The E(NK) model: extending the NK model to incorporate gene-by-environment interactions and epistasis for diploid genomes

The haploid NK model developed by Kauffman can be extended to diploid genomes and to incorporate gene-by-environment interaction effects in combination with epistasis. To provide the flexibility to include a wide range of forms of gene-by-environment interactions, a target population of environment types (TPE) is defined. The TPE consists of a set of E different environment types, each with their own frequency of occurrence. Each environment type conditions a different NK gene network structure or series of gene effects for a given network structure, providing the framework for defining gene-by-environment interactions. Thus, different NK models can be partially or completely nested within the E environment types of a TPE, giving rise to the E(NK) model for a biological system. With this model it is possible to examine how populations of genotypes evolve in context with properties of the environment that influence the contributions of genes to the fitness values of genotypes. We are using the E(NK) model to investigate how both epistasis and gene-by-environment interactions influence the genetic improvement of quantitative traits by plant breeding strategies applied to agricultural systems. © 2002 Wiley Periodicals, Inc.

Positive Epistasis Drives the Acquisition of Multidrug Resistance

The evolution of multiple antibiotic resistance is an increasing global problem. Resistance mutations are known to impair fitness, and the evolution of resistance to multiple drugs depends both on their costs individually and on how they interact-epistasis. Information on the level of epistasis between antibiotic resistance mutations is of key importance to understanding epistasis amongst deleterious alleles, a key theoretical question, and to improving public health measures. Here we show that in an antibiotic-free environment the cost of multiple resistance is smaller than expected, a signature of pervasive positive epistasis among alleles that confer resistance to antibiotics. Competition assays reveal that the cost of resistance to a given antibiotic is dependent on the presence of resistance alleles for other antibiotics. Surprisingly we find that a significant fraction of resistant mutations can be beneficial in certain resistant genetic backgrounds, that some double resistances entail no measurable cost, and that some allelic combinations are hotspots for rapid compensation. These results provide additional insight as to why multi-resistant bacteria are so prevalent and reveal an extra layer of complexity on epistatic patterns previously unrecognized, since it is hidden in genome-wide studies of genetic interactions using gene knockouts.

Synergistic epistasis and alternative hypotheses.

Inbreeding generally results in deleterious shifts in mean fitness. If the fitness response to increasing inbreeding coefficient is non-linear, this suggests a contribution of epistasis to inbreeding depression. In a cross-breeding experiment, Salathe & Ebert (2003. J. Evol. Biol. 16: 976-985) tested and found the presence of this non-linearity in Daphnia magna. They argue that epistatic interactions cause this non-linearity. We argue here that their experimental protocol does not allow disentangling the effect of synergistic epistasis from two alternative hypotheses, namely hybrid vigour and statistical non-independence of data.

Epistasis and maternal effects in experimental adaptation to chronic nutritional stress in Drosophila.

Based on ecological and metabolic arguments, some authors predict that adaptation to novel, harsh environments should involve alleles showing negative (diminishing return) epistasis and/or that it should be mediated in part by evolution of maternal effects. Although the first prediction has been supported in microbes, there has been little experimental support for either prediction in multicellular eukaryotes. Here we use a line-cross design to study the genetic architecture of adaptation to chronic larval malnutrition in a population of Drosophila melanogaster that evolved on an extremely nutrient-poor larval food for 84 generations. We assayed three fitness-related traits (developmental rate, adult female weight and egg-to-adult viability) under the malnutrition conditions in 14 crosses between this selected population and a nonadapted control population originally derived from the same base population. All traits showed a pattern of negative epistasis between alleles improving performance under malnutrition. Furthermore, evolutionary changes in maternal traits accounted for half of the 68% increase in viability and for the whole of 8% reduction in adult female body weight in the selected population (relative to unselected controls). These results thus support both of the above predictions and point to the importance of nonadditive effects in adaptive microevolution.

Detecting epistasis with restricted response patterns in pairs of biallelic loci.

Well-established examples of genetic epistasis between a pair of loci typically show characteristic patterns of phenotypic distributions in joint genotype tables. However, inferring epistasis given such data is difficult due to the lack of power in commonly used approaches, which decompose the epistatic patterns into main plus interaction effects followed by testing the interaction term. Testing additive-only or all terms may have more power, but they are sensitive to nonepistatic patterns. Alternatively, the epistatic patterns of interest can be enumerated and the best matching one is found by searching through the possibilities. Although this approach requires multiple testing correction over possible patterns, each pattern can be fitted with a regression model with just one degree of freedom and thus the overall power can still be high, if the number of possible patterns is limited. Here we compare the power of the linear decomposition and pattern search methods, by applying them to simulated data generated under several patterns of joint genotype effects with simple biological interpretations. Interaction-only tests are the least powerful; while pattern search approach is the most powerful if the range of possibilities is restricted, but still includes the true pattern.

Dominant PRPF31 Mutations Are Hypostatic to a Recessive CNOT3 Polymorphism in Retinitis Pigmentosa: A Novel Phenomenon of "Linked Trans-Acting Epistasis".

Mutations in PRPF31 are responsible for autosomal dominant retinitis pigmentosa (adRP, RP11 form) and affected families show nonpenetrance. Differential expression of the wildtype PRPF31 allele is responsible for this phenomenon: coinheritance of a mutation and a higher expressing wildtype allele provide protection against development of disease. It has been suggested that a major modulating factor lies in close proximity to the wildtype PRPF31 gene on Chromosome 19, implying that a cis-acting factor directly alters PRPF31 expression. Variable expression of CNOT3 is one determinant of PRPF31 expression. This study explored the relationship between CNOT3 (a trans-acting factor) and its paradoxical cis-acting nature in relation to RP11. Linkage analysis on Chromosome 19 was performed in mutation-carrying families, and the inheritance of the wildtype PRPF31 allele in symptomatic-asymptomatic sibships was assessed-confirming that differential inheritance of wildtype chromosome 19q13 determines the clinical phenotype (P < 2.6 × 10(-7) ). A theoretical model was constructed that explains the apparent conflict between the linkage data and the recent demonstration that a trans-acting factor (CNOT3) is a major nonpenetrance factor: we propose that this apparently cis-acting effect arises due to the intimate linkage of CNOT3 and PRPF31 on Chromosome 19q13-a novel mechanism that we have termed "linked trans-acting epistasis."

Comparison of Strategies to Detect Epistasis from eQTL Data.

Genome-wide association studies have been instrumental in identifying genetic variants associated with complex traits such as human disease or gene expression phenotypes. It has been proposed that extending existing analysis methods by considering interactions between pairs of loci may uncover additional genetic effects. However, the large number of possible two-marker tests presents significant computational and statistical challenges. Although several strategies to detect epistasis effects have been proposed and tested for specific phenotypes, so far there has been no systematic attempt to compare their performance using real data. We made use of thousands of gene expression traits from linkage and eQTL studies, to compare the performance of different strategies. We found that using information from marginal associations between markers and phenotypes to detect epistatic effects yielded a lower false discovery rate (FDR) than a strategy solely using biological annotation in yeast, whereas results from human data were inconclusive. For future studies whose aim is to discover epistatic effects, we recommend incorporating information about marginal associations between SNPs and phenotypes instead of relying solely on biological annotation. Improved methods to discover epistatic effects will result in a more complete understanding of complex genetic effects.

Generation mean analysis in relation to polygenic systems with epistasis and fixed genes

Epistatic effects involving genic combinations of fixed and non fixed genes are shown to contribute to the genotypic mean of any population. These effects define specific additive x additive and additive x dominant epistatic components. As such components are not estimable, their relative importance cannot be assessed. These epistatic effects can cause bias in the estimates of the additive and dominance components to which they are confounded. The magnitude of the bias depends on the relative values of the epistatic effects, comparatively to deviations d and h, type of prevailing epistasis and direction of dominance.

FastEpistasis: a high performance computing solution for quantitative trait epistasis.

Motivation: Genome-wide association studies have become widely used tools to study effects of genetic variants on complex diseases. While it is of great interest to extend existing analysis methods by considering interaction effects between pairs of loci, the large number of possible tests presents a significant computational challenge. The number of computations is further multiplied in the study of gene expression quantitative trait mapping, in which tests are performed for thousands of gene phenotypes simultaneously. Results: We present FastEpistasis, an efficient parallel solution extending the PLINK epistasis module, designed to test for epistasis effects when analyzing continuous phenotypes. Our results show that the algorithm scales with the number of processors and offers a reduction in computation time when several phenotypes are analyzed simultaneously. FastEpistasis is capable of testing the association of a continuous trait with all single nucleotide polymorphism ( SNP) pairs from 500 000 SNPs, totaling 125 billion tests, in a population of 5000 individuals in 29, 4 or 0.5 days using 8, 64 or 512 processors.

FAM-MDR: a flexible family-based multifactor dimensionality reduction technique to detect epistasis using related individuals

We propose a novel multifactor dimensionality reduction method for epistasis detection in small or extended pedigrees, FAM-MDR. It combines features of the Genome-wide Rapid Association using Mixed Model And Regression approach (GRAMMAR) with Model-Based MDR (MB-MDR). We focus on continuous traits, although the method is general and can be used for outcomes of any type, including binary and censored traits. When comparing FAM-MDR with Pedigree-based Generalized MDR (PGMDR), which is a generalization of Multifactor Dimensionality Reduction (MDR) to continuous traits and related individuals, FAM-MDR was found to outperform PGMDR in terms of power, in most of the considered simulated scenarios. Additional simulations revealed that PGMDR does not appropriately deal with multiple testing and consequently gives rise to overly optimistic results. FAM-MDR adequately deals with multiple testing in epistasis screens and is in contrast rather conservative, by construction. Furthermore, simulations show that correcting for lower order (main) effects is of utmost importance when claiming epistasis. As Type 2 Diabetes Mellitus (T2DM) is a complex phenotype likely influenced by gene-gene interactions, we applied FAM-MDR to examine data on glucose area-under-the-curve (GAUC), an endophenotype of T2DM for which multiple independent genetic associations have been observed, in the Amish Family Diabetes Study (AFDS). This application reveals that FAM-MDR makes more efficient use of the available data than PGMDR and can deal with multi-generational pedigrees more easily. In conclusion, we have validated FAM-MDR and compared it to PGMDR, the current state-of-the-art MDR method for family data, using both simulations and a practical dataset. FAM-MDR is found to outperform PGMDR in that it handles the multiple testing issue more correctly, has increased power, and efficiently uses all available information.

An efficient algorithm to perform multiple testing in epistasis screening

Background: Research in epistasis or gene-gene interaction detection for human complex traits has grown over the last few years. It has been marked by promising methodological developments, improved translation efforts of statistical epistasis to biological epistasis and attempts to integrate different omics information sources into the epistasis screening to enhance power. The quest for gene-gene interactions poses severe multiple-testing problems. In this context, the maxT algorithm is one technique to control the false-positive rate. However, the memory needed by this algorithm rises linearly with the amount of hypothesis tests. Gene-gene interaction studies will require a memory proportional to the squared number of SNPs. A genome-wide epistasis search would therefore require terabytes of memory. Hence, cache problems are likely to occur, increasing the computation time. In this work we present a new version of maxT, requiring an amount of memory independent from the number of genetic effects to be investigated. This algorithm was implemented in C++ in our epistasis screening software MBMDR-3.0.3. We evaluate the new implementation in terms of memory efficiency and speed using simulated data. The software is illustrated on real-life data for Crohn’s disease. Results: In the case of a binary (affected/unaffected) trait, the parallel workflow of MBMDR-3.0.3 analyzes all gene-gene interactions with a dataset of 100,000 SNPs typed on 1000 individuals within 4 days and 9 hours, using 999 permutations of the trait to assess statistical significance, on a cluster composed of 10 blades, containing each four Quad-Core AMD Opteron(tm) Processor 2352 2.1 GHz. In the case of a continuous trait, a similar run takes 9 days. Our program found 14 SNP-SNP interactions with a multiple-testing corrected p-value of less than 0.05 on real-life Crohn’s disease (CD) data. Conclusions: Our software is the first implementation of the MB-MDR methodology able to solve large-scale SNP-SNP interactions problems within a few days, without using much memory, while adequately controlling the type I error rates. A new implementation to reach genome-wide epistasis screening is under construction. In the context of Crohn’s disease, MBMDR-3.0.3 could identify epistasis involving regions that are well known in the field and could be explained from a biological point of view. This demonstrates the power of our software to find relevant phenotype-genotype higher-order associations.

Marker-trait association and epistasis for brown rust resistance in sugarcane

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Epistasis among eNOS, MMP-9 and VEGF maternal genotypes in hypertensive disorders of pregnancy

Polymorphisms of the endothelial nitric oxide synthase (eNOS), matrix metalloproteinase-9 (MMP-9) and vascular endothelial growth factor (VEGF) genes were shown to be associated with hypertensive disorders of pregnancy. However, epistasis is suggested to be an important component of the genetic susceptibility to preeclampsia (PE). The aim of this study was to characterize the interactions among these genes in PE and gestational hypertension (GH). Seven clinically relevant polymorphisms of eNOS (T-786C, rs2070744, a variable number of tandem repeats in intron 4 and Glu298Asp, rs1799983), MMP-9 (C-1562T, rs3918242 and -90(CA)(13-25), rs2234681) and VEGF (C-2578A, rs699947 and G-634C, rs2010963) were genotyped by TaqMan allelic discrimination assays or PCR and fragment separation by electrophoresis in 122 patients with PE, 107 patients with GH and a control group of 102 normotensive pregnant (NP) women. A robust multifactor dimensionality reduction analysis was used to characterize gene-gene interactions. Although no significant genotype combinations were observed for the comparison between the GH and NP groups (P>0.05), the combination of MMP-9-1562CC with VEGF-634GG was more frequent in NP women than in women with PE (P<0.05). Moreover, the combination of MMP-9-1562CC with VEGF-634CC or MMP-9-1562CT with VEGF-634CC or-634GG was more frequent in women with PE than in NP women (P<0.05). These results are obscured when single polymorphisms in these genes are considered and suggest that specific genotype combinations of MMP-9 and VEGF contribute to PE susceptibility. Hypertension Research (2012) 35, 917-921; doi:10.1038/hr.2012.60; published online 10 May 2012

The role of epistasis in the manifestation of heterosis: a systems-oriented approach

Heterosis is widely used in breeding, but the genetic basis of this biological phenomenon has not been elucidated. We postulate that additive and dominance genetic effects as well as two-locus interactions estimated in classical QTL analyses are not sufficient for quantifying the contributions of QTL to heterosis. A general theoretical framework for determining the contributions of different types of genetic effects to heterosis was developed. Additive x additive epistatic interactions of individual loci with the entire genetic background were identified as a major component of midparent heterosis. On the basis of these findings we defined a new type of heterotic effect denoted as augmented dominance effect di* that comprises the dominance effect at each QTL minus half the sum of additive x additive interactions with all other QTL. We demonstrate that genotypic expectations of QTL effects obtained from analyses with the design III using testcrosses of recombinant inbred lines and composite-interval mapping precisely equal genotypic expectations of midparent heterosis, thus identifying genomic regions relevant for expression of heterosis. The theory for QTL mapping of multiple traits is extended to the simultaneous mapping of newly defined genetic effects to improve the power of QTL detection and distinguish between dominance and overdominance.