying architecture of the fitness landscape.     

Robustness to noise in gene expression evolves despite epistatic constraints in a model of gene networks

Stochastic noise in gene expression causes variation in the development of phenotypes, making such noise a potential target of stabilizing selection. Here, we develop a new simulation model of gene networks to study the adaptive landscape underlying the evolution of robustness to noise. We find that epistatic interactions between the determinants of the expression of a gene and its downstream effect impose significant constraints on evolution, but these interactions do allow the gradual evolution of increased robustness. Despite strong sign epistasis, adaptation rarely proceeds via deleterious intermediate steps, but instead occurs primarily through small beneficial mutations. A simple mathematical model captures the relevant features of the single‐gene fitness landscape and explains counterintuitive patterns, such as a correlation between the mean and standard deviation of phenotypes. In more complex networks, mutations in regulatory regions provide evolutionary pathways to increased robustness. These results chart the constraints and possibilities of adaptation to reduce expression noise and demonstrate the potential of a novel modeling framework for gene networks.     

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.     

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 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.     

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.     

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.     

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.     

SELECTION BIASES THE PREVALENCE AND TYPE OF EPISTASIS ALONG ADAPTIVE TRAJECTORIES

The contribution to an organism's phenotype from one genetic locus may depend upon the status of other loci. Such epistatic interactions among loci are now recognized as fundamental to shaping the process of adaptation in evolving populations. Although little is known about the structure of epistasis in most organisms, recent experiments with bacterial populations have concluded that antagonistic interactions abound and tend to deaccelerate the pace of adaptation over time. Here, we use the NK model of fitness landscapes to examine how natural selection biases the mutations that substitute during evolution based on their epistatic interactions. We find that, even when beneficial mutations are rare, these biases are strong and change substantially throughout the course of adaptation. In particular, epistasis is less prevalent than the neutral expectation early in adaptation and much more prevalent later, with a concomitant shift from predominantly antagonistic interactions early in adaptation to synergistic and sign epistasis later in adaptation. We observe the same patterns when reanalyzing data from a recent microbial evolution experiment. These results show that when the order of substitutions is not known, standard methods of analysis may suggest that epistasis retards adaptation when in fact it accelerates it.     

Reciprocal sign epistasis between frequently experimentally evolved adaptive mutations causes a rugged fitness landscape

The fitness landscape captures the relationship between genotype and evolutionary fitness and is a pervasive metaphor used to describe the possible evolutionary trajectories of adaptation. However, little is known about the actual shape of fitness landscapes, including whether valleys of low fitness create local fitness optima, acting as barriers to adaptive change. Here we provide evidence of a rugged molecular fitness landscape arising during an evolution experiment in an asexual population of Saccharomyces cerevisiae. We identify the mutations that arose during the evolution using whole-genome sequencing and use competitive fitness assays to describe the mutations individually responsible for adaptation. In addition, we find that a fitness valley between two adaptive mutations in the genes MTH1 and HXT6/HXT7 is caused by reciprocal sign epistasis, where the fitness cost of the double mutant prohibits the two mutations from being selected in the same genetic background. The constraint enforced by reciprocal sign epistasis causes the mutations to remain mutually exclusive during the experiment, even though adaptive mutations in these two genes occur several times in independent lineages during the experiment. Our results show that epistasis plays a key role during adaptation and that inter-genic interactions can act as barriers between adaptive solutions. These results also provide a new interpretation on the classic Dobzhansky-Muller model of reproductive isolation and display some surprising parallels with mutations in genes often associated with tumors.     

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.     

Genomewide Patterns of Substitution in Adaptively Evolving Populations of the RNA Bacteriophage MS2

Experimental evolution of bacteriophage provides a powerful means of studying the genetics of adaptation, as every substitution contributing to adaptation can be identified and characterized. Here, I use experimental evolution of MS2, an RNA bacteriophage, to study its adaptive response to a novel environment. To this end, three lines of MS2 were adapted to rapid growth and lysis at cold temperature for a minimum of 50 phage generations and subjected to whole-genome sequencing. Using this system, I identified adaptive substitutions, monitored changes in frequency of adaptive mutations through the course of the experiment, and measured the effect on phage growth rate of each substitution. All three lines showed a substantial increase in fitness (a two- to threefold increase in growth rate) due to a modest number of substitutions (three to four). The data show some evidence that the substitutions occurring early in the experiment have larger beneficial effects than later ones, in accordance with the expected diminishing returns relationship between the fitness effects of a mutation and its order of substitution. Patterns of molecular evolution seen here—primarily a paucity of hitchhiking mutations—suggest an abundant supply of beneficial mutations in this system. Nevertheless, some beneficial mutations appear to have been lost, possibly due to accumulation of beneficial mutations on other genetic backgrounds, clonal interference, and negatively epistatic interactions with other beneficial mutations.     

Pervasive sign epistasis between conjugative plasmids and drug-resistance chromosomal mutations

Multidrug-resistant bacteria arise mostly by the accumulation of plasmids and chromosomal mutations. Typically, these resistant determinants are costly to the bacterial cell. Yet, recently, it has been found that, in Escherichia coli bacterial cells, a mutation conferring resistance to an antibiotic can be advantageous to the bacterial cell if another antibiotic-resistance mutation is already present, a phenomenon called sign epistasis. Here we study the interaction between antibiotic-resistance chromosomal mutations and conjugative (i.e., self-transmissible) plasmids and find many cases of sign epistasis (40%)--including one of reciprocal sign epistasis where the strain carrying both resistance determinants is fitter than the two strains carrying only one of the determinants. This implies that the acquisition of an additional resistance plasmid or of a resistance mutation often increases the fitness of a bacterial strain already resistant to antibiotics. We further show that there is an overall antagonistic interaction between mutations and plasmids (52%). These results further complicate expectations of resistance reversal by interdiction of antibiotic use.     

The genetic code constrains yet facilitates Darwinian evolution

An important goal of evolutionary biology is to understand the constraints that shape the dynamics and outcomes of evolution. Here, we address the extent to which the structure of the standard genetic code constrains evolution by analyzing adaptive mutations of the antibiotic resistance gene TEM-1 β-lactamase and the fitness distribution of codon substitutions in two influenza hemagglutinin inhibitor genes. We find that the architecture of the genetic code significantly constrains the adaptive exploration of sequence space. However, the constraints endow the code with two advantages: the ability to restrict access to amino acid mutations with a strong negative effect and, most remarkably, the ability to enrich for adaptive mutations. Our findings support the hypothesis that the standard genetic code was shaped by selective pressure to minimize the deleterious effects of mutation yet facilitate the evolution of proteins through imposing an adaptive mutation bias.