Idiosyncratic epistasis creates universals in mutational effects and evolutionary trajectories

Environment-independent distribution of mutational effects emerges from microscopic epistasis

Predicting how new mutations alter phenotypes is difficult because mutational effects vary across genotypes and environments. Recently discovered global epistasis, where the fitness effects of mutations scale with the fitness of the background genotype, can improve predictions, but how the environment modulates this scaling is unknown. We measured the fitness effects of ~100 insertion mutations in 42 strains of Saccharomyces cerevisiae in six laboratory environments and found that the global-epistasis scaling is nearly invariant across environments. Instead, the environment tunes one global parameter, the background fitness at which most mutations switch sign. As a consequence, the distribution of mutational effects is predictable across genotypes and environments. Our results suggest that the effective dimensionality of genotype-to-phenotype maps across environments is surprisingly low.

The loci of environmental adaptation in a model eukaryote

While the underlying genetic changes have been uncovered in some cases of adaptive evolution, the lack of a systematic study prevents a general understanding of the genomic basis of adaptation. For example, it is unclear whether protein-coding or noncoding mutations are more important to adaptive evolution and whether adaptations to different environments are brought by genetic changes distributed in diverse genes and biological processes or concentrated in a core set. We here perform laboratory evolution of 3360 Saccharomyces cerevisiae populations in 252 environments of varying levels of stress. We find the yeast adaptations to be primarily fueled by large-effect coding mutations overrepresented in a relatively small gene set, despite prevalent antagonistic pleiotropy across environments. Populations generally adapt faster in more stressful environments, partly because of greater benefits of the same mutations in more stressful environments. These and other findings from this model eukaryote help unravel the genomic principles of environmental adaptation.

Epistasis facilitates functional evolution in an ancient transcription factor

A protein's genetic architecture - the set of causal rules by which its sequence produces its functions - also determines its possible evolutionary trajectories. Prior research has proposed that the genetic architecture of proteins is very complex, with pervasive epistatic interactions that constrain evolution and make function difficult to predict from sequence. Most of this work has analyzed only the direct paths between two proteins of interest - excluding the vast majority of possible genotypes and evolutionary trajectories - and has considered only a single protein function, leaving unaddressed the genetic architecture of functional specificity and its impact on the evolution of new functions. Here, we develop a new method based on ordinal logistic regression to directly characterize the global genetic determinants of multiple protein functions from 20-state combinatorial deep mutational scanning (DMS) experiments. We use it to dissect the genetic architecture and evolution of a transcription factor's specificity for DNA, using data from a combinatorial DMS of an ancient steroid hormone receptor's capacity to activate transcription from two biologically relevant DNA elements. We show that the genetic architecture of DNA recognition consists of a dense set of main and pairwise effects that involve virtually every possible amino acid state in the protein-DNA interface, but higher-order epistasis plays only a tiny role. Pairwise interactions enlarge the set of functional sequences and are the primary determinants of specificity for different DNA elements. They also massively expand the number of opportunities for single-residue mutations to switch specificity from one DNA target to another. By bringing variants with different functions close together in sequence space, pairwise epistasis therefore facilitates rather than constrains the evolution of new functions.

Pathway Evolution Through a Bottlenecking-Debottlenecking Strategy and Machine Learning-Aided Flux Balancing

The evolution of pathway enzymes enhances the biosynthesis of high-value chemicals, crucial for pharmaceutical, and agrochemical applications. However, unpredictable evolutionary landscapes of pathway genes often hinder successful evolution. Here, the presence of complex epistasis is identifued within the representative naringenin biosynthetic pathway enzymes, hampering straightforward directed evolution. Subsequently, a biofoundry-assisted strategy is developed for pathway bottlenecking and debottlenecking, enabling the parallel evolution of all pathway enzymes along a predictable evolutionary trajectory in six weeks. This study then utilizes a machine learning model, ProEnsemble, to further balance the pathway by optimizing the transcription of individual genes. The broad applicability of this strategy is demonstrated by constructing an Escherichia coli chassis with evolved and balanced pathway genes, resulting in 3.65 g L-1 naringenin. The optimized naringenin chassis also demonstrates enhanced production of other flavonoids. This approach can be readily adapted for any given number of enzymes in the specific metabolic pathway, paving the way for automated chassis construction in contemporary biofoundries.

Global epistasis in plasmid-mediated antimicrobial resistance

Antimicrobial resistance (AMR) in bacteria is a major public health threat and conjugative plasmids play a key role in the dissemination of AMR genes among bacterial pathogens. Interestingly, the association between AMR plasmids and pathogens is not random and certain associations spread successfully at a global scale. The burst of genome sequencing has increased the resolution of epidemiological programs, broadening our understanding of plasmid distribution in bacterial populations. Despite the immense value of these studies, our ability to predict future plasmid-bacteria associations remains limited. Numerous empirical studies have recently reported systematic patterns in genetic interactions that enable predictability, in a phenomenon known as global epistasis. In this perspective, we argue that global epistasis patterns hold the potential to predict interactions between plasmids and bacterial genomes, thereby facilitating the prediction of future successful associations. To assess the validity of this idea, we use previously published data to identify global epistasis patterns in clinically relevant plasmid-bacteria associations. Furthermore, using simple mechanistic models of antibiotic resistance, we illustrate how global epistasis patterns may allow us to generate new hypotheses on the mechanisms associated with successful plasmid-bacteria associations. Collectively, we aim at illustrating the relevance of exploring global epistasis in the context of plasmid biology.

A dynamical limit to evolutionary adaptation

Natural selection makes evolutionary adaptation possible even if the overwhelming majority of new mutations are deleterious. However, in rapidly evolving populations where numerous linked mutations occur and segregate simultaneously, clonal interference and genetic hitchhiking can limit the efficiency of selection, allowing deleterious mutations to accumulate over time. This can in principle overwhelm the fitness increases provided by beneficial mutations, leading to an overall fitness decline. Here, we analyze the conditions under which evolution will tend to drive populations to higher versus lower fitness. Our analysis focuses on quantifying the boundary between these two regimes, as a function of parameters such as population size, mutation rates, and selection pressures. This boundary represents a state in which adaptation is precisely balanced by Muller's ratchet, and we show that it can be characterized by rapid molecular evolution without any net fitness change. Finally, we consider the implications of global fitness-mediated epistasis and find that under some circumstances, this can drive populations toward the boundary state, which can thus represent a long-term evolutionary attractor.

Biophysical principles predict fitness of SARS-CoV-2 variants

SARS-CoV-2 employs its spike protein's receptor binding domain (RBD) to enter host cells. The RBD is constantly subjected to immune responses, while requiring efficient binding to host cell receptors for successful infection. However, our understanding of how RBD's biophysical properties contribute to SARS-CoV-2's epidemiological fitness remains largely incomplete. Through a comprehensive approach, comprising large-scale sequence analysis of SARS-CoV-2 variants and the discovery of a fitness function based on binding thermodynamics, we unravel the relationship between the biophysical properties of RBD variants and their contribution to viral fitness. We developed a biophysical model that uses statistical mechanics to map the molecular phenotype space, characterized by binding constants of RBD to ACE2, LY-CoV016, LY-CoV555, REGN10987, and S309, onto a epistatic fitness landscape. We validate our findings through experimentally measured and machine learning (ML) estimated binding affinities, coupled with infectivity data derived from population-level sequencing. Our analysis reveals that this model effectively predicts the fitness of novel RBD variants and can account for the epistatic interactions among mutations, including explaining the later reversal of Q493R. Our study sheds light on the impact of specific mutations on viral fitness and delivers a tool for predicting the future epidemiological trajectory of previously unseen or emerging low frequency variants. These insights offer not only greater understanding of viral evolution but also potentially aid in guiding public health decisions in the battle against COVID-19 and future pandemics.

Pervasive epistasis exposes intramolecular networks in adaptive enzyme evolution

Enzyme evolution is characterized by constant alterations of the intramolecular residue networks supporting their functions. The rewiring of these network interactions can give rise to epistasis. As mutations accumulate, the epistasis observed across diverse genotypes may appear idiosyncratic, that is, exhibit unique effects in different genetic backgrounds. Here, we unveil a quantitative picture of the prevalence and patterns of epistasis in enzyme evolution by analyzing 41 fitness landscapes generated from seven enzymes. We show that >94% of all mutational and epistatic effects appear highly idiosyncratic, which greatly distorted the functional prediction of the evolved enzymes. By examining seemingly idiosyncratic changes in epistasis along adaptive trajectories, we expose several instances of higher-order, intramolecular rewiring. Using complementary structural data, we outline putative molecular mechanisms explaining higher-order epistasis along two enzyme trajectories. Our work emphasizes the prevalence of epistasis and provides an approach to exploring this phenomenon through a molecular lens.

Environmental modulation of global epistasis in a drug resistance fitness landscape

Interactions between mutations (epistasis) can add substantial complexity to genotype-phenotype maps, hampering our ability to predict evolution. Yet, recent studies have shown that the fitness effect of a mutation can often be predicted from the fitness of its genetic background using simple, linear relationships. This phenomenon, termed global epistasis, has been leveraged to reconstruct fitness landscapes and infer adaptive trajectories in a wide variety of contexts. However, little attention has been paid to how patterns of global epistasis may be affected by environmental variation, despite this variation frequently being a major driver of evolution. This is particularly relevant for the evolution of drug resistance, where antimicrobial drugs may change the environment faced by pathogens and shape their adaptive trajectories in ways that can be difficult to predict. By analyzing a fitness landscape of four mutations in a gene encoding an essential enzyme of P. falciparum (a parasite cause of malaria), here we show that patterns of global epistasis can be strongly modulated by the concentration of a drug in the environment. Expanding on previous theoretical results, we demonstrate that this modulation can be quantitatively explained by how specific gene-by-gene interactions are modified by drug dose. Importantly, our results highlight the need to incorporate potential environmental variation into the global epistasis framework in order to predict adaptation in dynamic environments.

Statistically learning the functional landscape of microbial communities

Microbial consortia exhibit complex functional properties in contexts ranging from soils to bioreactors to human hosts. Understanding how community composition determines function is a major goal of microbial ecology. Here we address this challenge using the concept of community-function landscapes-analogues to fitness landscapes-that capture how changes in community composition alter collective function. Using datasets that represent a broad set of community functions, from production/degradation of specific compounds to biomass generation, we show that statistically inferred landscapes quantitatively predict community functions from knowledge of species presence or absence. Crucially, community-function landscapes allow prediction without explicit knowledge of abundance dynamics or interactions between species and can be accurately trained using measurements from a small subset of all possible community compositions. The success of our approach arises from the fact that empirical community-function landscapes appear to be not rugged, meaning that they largely lack high-order epistatic contributions that would be difficult to fit with limited data. Finally, we show that this observation holds across a wide class of ecological models, suggesting community-function landscapes can be efficiently inferred across a broad range of ecological regimes. Our results open the door to the rational design of consortia without detailed knowledge of abundance dynamics or interactions.

Idiosyncratic and dose-dependent epistasis drives variation in tomato fruit size

Epistasis between genes is traditionally studied with mutations that eliminate protein activity, but most natural genetic variation is in cis-regulatory DNA and influences gene expression and function quantitatively. In this study, we used natural and engineered cis-regulatory alleles in a plant stem-cell circuit to systematically evaluate epistatic relationships controlling tomato fruit size. Combining a promoter allelic series with two other loci, we collected over 30,000 phenotypic data points from 46 genotypes to quantify how allele strength transforms epistasis. We revealed a saturating dose-dependent relationship but also allele-specific idiosyncratic interactions, including between alleles driving a step change in fruit size during domestication. Our approach and findings expose an underexplored dimension of epistasis, in which cis-regulatory allelic diversity within gene regulatory networks elicits nonlinear, unpredictable interactions that shape phenotypes.

Human deleterious mutation rate implies high fitness variance, with declining mean fitness compensated by rarer beneficial mutations of larger effect

Each new human has an expected Ud = 2 - 10 new deleterious mutations. This deluge of deleterious mutations cannot all be purged, and therefore accumulate in a declining fitness ratchet. Using a novel simulation framework designed to efficiently handle genome-wide linkage disequilibria across many segregating sites, we find that rarer, beneficial mutations of larger effect are sufficient to compensate fitness declines due to the fixation of many slightly deleterious mutations. Drift barrier theory posits a similar asymmetric pattern of fixations to explain ratcheting genome size and complexity, but in our theory, the cause is Ud > 1 rather than small population size. In our simulations, Ud ~2 - 10 generates high within-population variance in relative fitness; two individuals will typically differ in fitness by 15-40%. Ud ~2 - 10 also slows net adaptation by ~13%-39%. Surprisingly, fixation rates are more sensitive to changes in the beneficial than the deleterious mutation rate, e.g. a 10% increase in overall mutation rate leads to faster adaptation; this puts to rest dysgenic fears about increasing mutation rates due to rising paternal age.

A dynamical limit to evolutionary adaptation

Natural selection makes evolutionary adaptation possible even if the overwhelming majority of new mutations are deleterious. However, in rapidly evolving populations where numerous linked mutations occur and segregate simultaneously, clonal interference and genetic hitchhiking can limit the efficiency of selection, allowing deleterious mutations to accumulate over time. This can in principle overwhelm the fitness increases provided by beneficial mutations, leading to an overall fitness decline. Here, we analyze the conditions under which evolution will tend to drive populations to higher versus lower fitness. Our analysis focuses on quantifying the boundary between these two regimes, as a function of parameters such as population size, mutation rates, and selection pressures. This boundary represents a state in which adaptation is precisely balanced by Muller's ratchet, and we show that it can be characterized by rapid molecular evolution without any net fitness change. Finally, we consider the implications of global fitness-mediated epistasis, and find that under some circumstances this can drive populations towards the boundary state, which can thus represent a long-term evolutionary attractor.

Epistasis and evolution: recent advances and an outlook for prediction

As organisms evolve, the effects of mutations change as a result of epistatic interactions with other mutations accumulated along the line of descent. This can lead to shifts in adaptability or robustness that ultimately shape subsequent evolution. Here, we review recent advances in measuring, modeling, and predicting epistasis along evolutionary trajectories, both in microbial cells and single proteins. We focus on simple patterns of global epistasis that emerge in this data, in which the effects of mutations can be predicted by a small number of variables. The emergence of these patterns offers promise for efforts to model epistasis and predict evolution.

Environment-dependent epistasis increases phenotypic diversity in gene regulatory networks

Mutations to gene regulatory networks can be maladaptive or a source of evolutionary novelty. Epistasis confounds our understanding of how mutations affect the expression patterns of gene regulatory networks, a challenge exacerbated by the dependence of epistasis on the environment. We used the toolkit of synthetic biology to systematically assay the effects of pairwise and triplet combinations of mutant genotypes on the expression pattern of a gene regulatory network expressed in Escherichia coli that interprets an inducer gradient across a spatial domain. We uncovered a preponderance of epistasis that can switch in magnitude and sign across the inducer gradient to produce a greater diversity of expression pattern phenotypes than would be possible in the absence of such environment-dependent epistasis. We discuss our findings in the context of the evolution of hybrid incompatibilities and evolutionary novelties.

Global epistasis on fitness landscapes

Epistatic interactions between mutations add substantial complexity to adaptive landscapes and are often thought of as detrimental to our ability to predict evolution. Yet, patterns of global epistasis, in which the fitness effect of a mutation is well-predicted by the fitness of its genetic background, may actually be of help in our efforts to reconstruct fitness landscapes and infer adaptive trajectories. Microscopic interactions between mutations, or inherent nonlinearities in the fitness landscape, may cause global epistasis patterns to emerge. In this brief review, we provide a succinct overview of recent work about global epistasis, with an emphasis on building intuition about why it is often observed. To this end, we reconcile simple geometric reasoning with recent mathematical analyses, using these to explain why different mutations in an empirical landscape may exhibit different global epistasis patterns—ranging from diminishing to increasing returns. Finally, we highlight open questions and research directions.

This article is part of the theme issue ‘Interdisciplinary approaches to predicting evolutionary biology’.

Widespread epistasis among beneficial genetic variants revealed by high-throughput genome editing

The phenotypic effect of any genetic variant can be altered by variation at other genomic loci. Known as epistasis, these genetic interactions shape the genotype-phenotype map of every species, yet their origins remain poorly understood. To investigate this, we employed high-throughput genome editing to measure the fitness effects of 1,826 naturally polymorphic variants in four strains of Saccharomyces cerevisiae. About 31% of variants affect fitness, of which 24% have strain-specific fitness effects indicative of epistasis. We found that beneficial variants are more likely to exhibit genetic interactions and that these interactions can be mediated by specific traits such as flocculation ability. This work suggests that adaptive evolution will often involve trade-offs where a variant is only beneficial in some genetic backgrounds, potentially explaining why many beneficial variants remain polymorphic. In sum, we provide a framework to understand the factors influencing epistasis with single-nucleotide resolution, revealing widespread epistasis among beneficial variants.

KLF4 transcription factor in tumorigenesis

Krüppel-like transcriptional factor is important in maintaining cellular functions. Deletion of Krüppel-like transcriptional factor usually causes abnormal embryonic development and even embryonic death. KLF4 is a prominent member of this family, and embryonic deletion of KLF4 leads to alterations in skin permeability and postnatal death. In addition to its important role in embryo development, it also plays a critical role in inflammation and malignancy. It has been investigated that KLF4 has a regulatory role in a variety of cancers, including lung, breast, prostate, colorectal, pancreatic, hepatocellular, ovarian, esophageal, bladder and brain cancer. However, the role of KLF4 in tumorigenesis is complex, which may link to its unique structure with both transcriptional activation and transcriptional repression domains, and to the regulation of its upstream and downstream signaling molecules. In this review, we will summarize the structural and functional aspects of KLF4, with a focus on KLF4 as a clinical biomarker and therapeutic target in different types of tumors.

What Has Genomics Taught An Evolutionary Biologist?

Genomics, an interdisciplinary field of biology on the structure, function, and evolution of genomes, has revolutionized many subdisciplines of life sciences, including my field of evolutionary biology, by supplying huge data, bringing high-throughput technologies, and offering a new approach to biology. In this review, I describe what I have learned from genomics and highlight the fundamental knowledge and mechanistic insights gained. I focus on three broad topics that are central to evolutionary biology and beyond-variation, interaction, and selection-and use primarily my own research and study subjects as examples. In the next decade or two, I expect that the most important contributions of genomics to evolutionary biology will be to provide genome sequences of nearly all known species on Earth, facilitate high-throughput phenotyping of natural variants and systematically constructed mutants for mapping genotype-phenotype-fitness landscapes, and assist the determination of causality in evolutionary processes using experimental evolution.

Epistasis and evolutionary dependencies in human cancers

Cancer evolution is driven by the concerted action of multiple molecular alterations, which emerge and are selected during tumor progression. An alteration is selected when it provides an advantage to the tumor cell. However, the advantage provided by a specific alteration depends on the tumor lineage, cell epigenetic state, and presence of additional alterations. In this case, we say that an evolutionary dependency exists between an alteration and what influences its selection. Epistatic interactions between altered genes lead to evolutionary dependencies (EDs), by favoring or vetoing specific combinations of events. Large-scale cancer genomics studies have discovered examples of such dependencies, and showed that they influence tumor progression, disease phenotypes, and therapeutic response. In the past decade, several algorithmic approaches have been proposed to infer EDs from large-scale genomics datasets. These methods adopt diverse strategies to address common challenges and shed new light on cancer evolutionary trajectories. Here, we review these efforts starting from a simple conceptualization of the problem, presenting the tackled and still unmet needs in the field, and discussing the implications of EDs in cancer biology and precision oncology.

Fitness of evolving bacterial populations is contingent on deep and shallow history but only shallow history creates predictable patterns

Long-term evolution experiments have tested the importance of genetic and environmental factors in influencing evolutionary outcomes. Differences in phylogenetic history, recent adaptation to distinct environments and chance events, all influence the fitness of a population. However, the interplay of these factors on a population's evolutionary potential remains relatively unexplored. We tracked the outcome of 2000 generations of evolution of four natural isolates of Escherichia coli bacteria that were engineered to also create differences in shallow history by adding previously identified mutations selected in a separate long-term experiment. Replicate populations started from each progenitor evolved in four environments. We found that deep and shallow phylogenetic histories both contributed significantly to differences in evolved fitness, though by different amounts in different selection environments. With one exception, chance effects were not significant. Whereas the effect of deep history did not follow any detectable pattern, effects of shallow history followed a pattern of diminishing returns whereby fitter ancestors had smaller fitness increases. These results are consistent with adaptive evolution being contingent on the interaction of several evolutionary forces but demonstrate that the nature of these interactions is not fixed and may not be predictable even when the role of chance is small.

Selection in a growing colony biases results of mutation accumulation experiments

Mutations provide the raw material for natural selection to act. Therefore, understanding the variety and relative frequency of different type of mutations is critical to understanding the nature of genetic diversity in a population. Mutation accumulation (MA) experiments have been used in this context to estimate parameters defining mutation rates, distribution of fitness effects (DFE), and spectrum of mutations. MA experiments can be performed with different effective population sizes. In MA experiments with bacteria, a single founder is grown to a size of a colony (~ 10⁸). It is assumed that natural selection plays a minimal role in dictating the dynamics of colony growth. In this work, we simulate colony growth via a mathematical model, and use our model to mimic an MA experiment. We demonstrate that selection ensures that, in an MA experiment, fraction of all mutations that are beneficial is over-represented by a factor of almost two, and that the distribution of fitness effects of beneficial and deleterious mutations are inaccurately captured in an MA experiment. Given this, the estimate of mutation rates from MA experiments is non-trivial. We then perform an MA experiment with 160 lines of E. coli, and show that due to the effect of selection in a growing colony, the size and sector of a colony from which the experiment is propagated impacts the results. Overall, we demonstrate that the results of MA experiments need to be revisited taking into account the action of selection in a growing colony.

Mutational robustness changes during long-term adaptation in laboratory budding yeast populations

As an adapting population traverses the fitness landscape, its local neighborhood (i.e., the collection of fitness effects of single-step mutations) can change shape because of interactions with mutations acquired during evolution. These changes to the distribution of fitness effects can affect both the rate of adaptation and the accumulation of deleterious mutations. However, while numerous models of fitness landscapes have been proposed in the literature, empirical data on how this distribution changes during evolution remains limited. In this study, we directly measure how the fitness landscape neighborhood changes during laboratory adaptation. Using a barcode-based mutagenesis system, we measure the fitness effects of 91 specific gene disruption mutations in genetic backgrounds spanning 8000–10,000 generations of evolution in two constant environments. We find that the mean of the distribution of fitness effects decreases in one environment, indicating a reduction in mutational robustness, but does not change in the other. We show that these distribution-level patterns result from differences in the relative frequency of certain patterns of epistasis at the level of individual mutations, including fitness-correlated and idiosyncratic epistasis.

Idiosyncratic epistasis leads to global fitness-correlated trends

Epistasis can markedly affect evolutionary trajectories. In recent decades, protein-level fitness landscapes have revealed extensive idiosyncratic epistasis among specific mutations. By contrast, other work has found ubiquitous and apparently nonspecific patterns of global diminishing-returns and increasing-costs epistasis among mutations across the genome. Here, we used a hierarchical CRISPR gene drive system to construct all combinations of 10 missense mutations from across the genome in budding yeast and measured their fitness in six environments. We show that the resulting fitness landscapes exhibit global fitness-correlated trends but that these trends emerge from specific idiosyncratic interactions. We thus provide experimental validation of recent theoretical work arguing that fitness-correlated trends can emerge as the generic consequence of idiosyncratic epistasis.

Transposon insertional mutagenesis of diverse yeast strains suggests coordinated gene essentiality polymorphisms

Due to epistasis, the same mutation can have drastically different phenotypic consequences in different individuals. This phenomenon is pertinent to precision medicine as well as antimicrobial drug development, but its general characteristics are largely unknown. We approach this question by genome-wide assessment of gene essentiality polymorphism in 16 Saccharomyces cerevisiae strains using transposon insertional mutagenesis. Essentiality polymorphism is observed for 9.8% of genes, most of which have had repeated essentiality switches in evolution. Genes exhibiting essentiality polymorphism lean toward having intermediate numbers of genetic and protein interactions. Gene essentiality changes tend to occur concordantly among components of the same protein complex or metabolic pathway and among a group of over 100 mitochondrial proteins, revealing molecular machines or functional modules as units of gene essentiality variation. Most essential genes tolerate transposon insertions consistently among strains in one or more coding segments, delineating nonessential regions within essential genes.

Ploidy and recombination proficiency shape the evolutionary adaptation to constitutive DNA replication stress

In haploid budding yeast, evolutionary adaptation to constitutive DNA replication stress alters three genome maintenance modules: DNA replication, the DNA damage checkpoint, and sister chromatid cohesion. We asked how these trajectories depend on genomic features by comparing the adaptation in three strains: haploids, diploids, and recombination deficient haploids. In all three, adaptation happens within 1000 generations at rates that are correlated with the initial fitness defect of the ancestors. Mutations in individual genes are selected at different frequencies in populations with different genomic features, but the benefits these mutations confer are similar in the three strains, and combinations of these mutations reproduce the fitness gains of evolved populations. Despite the differences in the selected mutations, adaptation targets the same three functional modules in strains with different genomic features, revealing a common evolutionary response to constitutive DNA replication stress.

An evolution-based high-fidelity method of epistasis measurement: Theory and application to influenza

Linkage effects in a multi-locus population strongly influence its evolution. The models based on the traveling wave approach enable us to predict the average speed of evolution and the statistics of phylogeny. However, predicting statistically the evolution of specific sites and pairs of sites in the multi-locus context remains a mathematical challenge. In particular, the effects of epistasis, the interaction of gene regions contributing to phenotype, is difficult to predict theoretically and detect experimentally in sequence data. A large number of false-positive interactions arises from stochastic linkage effects and indirect interactions, which mask true epistatic interactions. Here we develop a proof-of-principle method to filter out false-positive interactions. We start by demonstrating that the averaging of haplotype frequencies over multiple independent populations is necessary but not sufficient for epistatic detection, because it still leaves high numbers of false-positive interactions. To compensate for the residual stochastic noise, we develop a three-way haplotype method isolating true interactions. The fidelity of the method is confirmed analytically and on simulated genetic sequences evolved with a known epistatic network. The method is then applied to a large sequence database of neurominidase protein of influenza A H1N1 obtained from various geographic locations to infer the epistatic network responsible for the difference between the pre-pandemic virus and the pandemic strain of 2009. These results present a simple and reliable technique to measure epistatic interactions of any sign from sequence data.

Interactions between genomic sites create a fitness landscape. The knowledge of topology and strength of interactions is vital for predicting the escape of viruses from drugs and immune response and their passing through fitness valleys. Many efforts have been invested into measuring these interactions from DNA sequence sets. Unfortunately, reproducibility of the results remains low due partly to a very small fraction of interaction pairs and partly to stochastic linkage noise masking true interactions. Here we propose a method to separate stochastic linkage and indirect interactions from epistatic interactions and apply it to influenza virus sequence data.

Global epistasis emerges from a generic model of a complex trait

Epistasis between mutations can make adaptation contingent on evolutionary history. Yet despite widespread ‘microscopic’ epistasis between the mutations involved, microbial evolution experiments show consistent patterns of fitness increase between replicate lines. Recent work shows that this consistency is driven in part by global patterns of diminishing-returns and increasing-costs epistasis, which make mutations systematically less beneficial (or more deleterious) on fitter genetic backgrounds. However, the origin of this ‘global’ epistasis remains unknown. Here, we show that diminishing-returns and increasing-costs epistasis emerge generically as a consequence of pervasive microscopic epistasis. Our model predicts a specific quantitative relationship between the magnitude of global epistasis and the stochastic effects of microscopic epistasis, which we confirm by reanalyzing existing data. We further show that the distribution of fitness effects takes on a universal form when epistasis is widespread and introduce a novel fitness landscape model to show how phenotypic evolution can be repeatable despite sequence-level stochasticity.

Emergence and propagation of epistasis in metabolic networks

Epistasis is often used to probe functional relationships between genes, and it plays an important role in evolution. However, we lack theory to understand how functional relationships at the molecular level translate into epistasis at the level of whole-organism phenotypes, such as fitness. Here, I derive two rules for how epistasis between mutations with small effects propagates from lower- to higher-level phenotypes in a hierarchical metabolic network with first-order kinetics and how such epistasis depends on topology. Most importantly, weak epistasis at a lower level may be distorted as it propagates to higher levels. Computational analyses show that epistasis in more realistic models likely follows similar, albeit more complex, patterns. These results suggest that pairwise inter-gene epistasis should be common, and it should generically depend on the genetic background and environment. Furthermore, the epistasis coefficients measured for high-level phenotypes may not be sufficient to fully infer the underlying functional relationships.