Prevalence of epistasis in the evolution of influenza A surface proteins

The surface proteins of human influenza A viruses experience positive selection to escape both human immunity and, more recently, antiviral drug treatments. In bacteria and viruses, immune-escape and drug-resistant phenotypes often appear through a combination of several mutations that have epistatic effects on pathogen fitness. However, the extent and structure of epistasis in influenza viral proteins have not been systematically investigated. Here, we develop a novel statistical method to detect positive epistasis between pairs of sites in a protein, based on the observed temporal patterns of sequence evolution. The method rests on the simple idea that a substitution at one site should rapidly follow a substitution at another site if the sites are positively epistatic. We apply this method to the surface proteins hemagglutinin and neuraminidase of influenza A virus subtypes H3N2 and H1N1. Compared to a non-epistatic null distribution, we detect substantial amounts of epistasis and determine the identities of putatively epistatic pairs of sites. In particular, using sequence data alone, our method identifies epistatic interactions between specific sites in neuraminidase that have recently been demonstrated, in vitro, to confer resistance to the drug oseltamivir; these epistatic interactions are responsible for widespread drug resistance among H1N1 viruses circulating today. This experimental validation demonstrates the predictive power of our method to identify epistatic sites of importance for viral adaptation and public health. We conclude that epistasis plays a large role in shaping the molecular evolution of influenza viruses. In particular, sites with , which would normally not be identified as positively selected, can facilitate viral adaptation through epistatic interactions with their partner sites. The knowledge of specific interactions among sites in influenza proteins may help us to predict the course of antigenic evolution and, consequently, to select more appropriate vaccines and drugs.     

Multi-locus penetrance variance analysis method for association study in complex diseases

Common heritable diseases often result from the action of several different genes, each of which contributes to the total observed variability in the disease trait. Traditional single-locus association approaches rely heavily on the marginal effects of single-locus and tend to ignore the multigenic nature of complex diseases. The increasing request for localizing genes underlying traits in multi-gene diseases has led to the development of some statistical methods. In this study, we develop a multi-locus analysis method - multi-locus penetrance variance analysis (MPVA), and conduct systematical simulation studies to evaluate its performance. Our results show that compared with other multi-locus methods, MPVA has some advantage in detecting complicated interactions under different epistatic models, and its performance is stable and robust.     

Detecting purely epistatic multi-locus interactions by an omnibus permutation test on ensembles of two-locus analyses

Background  

Purely epistatic multi-locus interactions cannot generally be detected via single-locus analysis in case-control studies of complex diseases. Recently, many two-locus and multi-locus analysis techniques have been shown to be promising for the epistasis detection. However, exhaustive multi-locus analysis requires prohibitively large computational efforts when problems involve large-scale or genome-wide data. Furthermore, there is no explicit proof that a combination of multiple two-locus analyses can lead to the correct identification of multi-locus interactions.     

A penalized maximum likelihood method for estimating epistatic effects of QTL

Although epistasis is an important phenomenon in the genetics and evolution of complex traits, epistatic effects are hard to estimate. The main problem is due to the overparameterized epistatic genetic models. An epistatic genetic model should include potential pair-wise interaction effects of all loci. However, the model is saturated quickly as the number of loci increases. Therefore, a variable selection technique is usually considered to exclude those interactions with negligible effects. With such techniques, we may run a high risk of missing some important interaction effects by not fully exploring the extremely large parameter space of models. We develop a penalized maximum likelihood method. The method developed here adopts a penalty that depends on the values of the parameters. The penalized likelihood method allows spurious QTL effects to be shrunk towards zero, while QTL with large effects are estimated with virtually no shrinkage. A simulation study shows that the new method can handle a model with a number of effects 15 times larger than the sample size. Simulation studies also show that results of the penalized likelihood method are comparable to the Bayesian shrinkage analysis, but the computational speed of the penalized method is orders of magnitude faster.     

Inference on the strength of balancing selection for epistatically interacting loci

Existing inference methods for estimating the strength of balancing selection in multi-locus genotypes rely on the assumption that there are no epistatic interactions between loci. Complex systems in which balancing selection is prevalent, such as sets of human immune system genes, are known to contain components that interact epistatically. Therefore, current methods may not produce reliable inference on the strength of selection at these loci. In this paper, we address this problem by presenting statistical methods that can account for epistatic interactions in making inference about balancing selection. A theoretical result due to Fearnhead (2006) is used to build a multi-locus Wright-Fisher model of balancing selection, allowing for epistatic interactions among loci. Antagonistic and synergistic types of interactions are examined. The joint posterior distribution of the selection and mutation parameters is sampled by Markov chain Monte Carlo methods, and the plausibility of models is assessed via Bayes factors. As a component of the inference process, an algorithm to generate multi-locus allele frequencies under balancing selection models with epistasis is also presented. Recent evidence on interactions among a set of human immune system genes is introduced as a motivating biological system for the epistatic model, and data on these genes are used to demonstrate the methods.     

Effect of varying epistasis on the evolution of recombination

Whether recombination decelerates or accelerates a population's response to selection depends, at least in part, on how fitness-determining loci interact. Realistically, all genomes likely contain fitness interactions both with positive and with negative epistasis. Therefore, it is crucial to determine the conditions under which the potential beneficial effects of recombination with negative epistasis prevail over the detrimental effects of recombination with positive epistasis. Here, we examine the simultaneous effects of diverse epistatic interactions with different strengths and signs in a simplified model system with independent pairs of interacting loci and selection acting only on the haploid phase. We find that the average form of epistasis does not predict the average amount of linkage disequilibrium generated or the impact on a recombination modifier when compared to results using the entire distribution of epistatic effects and associated single-mutant effects. Moreover, we show that epistatic interactions of a given strength can produce very different effects, having the greatest impact when selection is weak. In summary, we observe that the evolution of recombination at mutation-selection balance might be driven by a small number of interactions with weak selection rather than by the average epistasis of all interactions. We illustrate this effect with an analysis of published data of Saccharomyces cerevisiae. Thus to draw conclusions on the evolution of recombination from experimental data, it is necessary to consider the distribution of epistatic interactions together with the associated selection coefficients.     

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.     

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.     

Bayesian model choice and search strategies for mapping interacting quantitative trait Loci

Most complex traits of animals, plants, and humans are influenced by multiple genetic and environmental factors. Interactions among multiple genes play fundamental roles in the genetic control and evolution of complex traits. Statistical modeling of interaction effects in quantitative trait loci (QTL) analysis must accommodate a very large number of potential genetic effects, which presents a major challenge to determining the genetic model with respect to the number of QTL, their positions, and their genetic effects. In this study, we use the methodology of Bayesian model and variable selection to develop strategies for identifying multiple QTL with complex epistatic patterns in experimental designs with two segregating genotypes. Specifically, we develop a reversible jump Markov chain Monte Carlo algorithm to determine the number of QTL and to select main and epistatic effects. With the proposed method, we can jointly infer the genetic model of a complex trait and the associated genetic parameters, including the number, positions, and main and epistatic effects of the identified QTL. Our method can map a large number of QTL with any combination of main and epistatic effects. Utility and flexibility of the method are demonstrated using both simulated data and a real data set. Sensitivity of posterior inference to prior specifications of the number and genetic effects of QTL is investigated.     

Where have all the interactions gone? Estimating the coverage of two-hybrid protein interaction maps

Yeast two-hybrid screens are an important method for mapping pairwise physical interactions between proteins. The fraction of interactions detected in independent screens can be very small, and an outstanding challenge is to determine the reason for the low overlap. Low overlap can arise from either a high false-discovery rate (interaction sets have low overlap because each set is contaminated by a large number of stochastic false-positive interactions) or a high false-negative rate (interaction sets have low overlap because each misses many true interactions). We extend capture-recapture theory to provide the first unified model for false-positive and false-negative rates for two-hybrid screens. Analysis of yeast, worm, and fly data indicates that 25% to 45% of the reported interactions are likely false positives. Membrane proteins have higher false-discovery rates on average, and signal transduction proteins have lower rates. The overall false-negative rate ranges from 75% for worm to 90% for fly, which arises from a roughly 50% false-negative rate due to statistical undersampling and a 55% to 85% false-negative rate due to proteins that appear to be systematically lost from the assays. Finally, statistical model selection conclusively rejects the Erd?s-Rényi network model in favor of the power law model for yeast and the truncated power law for worm and fly degree distributions. Much as genome sequencing coverage estimates were essential for planning the human genome sequencing project, the coverage estimates developed here will be valuable for guiding future proteomic screens. All software and datasets are available in and , -, and -, and are also available from our Web site, http://www.baderzone.org.     

Automated construction and testing of multi-locus gene-gene associations

It has been argued that the missing heritability in common diseases may be in part due to rare variants and gene-gene effects. Haplotype analyses provide more power for rare variants and joint analyses across genes can address multi-gene effects. Currently, methods are lacking to perform joint multi-locus association analyses across more than one gene/region. Here, we present a haplotype-mining gene-gene analysis method, which considers multi-locus data for two genes/regions simultaneously. This approach extends our single region haplotype-mining algorithm, hapConstructor, to two genes/regions. It allows construction of multi-locus SNP sets at both genes and tests joint gene-gene effects and interactions between single variants or haplotype combinations. A Monte Carlo framework is used to provide statistical significance assessment of the joint and interaction statistics, thus the method can also be used with related individuals. This tool provides a flexible data-mining approach to identifying gene-gene effects that otherwise is currently unavailable. AVAILABILITY: http://bioinformatics.med.utah.edu/Genie/hapConstructor.html.     

Evidence for subdivision of the root-endophyte Phialocephala fortinii into cryptic species and recombination within species

The genetic structure of the root-endophyte Phialocephala fortinii was analyzed in three study sites using 11 single-copy RFLP probes. A total of 541 strains isolated from surface-sterilized, fine roots (diameter 0.5-3 mm) of Norway spruce (Picea abies) were examined. The average gene diversity (H) was high in all three study sites. Cluster analysis showed that up to four well-separated clusters of multi-locus haplotypes were present within the sites. Significant population subdivision was detected among these clusters, suggesting that groups of multi-locus haplotypes were reproductively isolated and that P. fortinii is a species complex composed of several cryptic species. This hypothesis was supported by ISSR-PCR which showed clusters consistent with those of the multi-locus haplotypes identified by RFLP analysis. In contrast, ITS sequence analysis did not allow to separate the species as clearly. The index of association (IA) did not deviate significantly from zero within any cryptic species, suggesting that recombination occurs within these species. Cryptic species occurred sympatrically. Thalli of two cryptic species were detected in the same 5-mm-long root segment in one instance. No significant differentiation was observed among populations of the same cryptic species in forest stands located approximately 5 km from each other. This finding is consistent with significant gene flow over this spatial scale. In addition, several isolates with both identical multi-locus haplotype and identical ISSR fingerprint were found at each study site indicating genotype flow or a recent common history between study sites.     

A semi-symmetric two-locus model

The two-locus symmetric viability model characterized by its invariance with respect to the exchange of alleles at each locus, is a well-studied model of classical two-locus theory. The symmetric model introduced by Lewontin and Kojima is among the few multi-locus models with epistatic interactions between loci for which a polymorphism with linkage equilibrium can be stable and this happens when recombination is sufficiently large. We show that an analogous property holds true for a different model, in which symmetry need exist at only one locus. The properties of this new semi-symmetric model are compared with those of the classical symmetric model. For tight linkage, two classes of polymorphisms are possible, depending on the magnitude of additive epistasis. The recombination rate above which linkage equilibrium becomes stable is derived analytically. As in the symmetric model, intervals of recombination in which no polymorphism is stable are possible, and stable polymorphisms can coexist with stable fixations.     

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.     

Network models of TEM β-lactamase mutations coevolving under antibiotic selection show modular structure and anticipate evolutionary trajectories

Understanding how novel functions evolve (genetic adaptation) is a critical goal of evolutionary biology. Among asexual organisms, genetic adaptation involves multiple mutations that frequently interact in a non-linear fashion (epistasis). Non-linear interactions pose a formidable challenge for the computational prediction of mutation effects. Here we use the recent evolution of β-lactamase under antibiotic selection as a model for genetic adaptation. We build a network of coevolving residues (possible functional interactions), in which nodes are mutant residue positions and links represent two positions found mutated together in the same sequence. Most often these pairs occur in the setting of more complex mutants. Focusing on extended-spectrum resistant sequences, we use network-theoretical tools to identify triple mutant trajectories of likely special significance for adaptation. We extrapolate evolutionary paths (n = 3) that increase resistance and that are longer than the units used to build the network (n = 2). These paths consist of a limited number of residue positions and are enriched for known triple mutant combinations that increase cefotaxime resistance. We find that the pairs of residues used to build the network frequently decrease resistance compared to their corresponding singlets. This is a surprising result, given that their coevolution suggests a selective advantage. Thus, β-lactamase adaptation is highly epistatic. Our method can identify triplets that increase resistance despite the underlying rugged fitness landscape and has the unique ability to make predictions by placing each mutant residue position in its functional context. Our approach requires only sequence information, sufficient genetic diversity, and discrete selective pressures. Thus, it can be used to analyze recent evolutionary events, where coevolution analysis methods that use phylogeny or statistical coupling are not possible. Improving our ability to assess evolutionary trajectories will help predict the evolution of clinically relevant genes and aid in protein design.     

Epistasis and the mutation load: a measurement-theoretical approach

An approximate solution for the mean fitness in mutation-selection balance with arbitrary order of epistatic interaction is derived. The solution is based on the assumptions of coupling equilibrium and that the interaction effects are multilinear. We find that the effect of m-order epistatic interactions (i.e., interactions among groups of m loci) on the load is dependent on the total genomic mutation rate, U, to the mth power. Thus, higher-order gene interactions are potentially important if U is large and the interaction density among loci is not too low. The solution suggests that synergistic epistasis will decrease the mutation load and that variation in epistatic effects will elevate the load. Both of these results, however, are strictly true only if they refer to epistatic interaction strengths measured in the optimal genotype. If gene interactions are measured at mutation-selection equilibrium, only synergistic interactions among even numbers of genes will reduce the load. Odd-ordered synergistic interactions will then elevate the load. There is no systematic relationship between variation in epistasis and load at equilibrium. We argue that empirical estimates of gene interaction must pay attention to the genetic background in which the effects are measured and that it may be advantageous to refer to average interaction intensities as measured in mutation-selection equilibrium. We derive a simple criterion for the strength of epistasis that is necessary to overcome the twofold disadvantage of sex.     

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

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

How complete are current yeast and human protein-interaction networks?

We estimate the full yeast protein-protein interaction network to contain 37,800-75,500 interactions and the human network 154,000-369,000, but owing to a high false-positive rate, current maps are roughly only 50% and 10% complete, respectively. Paradoxically, releasing raw, unfiltered assay data might help separate true from false interactions.     

Epistatic models and pre-selection of markers improve prediction of performance in corn

In our previous papers, we demonstrated that the inclusion of epistatic interactions in marker models improved prediction for corn (Zea mays L.) grain quality traits. The utility of pre-selecting markers for epistatic models was not reported. In papers by other researchers, including epistatic effects in a model did not improve prediction efficacy for whole genome selection. The objectives of this study were therefore to evaluate the value of: (1) pre-selecting markers and interactions at different type 1 error levels to predict performance; (2) adding epistatic interactions to models including all markers, and (3) using marker-based models to predict performance of kernel weight (KWT), flowering date (FDT), and plant height (PHT). Data for KWT, FDT, PHT, and oil and protein concentrations were obtained for 500 S₂ lines and their testcrosses from the crosses of Illinois high oil × Illinois low oil and Illinois high protein × Illinois low protein corn strains. Pre-selection using an epistatic model including both single-locus and two-locus interaction effects significant at the P = 0.05 level significantly increased prediction efficacy over selection including all markers and epistatic interactions. Adding all epistatic interactions to a model including all markers did not improve prediction. For most traits, prediction based on the P = 0.05 epistatic pre-selection model was nearly as effective as prediction based on phenotype, suggesting subsequent marker-based selection would be effective.     

Evaluation of multi-locus models for genome-wide association studies: a case study in sugar beet

Association mapping has become a widely applied genomic approach to dissect the genetic architecture of complex traits. A major issue for association mapping is the need to control for the confounding effects of population structure, which is commonly done by mixed models incorporating kinship information. In this case study, we employed experimental data from a large sugar beet population to evaluate multi-locus models for association mapping. As in linkage mapping, markers are selected as cofactors to control for population structure and genetic background variation. We compared different biometric models with regard to important quantitative trait locus (QTL) mapping parameters like the false-positive rate, the QTL detection power and the predictive power for the proportion of explained genotypic variance. Employing different approaches we show that the multi-locus model, that is, incorporating cofactors, outperforms the other models, including the mixed model used as a reference model. Thus, multi-locus models are an attractive alternative for association mapping to efficiently detect QTL for knowledge-based breeding.