On the classification of epistatic interactions

Resolving discrepancies between chimeric and multiplicative measures of higher-order epistasis

Epistasis - the interaction between alleles at different genetic loci - plays a fundamental role in biology. However, several recent approaches quantify epistasis using a chimeric formula that measures deviations from a multiplicative fitness model on an additive scale, thus mixing two scales. Here, we show that for pairwise interactions, the chimeric formula yields a different magnitude but the same sign of epistasis compared to the multiplicative formula that measures both fitness and deviations on a multiplicative scale. However, for higher-order interactions, we show that the chimeric formula can have both different magnitude and sign compared to the multiplicative formula. We resolve these inconsistencies by deriving mathematical relationships between the different epistasis formulae and different parametrizations of the multivariate Bernoulli distribution. We argue that the chimeric formula does not appropriately model interactions between the Bernoulli random variables. In simulations, we show that the chimeric formula is less accurate than the classical multiplicative/additive epistasis formulae and may falsely detect higher-order epistasis. Analyzing multi-gene knockouts in yeast, multi-way drug interactions in E. coli, and deep mutational scanning of several proteins, we find that approximately 10% to 60% of inferred higher-order interactions change sign using the multiplicative/additive formula compared to the chimeric formula.

Quantifying higher-order epistasis: beware the chimera

Epistasis, or interactions in which alleles at one locus modify the fitness effects of alleles at other loci, plays a fundamental role in genetics, protein evolution, and many other areas of biology. Epistasis is typically quantified by computing the deviation from the expected fitness under an additive or multiplicative model using one of several formulae. However, these formulae are not all equivalent. Importantly, one widely used formula - which we call the chimeric formula - measures deviations from a multiplicative fitness model on an additive scale, thus mixing two measurement scales. We show that for pairwise interactions, the chimeric formula yields a different magnitude, but the same sign (synergistic vs. antagonistic) of epistasis compared to the multiplicative formula that measures both fitness and deviations on a multiplicative scale. However, for higher-order interactions, we show that the chimeric formula can have both different magnitude and sign compared to the multiplicative formula - thus confusing negative epistatic interactions with positive interactions, and vice versa. We resolve these inconsistencies by deriving fundamental connections between the different epistasis formulae and the parameters of the multivariate Bernoulli distribution . Our results demonstrate that the additive and multiplicative epistasis formulae are more mathematically sound than the chimeric formula. Moreover, we demonstrate that the mathematical issues with the chimeric epistasis formula lead to markedly different biological interpretations of real data. Analyzing multi-gene knockout data in yeast, multi-way drug interactions in E. coli , and deep mutational scanning (DMS) of several proteins, we find that 10 - 60% of higher-order interactions have a change in sign with the multiplicative or additive epistasis formula. These sign changes result in qualitatively different findings on functional divergence in the yeast genome, synergistic vs. antagonistic drug interactions, and and epistasis between protein mutations. In particular, in the yeast data, the more appropriate multiplicative formula identifies nearly 500 additional negative three-way interactions, thus extending the trigenic interaction network by 25%.

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.

On the incongruence of genotype-phenotype and fitness landscapes

The mapping from genotype to phenotype to fitness typically involves multiple nonlinearities that can transform the effects of mutations. For example, mutations may contribute additively to a phenotype, but their effects on fitness may combine non-additively because selection favors a low or intermediate value of that phenotype. This can cause incongruence between the topographical properties of a fitness landscape and its underlying genotype-phenotype landscape. Yet, genotype-phenotype landscapes are often used as a proxy for fitness landscapes to study the dynamics and predictability of evolution. Here, we use theoretical models and empirical data on transcription factor-DNA interactions to systematically study the incongruence of genotype-phenotype and fitness landscapes when selection favors a low or intermediate phenotypic value. Using the theoretical models, we prove a number of fundamental results. For example, selection for low or intermediate phenotypic values does not change simple sign epistasis into reciprocal sign epistasis, implying that genotype-phenotype landscapes with only simple sign epistasis motifs will always give rise to single-peaked fitness landscapes under such selection. More broadly, we show that such selection tends to create fitness landscapes that are more rugged than the underlying genotype-phenotype landscape, but this increased ruggedness typically does not frustrate adaptive evolution because the local adaptive peaks in the fitness landscape tend to be nearly as tall as the global peak. Many of these results carry forward to the empirical genotype-phenotype landscapes, which may help to explain why low- and intermediate-affinity transcription factor-DNA interactions are so prevalent in eukaryotic gene regulation.

Non-additive microbial community responses to environmental complexity

Environmental composition is a major, though poorly understood, determinant of microbiome dynamics. Here we ask whether general principles govern how microbial community growth yield and diversity scale with an increasing number of environmental molecules. By assembling hundreds of synthetic consortia in vitro, we find that growth yield can remain constant or increase in a non-additive manner with environmental complexity. Conversely, taxonomic diversity is often much lower than expected. To better understand these deviations, we formulate metrics for epistatic interactions between environments and use them to compare our results to communities simulated with experimentally-parametrized consumer resource models. We find that key metabolic and ecological factors, including species similarity, degree of specialization, and metabolic interactions, modulate the observed non-additivity and govern the response of communities to combinations of resource pools. Our results demonstrate that environmental complexity alone is not sufficient for maintaining community diversity, and provide practical guidance for designing and controlling microbial ecosystems.

Coevolved mutualists experience fluctuating costs and benefits over time

Understanding how mutualisms persist over time requires investigations of how mutualist species coevolve and adapt to the interaction. In particular, the key factors in the evolution of mutualisms are the costs and benefits mutualists experience during the interaction. Here, we used a yeast nutritional mutualism to test how mutualists coevolve and adapt in an obligate mutualism. We allowed two yeast mutualists to evolve together for 15 weeks (about 150 generations), and then we tested if the mutualists had coevolved using time-shift assays. We also examined two mutualistic traits associated with the costs and benefits: resource use efficiency and commodity production. We found that the mutualists quickly coevolved. Furthermore, the changes in benefits and costs were nonlinear and varied with evolutionary changes occurring in the mutualist partner. One mutualist initially evolved to reduce mutualistic commodity production and increase efficiency in mutualistic resource use; however, this negatively affected its mutualist partner that evolved reduced commodity production and resource use efficiency. As a result, the former increased commodity production, resulting in an increase in benefits for its partner. The quick, nonlinear, and asynchronous evolution of yeast mutualists closely resembles antagonistic coevolutionary patterns, supporting the view that mutualisms should be considered as reciprocal exploitation.

Compositional epistasis detection using a few prototype disease models

We study computational approaches for detecting SNP-SNP interactions that are characterized by a set of "two-locus, two-allele, two-phenotype and complete-penetrance" disease models. We argue that existing methods, which use data to determine a best-fitting disease model for each pair of SNPs prior to screening, may be too greedy. We present a less greedy strategy which, for each given pair of SNPs, limits the number of candidate disease models to a set of prototypes determined a priori.

Sexual recombination and increased mutation rate expedite evolution of Escherichia coli in varied fitness landscapes

Sexual recombination and mutation rate are theorized to play different roles in adaptive evolution depending on the fitness landscape; however, direct experimental support is limited. Here we examine how these factors affect the rate of adaptation utilizing a “genderless” strain of Escherichia coli capable of continuous in situ sexual recombination. The results show that the populations with increased mutation rate, and capable of sexual recombination, outperform all the other populations. We further characterize two sexual and two asexual populations with increased mutation rate and observe maintenance of beneficial mutations in the sexual populations through mutational sweeps. Furthermore, we experimentally identify the molecular signature of a mating event within the sexual population that combines two beneficial mutations to generate a fitter progeny; this evidence suggests that the recombination event partially alleviates clonal interference. We present additional data suggesting that stochasticity plays an important role in the combinations of mutations observed.

Sexual recombination and mutation rate may play different roles in adaptive evolution depending on the fitness landscape. Here, Peabody et al. examine how the two factors affect the rate of adaptation of an E. coli strain capable of sexual recombination, under different conditions during experimental evolution.

Pervasive antagonistic interactions among hybrid incompatibility loci

Species barriers, expressed as hybrid inviability and sterility, are often due to epistatic interactions between divergent loci from two lineages. Theoretical models indicate that the strength, direction, and complexity of these genetic interactions can strongly affect the expression of interspecific reproductive isolation and the rates at which new species evolve. Nonetheless, empirical analyses have not quantified the frequency with which loci are involved in interactions affecting hybrid fitness, and whether these loci predominantly interact synergistically or antagonistically, or preferentially involve loci that have strong individual effects on hybrid fitness. We systematically examined the prevalence of interactions between pairs of short chromosomal regions from one species (Solanum habrochaites) co-introgressed into a heterospecific genetic background (Solanum lycopersicum), using lines containing pairwise combinations of 15 chromosomal segments from S. habrochaites in the background of S. lycopersicum (i.e., 95 double introgression lines). We compared the strength of hybrid incompatibility (either pollen sterility or seed sterility) expressed in each double introgression line to the expected additive effect of its two component single introgressions. We found that epistasis was common among co-introgressed regions. Interactions for hybrid dysfunction were substantially more prevalent in pollen fertility compared to seed fertility phenotypes, and were overwhelmingly antagonistic (i.e., double hybrids were less unfit than expected from additive single introgression effects). This pervasive antagonism is expected to attenuate the rate at which hybrid infertility accumulates among lineages over time (i.e., giving diminishing returns as more reproductive isolation loci accumulate), as well as decouple patterns of accumulation of sterility loci and hybrid incompatibility phenotypes. This decoupling effect might explain observed differences between pollen and seed fertility in their fit to theoretical predictions of the accumulation of isolation loci, including the ‘snowball’ effect.

A characteristic feature of new species is their inability to produce fertile or viable hybrids with other lineages. This post-zygotic reproductive isolation is caused by dysfunctional interactions between genes that have newly evolved changes in the diverging lineages. Whether these interactions occur between pairs of divergent alleles, or involve more complex networks of genes, can have strong effects on how rapidly reproductive isolation—and therefore new species—evolve. The complexity of these interactions, however, is poorly understood in empirical systems. We examined the fertility of hybrids that carried one or two chromosomal regions from a close relative, finding that hybrids with two of these heterospecific regions were frequently less sterile than would be expected from the joint fitness of hybrids that have the same regions singly. This ‘less-than-additive’ effect on hybrid sterility was widespread (observed in 20% of pairwise combinations), and especially pronounced for male sterility. We infer that genes contributing to male sterility form a more tightly connected network than previously thought, implying that reproductive isolation is evolving by incremental dysfunction of complex interactions rather than by independent pairwise incompatibilities. We use simulations to illustrate these expected patterns of accumulation of reproductive isolation when it involves highly interconnected gene networks.

A double-mutant collection targeting MAP kinase related genes in Arabidopsis for studying genetic interactions

Mitogen-activated protein kinase cascades are conserved in all eukaryotes. In Arabidopsis thaliana there are approximately 80 genes encoding MAP kinase kinase kinases (MAP3K), 10 genes encoding MAP kinase kinases (MAP2K), and 20 genes encoding MAP kinases (MAPK). Reverse genetic analysis has failed to reveal abnormal phenotypes for a majority of these genes. One strategy for uncovering gene function when single-mutant lines do not produce an informative phenotype is to perform a systematic genetic interaction screen whereby double-mutants are created from a large library of single-mutant lines. Here we describe a new collection of 275 double-mutant lines derived from a library of single-mutants targeting genes related to MAP kinase signaling. To facilitate this study, we developed a high-throughput double-mutant generating pipeline using a system for growing Arabidopsis seedlings in 96-well plates. A quantitative root growth assay was used to screen for evidence of genetic interactions in this double-mutant collection. Our screen revealed four genetic interactions, all of which caused synthetic enhancement of the root growth defects observed in a MAP kinase 4 (MPK4) single-mutant line. Seeds for this double-mutant collection are publicly available through the Arabidopsis Biological Resource Center. Scientists interested in diverse biological processes can now screen this double-mutant collection under a wide range of growth conditions in order to search for additional genetic interactions that may provide new insights into MAP kinase signaling.

Effect of Host Species on Topography of the Fitness Landscape for a Plant RNA Virus

Adaptive fitness landscapes are a fundamental concept in evolutionary biology that relate the genotypes of individuals to their fitness. In the end, the evolutionary fate of evolving populations depends on the topography of the landscape, that is, the numbers of accessible mutational pathways and possible fitness peaks (i.e., adaptive solutions). For a long time, fitness landscapes were only theoretical constructions due to a lack of precise information on the mapping between genotypes and phenotypes. In recent years, however, efforts have been devoted to characterizing the properties of empirical fitness landscapes for individual proteins or for microbes adapting to artificial environments. In a previous study, we characterized the properties of the empirical fitness landscape defined by the first five mutations fixed during adaptation of tobacco etch potyvirus (TEV) to a new experimental host, Arabidopsis thaliana Here we evaluate the topography of this landscape in the ancestral host Nicotiana tabacum By comparing the topographies of the landscapes for the two hosts, we found that some features remained similar, such as the existence of fitness holes and the prevalence of epistasis, including cases of sign and reciprocal sign epistasis that created rugged, uncorrelated, and highly random topographies. However, we also observed significant differences in the fine-grained details between the two landscapes due to changes in the fitness and epistatic interactions of some genotypes. Our results support the idea that not only fitness tradeoffs between hosts but also topographical incongruences among fitness landscapes in alternative hosts may contribute to virus specialization. IMPORTANCE Despite its importance for understanding virus evolutionary dynamics, very little is known about the topography of virus adaptive fitness landscapes, and even less is known about the effects that different host species and environmental conditions may have on this topography. To bridge this gap, we evaluated the topography of a small fitness landscape formed by all genotypes that result from every possible combination of the first five mutations fixed during adaptation of TEV to the novel host A. thaliana To assess the effect that host species may have on this topography, we evaluated the fitness of every genotype in both the ancestral and novel hosts. We found that both landscapes share some macroscopic properties, such as the existence of holes and being highly rugged and uncorrelated, yet they differ in microscopic details due to changes in the magnitude and sign of fitness and epistatic effects.

Phenotypic characterization of a pair of molecules in tissues confer to classical Mendelian or non Mendelian ratios

Studies have reported a wide range of inflammatory responses in the nerve, skin and plasma of leprosy patients. The expression levels of each biomolecule was individualistic, however could be categorized as high and low based on their statistical mean level. Here we report for the first time, expression of a set of biomolecules relating with each other in a defined proportion. The hypothesis of this paper is that the segregation of high and low combinations of a set of biomolecules follows either classical Mendelian dihybrid ratio or epistatic ratios. This hypothesis was tested for 17 molecules in three tissues; nerve, skin and plasma and were confirmed to interact in 9:7, 9:3:4, 12:3:1, 13:3, 15:1 epistatic proportions. These findings suggest that there could be a significant role of networking of molecules in defined epistatic proportions and could be important in pathophysiology of peripheral nerve.

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.

Environmental Interactions and Epistasis Are Revealed in the Proteomic Responses to Complex Stimuli

Ultimately, the genotype of a cell and its interaction with the environment determine the cell’s biochemical state. While the cell’s response to a single stimulus has been studied extensively, a conceptual framework to model the effect of multiple environmental stimuli applied concurrently is not as well developed. In this study, we developed the concepts of environmental interactions and epistasis to explain the responses of the S. cerevisiae proteome to simultaneous environmental stimuli. We hypothesize that, as an abstraction, environmental stimuli can be treated as analogous to genetic elements. This would allow modeling of the effects of multiple stimuli using the concepts and tools developed for studying gene interactions. Mirroring gene interactions, our results show that environmental interactions play a critical role in determining the state of the proteome. We show that individual and complex environmental stimuli behave similarly to genetic elements in regulating the cellular responses to stimuli, including the phenomena of dominance and suppression. Interestingly, we observed that the effect of a stimulus on a protein is dominant over other stimuli if the response to the stimulus involves the protein. Using publicly available transcriptomic data, we find that environmental interactions and epistasis regulate transcriptomic responses as well.

The age related markers lipofuscin and apoptosis show different genetic architecture by QTL mapping in short-lived Nothobranchius fish

Annual fish of the genus Nothobranchius show large variations in lifespan and expression of age-related phenotypes between closely related populations. We studied N. kadleci and its sister species N. furzeri GRZ strain, and found that N.kadleci is longer-lived than the N. furzeri. Lipofuscin and apoptosis measured in the liver increased with age in N. kadleci with different profiles: lipofuscin increased linearly, while apoptosis declined in the oldest animals. More lipofuscin (P<0.001) and apoptosis (P<0.001) was observed in N. furzeri than in N. kadleci at 16w age. Lipofuscin and apoptotic cells were then quantified in hybrids from the mating of N. furzeri to N. kadleci. F₁individuals showed heterosis for lipofuscin but additive effects for apoptosis. These two age-related phenotypes were not correlated in F₂ hybrids. Quantitative trait loci analysis of 287 F₂ fish using 237 markers identified two QTL accounting for 10% of lipofuscin variance (P<0.001) with overdominance effect. Apoptotic cells revealed three significant- and two suggestive QTL explaining 19% of variance (P<0.001), showing additive and dominance effects, and two interacting loci. Our results show that lipofuscin and apoptosis are markers of different age-dependent biological processes controlled by different genetic mechanisms.

Biological knowledge-driven analysis of epistasis in human GWAS with application to lipid traits

While the importance of epistasis is well established, specific gene-gene interactions have rarely been identified in human genome-wide association studies (GWAS), mainly due to low power associated with such interaction tests. In this chapter, we integrate biological knowledge and human GWAS data to reveal epistatic interactions underlying quantitative lipid traits, which are major risk factors for coronary artery disease. To increase power to detect interactions, we only tested pairs of SNPs filtered by prior biological knowledge, including GWAS results, protein-protein interactions (PPIs), and pathway information. Using published GWAS and 9,713 European Americans (EA) from the Atherosclerosis Risk in Communities (ARIC) study, we identified an interaction between HMGCR and LIPC affecting high-density lipoprotein cholesterol (HDL-C) levels. We then validated this interaction in additional multiethnic cohorts from ARIC, the Framingham Heart Study, and the Multi-Ethnic Study of Atherosclerosis. Both HMGCR and LIPC are involved in the metabolism of lipids and lipoproteins, and LIPC itself has been marginally associated with HDL-C. Furthermore, no significant interaction was detected using PPI and pathway information, mainly due to the stringent significance level required after correcting for the large number of tests conducted. These results suggest the potential of biological knowledge-driven approaches to detect epistatic interactions in human GWAS, which may hold the key to exploring the role gene-gene interactions play in connecting genotypes and complex phenotypes in future GWAS.

Bacterial responses to antibiotics and their combinations

Antibiotics affect bacterial cell physiology at many levels. Rather than just compensating for the direct cellular defects caused by the drug, bacteria respond to antibiotics by changing their morphology, macromolecular composition, metabolism, gene expression and possibly even their mutation rate. Inevitably, these processes affect each other, resulting in a complex response with changes in the expression of numerous genes. Genome-wide approaches can thus help in gaining a comprehensive understanding of bacterial responses to antibiotics. In addition, a combination of experimental and theoretical approaches is needed for identifying general principles that underlie these responses. Here, we review recent progress in our understanding of bacterial responses to antibiotics and their combinations, focusing on effects at the levels of growth rate and gene expression. We concentrate on studies performed in controlled laboratory conditions, which combine promising experimental techniques with quantitative data analysis and mathematical modeling. While these basic research approaches are not immediately applicable in the clinic, uncovering the principles and mechanisms underlying bacterial responses to antibiotics may, in the long term, contribute to the development of new treatment strategies to cope with and prevent the rise of resistant pathogenic bacteria.

Epistasis from functional dependence of fitness on underlying traits

Epistasis between mutations in two genes is thought to reflect an interdependence of their functions. While sometimes epistasis is predictable using mechanistic models, its roots seem, in general, hidden in the complex architecture of biological networks. Here, we ask how epistasis can be quantified based on the mathematical dependence of a system-level trait (e.g. fitness) on lower-level traits (e.g. molecular or cellular properties). We first focus on a model in which fitness is the difference between a benefit and a cost trait, both pleiotropically affected by mutations. We show that despite its simplicity, this model can be used to analytically predict certain properties of the ensuing distribution of epistasis, such as a global negative bias, resulting in antagonism between beneficial mutations, and synergism between deleterious ones. We next extend these ideas to derive a general expression for epistasis given an arbitrary functional dependence of fitness on other traits. This expression demonstrates how epistasis relative to fitness can emerge despite the absence of epistasis relative to lower level traits, leading to a formalization of the concept of independence between biological processes. Our results suggest that epistasis may be largely shaped by the pervasiveness of pleiotropic effects and modular organization in biological networks.

Knowledge-driven analysis identifies a gene-gene interaction affecting high-density lipoprotein cholesterol levels in multi-ethnic populations

Total cholesterol, low-density lipoprotein cholesterol, triglyceride, and high-density lipoprotein cholesterol (HDL-C) levels are among the most important risk factors for coronary artery disease. We tested for gene–gene interactions affecting the level of these four lipids based on prior knowledge of established genome-wide association study (GWAS) hits, protein–protein interactions, and pathway information. Using genotype data from 9,713 European Americans from the Atherosclerosis Risk in Communities (ARIC) study, we identified an interaction between HMGCR and a locus near LIPC in their effect on HDL-C levels (Bonferroni corrected P_c = 0.002). Using an adaptive locus-based validation procedure, we successfully validated this gene–gene interaction in the European American cohorts from the Framingham Heart Study (P_c = 0.002) and the Multi-Ethnic Study of Atherosclerosis (MESA; P_c = 0.006). The interaction between these two loci is also significant in the African American sample from ARIC (P_c = 0.004) and in the Hispanic American sample from MESA (P_c = 0.04). Both HMGCR and LIPC are involved in the metabolism of lipids, and genome-wide association studies have previously identified LIPC as associated with levels of HDL-C. However, the effect on HDL-C of the novel gene–gene interaction reported here is twice as pronounced as that predicted by the sum of the marginal effects of the two loci. In conclusion, based on a knowledge-driven analysis of epistasis, together with a new locus-based validation method, we successfully identified and validated an interaction affecting a complex trait in multi-ethnic populations.

Genome-wide association studies (GWAS) have identified many loci associated with complex human traits or diseases. However, the fraction of heritable variation explained by these loci is often relatively low. Gene–gene interactions might play a significant role in complex traits or diseases and are one of the many possible factors contributing to the missing heritability. However, to date only a few interactions have been found and validated in GWAS due to the limited power caused by the need for multiple-testing correction for the very large number of tests conducted. Here, we used three types of prior knowledge, known GWAS hits, protein–protein interactions, and pathway information, to guide our search for gene–gene interactions affecting four lipid levels. We identified an interaction between HMGCR and a locus near LIPC in their effect on high-density lipoprotein cholesterol (HDL-C) and another pair of loci that interact in their effect on low-density lipoprotein cholesterol (LDL-C). We validated the interaction on HDL-C in a number of independent multiple-ethnic populations, while the interaction underlying LDL-C did not validate. The prior knowledge-driven searching approach and a locus-based validation procedure show the potential for dissecting and validating gene–gene interactions in current and future GWAS.

Current applications of models of genetic effects with interactions across the genome

Models of genetic effects integrate the action of genes, regulatory regions and interactions among alleles across the genome. Such theoretical frameworks are critical for applied studies in at least two ways. First, discovering genetic networks with specific effects underlying traits in populations requires the development of models that implement those effects as parameters-adjusting the implementation of epistasis parameters in genetic models has for instance been a requirement for properly testing for epistasis in gene-mapping studies. Second, studying the properties and implications of models of genetic effects that involve complex genetic networks has proven to be valuable, whether those networks have been revealed for particular organisms or inferred to be of interest from theoretical works and simulations. Here I review the current state of development and recent applications of models of genetic effects. I focus on general models aiming to depict complex genotype-to-phenotype maps and on applications of them to networks of interacting loci.

Travelling the world of gene-gene interactions

Over the last few years, main effect genetic association analysis has proven to be a successful tool to unravel genetic risk components to a variety of complex diseases. In the quest for disease susceptibility factors and the search for the 'missing heritability', supplementary and complementary efforts have been undertaken. These include the inclusion of several genetic inheritance assumptions in model development, the consideration of different sources of information, and the acknowledgement of disease underlying pathways of networks. The search for epistasis or gene-gene interaction effects on traits of interest is marked by an exponential growth, not only in terms of methodological development, but also in terms of practical applications, translation of statistical epistasis to biological epistasis and integration of omics information sources. The current popularity of the field, as well as its attraction to interdisciplinary teams, each making valuable contributions with sometimes rather unique viewpoints, renders it impossible to give an exhaustive review of to-date available approaches for epistasis screening. The purpose of this work is to give a perspective view on a selection of currently active analysis strategies and concerns in the context of epistasis detection, and to provide an eye to the future of gene-gene interaction analysis.

Quantitative maps of genetic interactions in yeast - comparative evaluation and integrative analysis

Background

High-throughput genetic screening approaches have enabled systematic means to study how interactions among gene mutations contribute to quantitative fitness phenotypes, with the aim of providing insights into the functional wiring diagrams of genetic interaction networks on a global scale. However, it is poorly known how well these quantitative interaction measurements agree across the screening approaches, which hinders their integrated use toward improving the coverage and quality of the genetic interaction maps in yeast and other organisms.

Results

Using large-scale data matrices from epistatic miniarray profiling (E-MAP), genetic interaction mapping (GIM), and synthetic genetic array (SGA) approaches, we carried out here a systematic comparative evaluation among these quantitative maps of genetic interactions in yeast. The relatively low association between the original interaction measurements or their customized scores could be improved using a matrix-based modelling framework, which enables the use of single- and double-mutant fitness estimates and measurements, respectively, when scoring genetic interactions. Toward an integrative analysis, we show how the detections from the different screening approaches can be combined to suggest novel positive and negative interactions which are complementary to those obtained using any single screening approach alone. The matrix approximation procedure has been made available to support the design and analysis of the future screening studies.

Conclusions

We have shown here that even if the correlation between the currently available quantitative genetic interaction maps in yeast is relatively low, their comparability can be improved by means of our computational matrix approximation procedure, which will enable integrative analysis and detection of a wider spectrum of genetic interactions using data from the complementary screening approaches.

The balance of weak and strong interactions in genetic networks

Genetic interactions are being quantitatively characterized in a comprehensive way in several model organisms. These data are then globally represented in terms of genetic networks. How are interaction strengths distributed in these networks? And what type of functional organization of the underlying genomic systems is revealed by such distribution patterns? Here, I found that weak interactions are important for the structure of genetic buffering between signaling pathways in Caenorhabditis elegans, and that the strength of the association between two genes correlates with the number of common interactors they exhibit. I also determined that this network includes genetic cascades balancing weak and strong links, and that its hubs act as particularly strong genetic modifiers; both patterns also identified in Saccharomyces cerevisae networks. In yeast, I further showed a relation, although weak, between interaction strengths and some phenotypic/evolutionary features of the corresponding target genes. Overall, this work demonstrates a non-random organization of interaction strengths in genetic networks, a feature common to other complex networks, and that could reflect in this context how genetic variation is eventually influencing the phenotype.

A systems-biology approach to modular genetic complexity

Multiple high-throughput genetic interaction studies have provided substantial evidence of modularity in genetic interaction networks. However, the correspondence between these network modules and specific pathways of information flow is often ambiguous. Genetic interaction and molecular interaction analyses have not generated large-scale maps comprising multiple clearly delineated linear pathways. We seek to clarify the situation by discerning the difference between genetic modules and classical pathways. We review a method to optimize the discovery of biologically meaningful genetic modules based on a previously described context-dependent information measure to obtain maximally informative networks. We compare the results of this method with the established measures of network clustering and find that it balances global and local clustering information in networks. We further discuss the consequences for genetic interaction networks and propose a framework for the analysis of genetic modularity.

Recursive expectation-maximization clustering: a method for identifying buffering mechanisms composed of phenomic modules

Interactions between genetic and/or environmental factors are ubiquitous, affecting the phenotypes of organisms in complex ways. Knowledge about such interactions is becoming rate-limiting for our understanding of human disease and other biological phenomena. Phenomics refers to the integrative analysis of how all genes contribute to phenotype variation, entailing genome and organism level information. A systems biology view of gene interactions is critical for phenomics. Unfortunately the problem is intractable in humans; however, it can be addressed in simpler genetic model systems. Our research group has focused on the concept of genetic buffering of phenotypic variation, in studies employing the single-cell eukaryotic organism, S. cerevisiae. We have developed a methodology, quantitative high throughput cellular phenotyping (Q-HTCP), for high-resolution measurements of gene-gene and gene-environment interactions on a genome-wide scale. Q-HTCP is being applied to the complete set of S. cerevisiae gene deletion strains, a unique resource for systematically mapping gene interactions. Genetic buffering is the idea that comprehensive and quantitative knowledge about how genes interact with respect to phenotypes will lead to an appreciation of how genes and pathways are functionally connected at a systems level to maintain homeostasis. However, extracting biologically useful information from Q-HTCP data is challenging, due to the multidimensional and nonlinear nature of gene interactions, together with a relative lack of prior biological information. Here we describe a new approach for mining quantitative genetic interaction data called recursive expectation-maximization clustering (REMc). We developed REMc to help discover phenomic modules, defined as sets of genes with similar patterns of interaction across a series of genetic or environmental perturbations. Such modules are reflective of buffering mechanisms, i.e., genes that play a related role in the maintenance of physiological homeostasis. To develop the method, 297 gene deletion strains were selected based on gene-drug interactions with hydroxyurea, an inhibitor of ribonucleotide reductase enzyme activity, which is critical for DNA synthesis. To partition the gene functions, these 297 deletion strains were challenged with growth inhibitory drugs known to target different genes and cellular pathways. Q-HTCP-derived growth curves were used to quantify all gene interactions, and the data were used to test the performance of REMc. Fundamental advantages of REMc include objective assessment of total number of clusters and assignment to each cluster a log-likelihood value, which can be considered an indicator of statistical quality of clusters. To assess the biological quality of clusters, we developed a method called gene ontology information divergence z-score (GOid_z). GOid_z summarizes total enrichment of GO attributes within individual clusters. Using these and other criteria, we compared the performance of REMc to hierarchical and K-means clustering. The main conclusion is that REMc provides distinct efficiencies for mining Q-HTCP data. It facilitates identification of phenomic modules, which contribute to buffering mechanisms that underlie cellular homeostasis and the regulation of phenotypic expression.

Missing heritability and strategies for finding the underlying causes of complex disease

Although recent genome-wide studies have provided valuable insights into the genetic basis of human disease, they have explained relatively little of the heritability of most complex traits, and the variants identified through these studies have small effect sizes. This has led to the important and hotly debated issue of where the 'missing heritability' of complex diseases might be found. Here, seven leading geneticists offer their opinion about where this heritability is likely to lie, what this could tell us about the underlying genetic architecture of common diseases and how this could inform research strategies for uncovering genetic risk factors.