The impact of high‐order epistasis in the within‐host fitness of a positive‐sense plant RNA virus

RNA viruses are the main source of emerging infectious diseases because of the evolutionary potential bestowed by their fast replication, large population sizes and high mutation and recombination rates. However, an equally important property, which is usually neglected, is the topography of the fitness landscape. How many fitness maxima exist and how well they are connected is especially interesting, as this determines the number of accessible evolutionary pathways. To address this question, we have reconstructed a region of the fitness landscape of tobacco etch potyvirus constituted by mutations observed during the experimental adaptation of the virus to the novel host Arabidopsis thaliana. Fitness was measured for many genotypes and showed the existence of multiple peaks and holes in the landscape. We found prevailing epistatic effects between mutations, with cases of reciprocal sign epistasis being common among pairs of mutations. We also found that high‐order epistasis was as important as pairwise epistasis in their contribution to fitness. Therefore, results suggest that the landscape was rugged due to the existence of holes caused by lethal genotypes, that a very limited number of potential neutral paths exist and that it contained a single adaptive peak.     

Fitness landscapes emerging from pharmacodynamic functions in the evolution of multidrug resistance

Adaptive evolution often involves beneficial mutations at more than one locus. In this case, the trajectory and rate of adaptation is determined by the underlying fitness landscape, that is, the fitness values and mutational connectivity of all genotypes under consideration. Drug resistance, especially resistance to multiple drugs simultaneously, is also often conferred by mutations at several loci so that the concept of fitness landscapes becomes important. However, fitness landscapes underlying drug resistance are not static but dependent on drug concentrations, which means they are influenced by the pharmacodynamics of the drugs administered. Here, I present a mathematical framework for fitness landscapes of multidrug resistance based on Hill functions describing how drug concentrations affect fitness. I demonstrate that these ‘pharmacodynamic fitness landscapes’ are characterized by pervasive epistasis that arises through (i) fitness costs of resistance (even when these costs are additive), (ii) nonspecificity of resistance mutations to drugs, in particular cross‐resistance, and (iii) drug interactions (both synergistic and antagonistic). In the latter case, reciprocal drug suppression may even lead to reciprocal sign epistasis, so that the doubly resistant genotype occupies a local fitness peak that may be difficult to access by evolution. Simulations exploring the evolutionary dynamics on some pharmacodynamic fitness landscapes with both constant and changing drug concentrations confirm the crucial role of epistasis in determining the rate of multidrug resistance evolution.     

Epistatic interactions between ancestral genotype and beneficial mutations shape evolvability in Pseudomonas aeruginosa

The idea that interactions between mutations influence adaptation by driving populations to low and high fitness peaks on adaptive landscapes is deeply ingrained in evolutionary theory. Here, we investigate the impact of epistasis on evolvability by challenging populations of two Pseudomonas aeruginosa clones bearing different initial mutations (in rpoB conferring rifampicin resistance, and the type IV pili gene network) to adaptation to a medium containing l ‐serine as the sole carbon source. Despite being initially indistinguishable in fitness, populations founded by the two ancestral genotypes reached different fitness following 300 generations of evolution. Genome sequencing revealed that the difference could not be explained by acquiring mutations in different targets of selection; the majority of clones from both ancestors converged on one of the following two strategies: (1) acquiring mutations in either PA2449 (gcsR, an l ‐serine‐metabolism RpoN enhancer binding protein) or (2) protease genes. Additionally, populations from both ancestors converged on loss‐of‐function mutations in the type IV pili gene network, either due to ancestral or acquired mutations. No compensatory or reversion mutations were observed in RNA polymerase (RNAP) genes, in spite of the large fitness costs typically associated with mutations in rpoB. Although current theory points to sign epistasis as the dominant constraint on evolvability, these results suggest that the role of magnitude epistasis in constraining evolvability may be underappreciated. The contribution of magnitude epistasis is likely to be greatest under the biologically relevant mutation supply rates that make back mutations probabilistically unlikely.     

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.     

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.     

Mapping the Fitness Landscape of Gene Expression Uncovers the Cause of Antagonism and Sign Epistasis between Adaptive Mutations

How do adapting populations navigate the tensions between the costs of gene expression and the benefits of gene products to optimize the levels of many genes at once? Here we combined independently-arising beneficial mutations that altered enzyme levels in the central metabolism of Methylobacterium extorquens to uncover the fitness landscape defined by gene expression levels. We found strong antagonism and sign epistasis between these beneficial mutations. Mutations with the largest individual benefit interacted the most antagonistically with other mutations, a trend we also uncovered through analyses of datasets from other model systems. However, these beneficial mutations interacted multiplicatively (i.e., no epistasis) at the level of enzyme expression. By generating a model that predicts fitness from enzyme levels we could explain the observed sign epistasis as a result of overshooting the optimum defined by a balance between enzyme catalysis benefits and fitness costs. Knowledge of the phenotypic landscape also illuminated that, although the fitness peak was phenotypically far from the ancestral state, it was not genetically distant. Single beneficial mutations jumped straight toward the global optimum rather than being constrained to change the expression phenotypes in the correlated fashion expected by the genetic architecture. Given that adaptation in nature often results from optimizing gene expression, these conclusions can be widely applicable to other organisms and selective conditions. Poor interactions between individually beneficial alleles affecting gene expression may thus compromise the benefit of sex during adaptation and promote genetic differentiation.     

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.     

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.     

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.     

The Adaptive Potential of Hybridization Demonstrated with Bacteriophages

The success or failure of hybrids and the factors that determine their fitness have ecological, evolutionary, medical, and economic implications. Hybrid fitness is a major determinant of the size of hybrid zones and the maintenance of related species with overlapping ranges. It also influences the evolution of emerging pathogens and the success of economically important crop species experimentally hybridized in search of strains with increased yields or disease resistance. Hybrid fitness may largely be determined by the pervasiveness of epistasis in the genome, as epistasis is known to debilitate hybrids through disrupted inter- and intragenic interactions. We identified two bacteriophages isolated from their natural environment, one the result of a past hybridization event involving an ancestor of the other phage and a third, unknown phage. By performing a reciprocal cross of the affected region of the genome, consisting of a single complete gene, we both approximately recreated and reversed this original hybridization event in two chimeric bacteriophage genomes. Subsequent adaptation of the hybrid phages allowed for the recovery of fitness losses incurred by the hybrid genotypes. Furthermore, adaptation led to the ascension of a substantially higher and previously inaccessible adaptive peak. We show that by allowing genotypes to take large leaps across the adaptive landscape rather than single mutational steps, hybridization can lead to huge long-term fitness gains in spite of short-term costs resulting from disrupted epistatic interactions, demonstrating that the success or failure of hybrids may be determined not by their initial fitness, but rather by their adaptive potential.     

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.     

The rank ordering of genotypic fitness values predicts genetic constraint on natural selection on landscapes lacking sign epistasis

Sewall Wright's genotypic fitness landscape makes explicit one mechanism by which epistasis for fitness can constrain evolution by natural selection. Wright distinguished between landscapes possessing multiple fitness peaks and those with only a single peak and emphasized that the former class imposes substantially greater constraint on natural selection. Here I present novel formalism that more finely partitions the universe of possible fitness landscapes on the basis of the rank ordering of their genotypic fitness values. In this report I focus on fitness landscapes lacking sign epistasis (i.e., landscapes that lack mutations the sign of whose fitness effect varies epistatically), which constitute a subset of Wright's single peaked landscapes. More than one fitness rank ordering lacking sign epistasis exists for L > 2 (where L is the number of interacting loci), and I find that a highly statistically significant effect exists between landscape membership in fitness rank-ordering partition and two different proxies for genetic constraint, even within this subset of landscapes. This statistical association is robust to population size, permitting general inferences about some of the characteristics of fitness rank orderings responsible for genetic constraint on natural selection.     

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.     

Selection history and epistatic interactions impact dynamics of adaptation to novel environmental stresses

In rapidly changing environments, selection history may impact the dynamics of adaptation. Mutations selected in one environment may result in pleiotropic fitness trade-offs in subsequent novel environments, slowing the rates of adaptation. Epistatic interactions between mutations selected in sequential stressful environments may slow or accelerate subsequent rates of adaptation, depending on the nature of that interaction. We explored the dynamics of adaptation during sequential exposure to herbicides with different modes of action in Chlamydomonas reinhardtii. Evolution of resistance to two of the herbicides was largely independent of selection history. For carbetamide, previous adaptation to other herbicide modes of action positively impacted the likelihood of adaptation to this herbicide. Furthermore, while adaptation to all individual herbicides was associated with pleiotropic fitness costs in stress-free environments, we observed that accumulation of resistance mechanisms was accompanied by a reduction in overall fitness costs. We suggest that antagonistic epistasis may be a driving mechanism that enables populations to more readily adapt in novel environments. These findings highlight the potential for sequences of xenobiotics to facilitate the rapid evolution of multiple-drug and -pesticide resistance, as well as the potential for epistatic interactions between adaptive mutations to facilitate evolutionary rescue in rapidly changing environments.     

The causes of epistasis

Since Bateson's discovery that genes can suppress the phenotypic effects of other genes, gene interactions-called epistasis-have been the topic of a vast research effort. Systems and developmental biologists study epistasis to understand the genotype-phenotype map, whereas evolutionary biologists recognize the fundamental importance of epistasis for evolution. Depending on its form, epistasis may lead to divergence and speciation, provide evolutionary benefits to sex and affect the robustness and evolvability of organisms. That epistasis can itself be shaped by evolution has only recently been realized. Here, we review the empirical pattern of epistasis, and some of the factors that may affect the form and extent of epistasis. Based on their divergent consequences, we distinguish between interactions with or without mean effect, and those affecting the magnitude of fitness effects or their sign. Empirical work has begun to quantify epistasis in multiple dimensions in the context of metabolic and fitness landscape models. We discuss possible proximate causes (such as protein function and metabolic networks) and ultimate factors (including mutation, recombination, and the importance of natural selection and genetic drift). We conclude that, in general, pleiotropy is an important prerequisite for epistasis, and that epistasis may evolve as an adaptive or intrinsic consequence of changes in genetic robustness and evolvability.     

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.     

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.     

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.     

Expression profiles reveal parallel evolution of epistatic interactions involving the CRP regulon in Escherichia coli

The extent and nature of epistatic interactions between mutations are issues of fundamental importance in evolutionary biology. However, they are difficult to study and their influence on adaptation remains poorly understood. Here, we use a systems-level approach to examine epistatic interactions that arose during the evolution of Escherichia coli in a defined environment. We used expression arrays to compare the effect on global patterns of gene expression of deleting a central regulatory gene, crp. Effects were measured in two lineages that had independently evolved for 20,000 generations and in their common ancestor. We found that deleting crp had a much more dramatic effect on the expression profile of the two evolved lines than on the ancestor. Because the sequence of the crp gene was unchanged during evolution, these differences indicate epistatic interactions between crp and mutations at other loci that accumulated during evolution. Moreover, a striking degree of parallelism was observed between the two independently evolved lines; 115 genes that were not crp-dependent in the ancestor became dependent on crp in both evolved lines. An analysis of changes in crp dependence of well-characterized regulons identified a number of regulatory genes as candidates for harboring beneficial mutations that could account for these parallel expression changes. Mutations within three of these genes have previously been found and shown to contribute to fitness. Overall, these findings indicate that epistasis has been important in the adaptive evolution of these lines, and they provide new insight into the types of genetic changes through which epistasis can evolve. More generally, we demonstrate that expression profiles can be profitably used to investigate epistatic interactions.