Traversing the conceptual divide between biological and statistical epistasis: systems biology and a more modern synthesis

Epistasis plays an important role in the genetic architecture of common human diseases and can be viewed from two perspectives, biological and statistical, each derived from and leading to different assumptions and research strategies. Biological epistasis is the result of physical interactions among biomolecules within gene regulatory networks and biochemical pathways in an individual such that the effect of a gene on a phenotype is dependent on one or more other genes. In contrast, statistical epistasis is defined as deviation from additivity in a mathematical model summarizing the relationship between multilocus genotypes and phenotypic variation in a population. The goal of this essay is to review definitions and examples of biological and statistical epistasis and to explore the relationship between the two. Specifically, we present and discuss the following two questions in the context of human health and disease. First, when does statistical evidence of epistasis in human populations imply underlying biomolecular interactions in the etiology of disease? Second, when do biomolecular interactions produce patterns of statistical epistasis in human populations?Answers to these two reciprocal questions will provide an important framework for using genetic information to improve our ability to diagnose, prevent and treat common human diseases. We propose that systems biology will provide the necessary information for addressing these questions and that model systems such as bacteria, yeast and digital organisms will be a useful place to start. BioEssays 27:637–646, 2005. © 2005 Wiley Periodicals, Inc.     

No evidence of association or interaction between the IL4RA, IL4, and IL13 genes in type 1 diabetes

Attempts to identify susceptibility loci that, on their own, have marginal main effects by use of gene-gene interaction tests have increased in popularity. The results obtained from analyses of epistasis are, however, difficult to interpret. Gene-gene interaction, albeit only marginally significant, has recently been reported for the interleukin-4 and interleukin-13 genes (IL4 and IL13) with the interleukin-4 receptor A gene (IL4RA), contributing to the susceptibility of type 1 diabetes (T1D). We aimed to replicate these findings by genotyping both large family and case-control data sets and by using previously published data. Gene-gene interaction tests were performed using linear regression models in cases only. We did not find any single-locus associations with T1D and did not obtain evidence of gene-gene interaction. Additional support from independent samples will be even more important in the study of gene-gene interactions and other subgroup analyses.     

Epistasis and Its Implications for Personal Genetics

The widespread availability of high-throughput genotyping technology has opened the door to the era of personal genetics, which brings to consumers the promise of using genetic variations to predict individual susceptibility to common diseases. Despite easy access to commercial personal genetics services, our knowledge of the genetic architecture of common diseases is still very limited and has not yet fulfilled the promise of accurately predicting most people at risk. This is partly because of the complexity of the mapping relationship between genotype and phenotype that is a consequence of epistasis (gene-gene interaction) and other phenomena such as gene-environment interaction and locus heterogeneity. Unfortunately, these aspects of genetic architecture have not been addressed in most of the genetic association studies that provide the knowledge base for interpreting large-scale genetic association results. We provide here an introductory review of how epistasis can affect human health and disease and how it can be detected in population-based studies. We provide some thoughts on the implications of epistasis for personal genetics and some recommendations for improving personal genetics in light of this complexity.     

Machine Learning for Detecting Gene-Gene Interactions

Complex interactions among genes and environmental factors are known to play a role in common human disease aetiology. There is a growing body of evidence to suggest that complex interactions are 'the norm' and, rather than amounting to a small perturbation to classical Mendelian genetics, interactions may be the predominant effect. Traditional statistical methods are not well suited for detecting such interactions, especially when the data are high dimensional (many attributes or independent variables) or when interactions occur between more than two polymorphisms. In this review, we discuss machine-learning models and algorithms for identifying and characterising susceptibility genes in common, complex, multifactorial human diseases. We focus on the following machine-learning methods that have been used to detect gene-gene interactions: neural networks, cellular automata, random forests, and multifactor dimensionality reduction. We conclude with some ideas about how these methods and others can be integrated into a comprehensive and flexible framework for data mining and knowledge discovery in human genetics.     

Gene-gene interaction between tuberculosis candidate genes in a South African population

In a complex disease such as tuberculosis (TB) it is increasingly evident that gene-gene interactions play a far more important role in an individual??s susceptibility to develop the disease than single polymorphisms on their own, as one gene can enhance or hinder the expression of another gene. Gene-gene interaction analysis is a new approach to elucidate susceptibility to TB. The possibility of gene-gene interactions was assessed, focusing on 11 polymorphisms in nine genes (DC-SIGN, IFN-??, IFNGR1, IL-8, IL-1Ra, MBL, NRAMP1, RANTES, and SP-D) that have been associated with TB, some repeatedly. An optimal model, which best describes and predicts TB case?Ccontrol status, was constructed. Significant interactions were detected between eight pairs of variants. The models fitted the observed data extremely well, with p?<?0.0001 for all eight models. A highly significant interaction was detected between INFGR1 and NRAMP1, which is not surprising because macrophage activation is greatly enhanced by IFN-?? and IFN-?? response elements that are present in the human NRAMP1 promoter region, providing further evidence for their interaction. This study enabled us to test the theory that disease outcome may be due to interaction of several gene effects. With eight instances of statistically significant gene-gene interactions, the importance of epistasis is clearly identifiable in this study. Methods for studying gene-gene interactions are based on a multilocus and multigene approach, consistent with the nature of complex-trait diseases, and may provide the paradigm for future genetic studies of TB.     

A flexible computational framework for detecting, characterizing, and interpreting statistical patterns of epistasis in genetic studies of human disease susceptibility

Detecting, characterizing, and interpreting gene-gene interactions or epistasis in studies of human disease susceptibility is both a mathematical and a computational challenge. To address this problem, we have previously developed a multifactor dimensionality reduction (MDR) method for collapsing high-dimensional genetic data into a single dimension (i.e. constructive induction) thus permitting interactions to be detected in relatively small sample sizes. In this paper, we describe a comprehensive and flexible framework for detecting and interpreting gene-gene interactions that utilizes advances in information theory for selecting interesting single-nucleotide polymorphisms (SNPs), MDR for constructive induction, machine learning methods for classification, and finally graphical models for interpretation. We illustrate the usefulness of this strategy using artificial datasets simulated from several different two-locus and three-locus epistasis models. We show that the accuracy, sensitivity, specificity, and precision of a na?ve Bayes classifier are significantly improved when SNPs are selected based on their information gain (i.e. class entropy removed) and reduced to a single attribute using MDR. We then apply this strategy to detecting, characterizing, and interpreting epistatic models in a genetic study (n = 500) of atrial fibrillation and show that both classification and model interpretation are significantly improved.     

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.     

Lower-order effects adjustment in quantitative traits model-based multifactor dimensionality reduction

Identifying gene-gene interactions or gene-environment interactions in studies of human complex diseases remains a big challenge in genetic epidemiology. An additional challenge, often forgotten, is to account for important lower-order genetic effects. These may hamper the identification of genuine epistasis. If lower-order genetic effects contribute to the genetic variance of a trait, identified statistical interactions may simply be due to a signal boost of these effects. In this study, we restrict attention to quantitative traits and bi-allelic SNPs as genetic markers. Moreover, our interaction study focuses on 2-way SNP-SNP interactions. Via simulations, we assess the performance of different corrective measures for lower-order genetic effects in Model-Based Multifactor Dimensionality Reduction epistasis detection, using additive and co-dominant coding schemes. Performance is evaluated in terms of power and familywise error rate. Our simulations indicate that empirical power estimates are reduced with correction of lower-order effects, likewise familywise error rates. Easy-to-use automatic SNP selection procedures, SNP selection based on "top" findings, or SNP selection based on p-value criterion for interesting main effects result in reduced power but also almost zero false positive rates. Always accounting for main effects in the SNP-SNP pair under investigation during Model-Based Multifactor Dimensionality Reduction analysis adequately controls false positive epistasis findings. This is particularly true when adopting a co-dominant corrective coding scheme. In conclusion, automatic search procedures to identify lower-order effects to correct for during epistasis screening should be avoided. The same is true for procedures that adjust for lower-order effects prior to Model-Based Multifactor Dimensionality Reduction and involve using residuals as the new trait. We advocate using "on-the-fly" lower-order effects adjusting when screening for SNP-SNP interactions using Model-Based Multifactor Dimensionality Reduction analysis.     

A simple and computationally efficient sampling approach to covariate adjustment for multifactor dimensionality reduction analysis of epistasis

Epistasis or gene-gene interaction is a fundamental component of the genetic architecture of complex traits such as disease susceptibility. Multifactor dimensionality reduction (MDR) was developed as a nonparametric and model-free method to detect epistasis when there are no significant marginal genetic effects. However, in many studies of complex disease, other covariates like age of onset and smoking status could have a strong main effect and may potentially interfere with MDR's ability to achieve its goal. In this paper, we present a simple and computationally efficient sampling method to adjust for covariate effects in MDR. We use simulation to show that after adjustment, MDR has sufficient power to detect true gene-gene interactions. We also compare our method with the state-of-art technique in covariate adjustment. The results suggest that our proposed method performs similarly, but is more computationally efficient. We then apply this new method to an analysis of a population-based bladder cancer study in New Hampshire.     

Genetic susceptibility to sporadic ovarian cancer: A systematic review

Ovarian cancer is a highly lethal disease. Many researchers have, therefore, attempted to identify high risk populations. In this perspective, numerous genetic association studies have been performed to discover common ovarian cancer susceptibility variants. Accordingly, there is an increasing need to synthesize the evidence in order to identify true associations. A comprehensive and systematic assessment of all available data on genetic susceptibility to sporadic ovarian cancer was carried out. The evidence of statistically significant findings was evaluated based on the number of positive replications, the ratio of positive and negative studies, and the false-positive report probability (FPRP). The authors reviewed three genome-wide association studies (GWAS) and 147 candidate gene studies, published from 1990 to October 2010, including around 1100 genetic variants in more than 200 candidate genes and 20 intergenic regions. Genetic variants with the strongest evidence for an association with ovarian cancer include the rs2854344 in the RB1 gene and SNPs on chromosomes 9p22.2, 8q24, 2q31, and 19p13. Promising genetic pathways for ovarian cancer include the cell cycle, DNA repair, sex steroid hormone and oncogenic pathway. Concluding, this review shows that many genetic association studies have been performed, but only a few genetic variants show strong evidence for an association with ovarian cancer. More research is needed to elucidate causal genetic variants, taking into consideration gene-gene and gene-environment interactions, combined effects of common and rare variants, and differences between histological subtypes of this cancer.     

Investigating the Role of Gene-Gene Interactions in TB Susceptibility

Tuberculosis (TB) is the second leading cause of mortality from infectious disease worldwide. One of the factors involved in developing disease is the genetics of the host, yet the field of TB susceptibility genetics has not yielded the answers that were expected. A commonly posited explanation for the missing heritability of complex disease is gene-gene interactions, also referred to as epistasis. In this study we investigate the role of gene-gene interactions in genetic susceptibility to TB using a cohort recruited from a high TB incidence community from Cape Town, South Africa. Our discovery data set incorporates genotypes from a large a number of candidate gene studies as well as genome-wide data. After limiting our search space to pairs of putative TB susceptibility genes, as well as pairs of genes that have been curated in online databases as potential interactors, we use statistical modelling to identify pairs of interacting SNPs. We attempt to validate the top models identified in our discovery data set using an independent genome-wide TB case-control data set from The Gambia. A number of models were successfully validated, indicating that interplay between the NRG1 - NRG3, GRIK1 - GRIK3 and IL23R - ATG4C gene pairs may modify susceptibility to TB. Gene pairs involved in the NF-κB pathway were also identified in the discovery data set (SFTPD - NOD2, ISG15 - TLR8 and NLRC5 - IL12RB1), but could not be tested in the Gambian study group due to lack of overlapping data.     

GxGrare: gene-gene interaction analysis method for rare variants from high-throughput sequencing data

Background

With the rapid advancement of array-based genotyping techniques, genome-wide association studies (GWAS) have successfully identified common genetic variants associated with common complex diseases. However, it has been shown that only a small proportion of the genetic etiology of complex diseases could be explained by the genetic factors identified from GWAS. This missing heritability could possibly be explained by gene-gene interaction (epistasis) and rare variants. There has been an exponential growth of gene-gene interaction analysis for common variants in terms of methodological developments and practical applications. Also, the recent advancement of high-throughput sequencing technologies makes it possible to conduct rare variant analysis. However, little progress has been made in gene-gene interaction analysis for rare variants.

Results

Here, we propose GxGrare which is a new gene-gene interaction method for the rare variants in the framework of the multifactor dimensionality reduction (MDR) analysis. The proposed method consists of three steps; 1) collapsing the rare variants, 2) MDR analysis for the collapsed rare variants, and 3) detect top candidate interaction pairs. GxGrare can be used for the detection of not only gene-gene interactions, but also interactions within a single gene. The proposed method is illustrated with 1080 whole exome sequencing data of the Korean population in order to identify causal gene-gene interaction for rare variants for type 2 diabetes.

Conclusion

The proposed GxGrare performs well for gene-gene interaction detection with collapsing of rare variants. GxGrare is available at http://bibs.snu.ac.kr/software/gxgrare which contains simulation data and documentation. Supported operating systems include Linux and OS X.

     

Mechanistic Explanations for Restricted Evolutionary Paths That Emerge from Gene Regulatory Networks

The extent and the nature of the constraints to evolutionary trajectories are central issues in biology. Constraints can be the result of systems dynamics causing a non-linear mapping between genotype and phenotype. How prevalent are these developmental constraints and what is their mechanistic basis? Although this has been extensively explored at the level of epistatic interactions between nucleotides within a gene, or amino acids within a protein, selection acts at the level of the whole organism, and therefore epistasis between disparate genes in the genome is expected due to their functional interactions within gene regulatory networks (GRNs) which are responsible for many aspects of organismal phenotype. Here we explore epistasis within GRNs capable of performing a common developmental function – converting a continuous morphogen input into discrete spatial domains. By exploring the full complement of GRN wiring designs that are able to perform this function, we analyzed all possible mutational routes between functional GRNs. Through this study we demonstrate that mechanistic constraints are common for GRNs that perform even a simple function. We demonstrate a common mechanistic cause for such a constraint involving complementation between counter-balanced gene-gene interactions. Furthermore we show how such constraints can be bypassed by means of “permissive” mutations that buffer changes in a direct route between two GRN topologies that would normally be unviable. We show that such bypasses are common and thus we suggest that unlike what was observed in protein sequence-function relationships, the “tape of life” is less reproducible when one considers higher levels of biological organization.     

Dynamic Epistasis under Varying Environmental Perturbations

Epistasis describes the phenomenon that mutations at different loci do not have independent effects with regard to certain phenotypes. Understanding the global epistatic landscape is vital for many genetic and evolutionary theories. Current knowledge for epistatic dynamics under multiple conditions is limited by the technological difficulties in experimentally screening epistatic relations among genes. We explored this issue by applying flux balance analysis to simulate epistatic landscapes under various environmental perturbations. Specifically, we looked at gene-gene epistatic interactions, where the mutations were assumed to occur in different genes. We predicted that epistasis tends to become more positive from glucose-abundant to nutrient-limiting conditions, indicating that selection might be less effective in removing deleterious mutations in the latter. We also observed a stable core of epistatic interactions in all tested conditions, as well as many epistatic interactions unique to each condition. Interestingly, genes in the stable epistatic interaction network are directly linked to most other genes whereas genes with condition-specific epistasis form a scale-free network. Furthermore, genes with stable epistasis tend to have similar evolutionary rates, whereas this co-evolving relationship does not hold for genes with condition-specific epistasis. Our findings provide a novel genome-wide picture about epistatic dynamics under environmental perturbations.     

Ultrahigh-dimensional variable selection method for whole-genome gene-gene interaction analysis

ABSTRACT: BACKGROUND: Genome-wide gene-gene interaction analysis using single nucleotide polymorphisms (SNPs) is an attractive way for identification of genetic components that confers susceptibility of human complex diseases. Individual hypothesis testing for SNP-SNP pairs as in common genome-wide association study (GWAS) however involves difficulty in setting overall p-value due to complicated correlation structure, namely, the multiple testing problem that causes unacceptable false negative results. A large number of SNP-SNP pairs than sample size, so-called the large p small n problem, precludes simultaneous analysis using multiple regression. The method that overcomes above issues is thus needed. RESULTS: We adopt an up-to-date method for ultrahigh-dimensional variable selection termed the sure independence screening (SIS) [17] for appropriate handling of numerous number of SNP-SNP interactions by including them as predictor variables in logistic regression. We propose ranking strategy using promising dummy coding methods and following variable selection procedure in the SIS method suitably modified for gene-gene interaction analysis. We also implemented the procedures in a software program, EPISIS, using the cost-effective GPGPU (General-purpose computing on graphics processing units) technology. EPISIS can complete exhaustive search for SNP-SNP interactions in standard GWAS dataset within several hours. The proposed method works successfully in simulation experiments and in application to real WTCCC (Wellcome Trust Case-Control Consortium) data. CONCLUSIONS: Based on the machine-learning principle, the proposed method gives powerful and flexible genome-wide search for various patterns of gene-gene interaction.     

A model of gene-gene and gene-environment interactions and its implications for targeting environmental interventions by genotype

Background  

The potential public health benefits of targeting environmental interventions by genotype depend on the environmental and genetic contributions to the variance of common diseases, and the magnitude of any gene-environment interaction. In the absence of prior knowledge of all risk factors, twin, family and environmental data may help to define the potential limits of these benefits in a given population. However, a general methodology to analyze twin data is required because of the potential importance of gene-gene interactions (epistasis), gene-environment interactions, and conditions that break the 'equal environments' assumption for monozygotic and dizygotic twins.     

Petri net modeling of high-order genetic systems using grammatical evolution

Understanding how DNA sequence variations impact human health through a hierarchy of biochemical and physiological systems is expected to improve the diagnosis, prevention, and treatment of common, complex human diseases. We have previously developed a hierarchical dynamic systems approach based on Petri nets for generating biochemical network models that are consistent with genetic models of disease susceptibility. This modeling approach uses an evolutionary computation approach called grammatical evolution as a search strategy for optimal Petri net models. We have previously demonstrated that this approach routinely identifies biochemical network models that are consistent with a variety of genetic models in which disease susceptibility is determined by nonlinear interactions between two DNA sequence variations. In the present study, we evaluate whether the Petri net approach is capable of identifying biochemical networks that are consistent with disease susceptibility due to higher order nonlinear interactions between three DNA sequence variations. The results indicate that our model-building approach is capable of routinely identifying good, but not perfect, Petri net models. Ideas for improving the algorithm for this high-dimensional problem are presented.     

Assessing gene-gene interactions in pharmacogenomics

In pharmacogenomics studies, gene-gene interactions play an important role in characterizing a trait that involves complex pharmacokinetic and pharmacodynamic mechanisms, particularly when each involved feature only demonstrates a minor effect. In addition to the candidate gene approach, genome-wide association studies (GWAS) are widely utilized to identify common variants that are associated with treatment response. In the wake of recent advances in scientific research, a paradigm shift from GWAS to whole-genome sequencing is expected, because of the reduced cost and the increased throughput of next-generation sequencing technologies. This review first outlines several promising methods for addressing gene-gene interactions in pharmacogenomics studies. We then summarize some candidate gene studies for various treatments with consideration of gene-gene interactions. Furthermore, we give a brief overview for the pharmacogenomics studies with the GWAS approach and describe the limitations of these GWAS in terms of gene-gene interactions. Future research in translational medicine promises to lead to mechanistic findings related to drug responsiveness in light of complex gene-gene interactions and will probably make major contributions to individualized medicine and therapeutic decision-making.     

基于单核苷酸多态性的基因互作分析方法学进展

基于单核苷酸多态性的关联分析已成为当前解析人类常见复杂疾病遗传机制的重要手段之一, 然而, 目前普遍使用的单位点分析策略仅能发现部分单独效应显著的易感SNP位点, 因此遗漏了重要的遗传力组分——基因上位效应或联合效应。识别全基因组多基因间复杂的互作关系已成为全面解析复杂疾病致病分子机制必不可少的一项任务。已有很多方法被应用于全基因组交互作用分析, 加深了人类对复杂疾病遗传机制的进一步认识。基于各类方法的理论基础及算法的异同, 文章对目前应用较为广泛的基于遗传互作模型的方法、不基于互作模型的方法和数据挖掘类算法3类方法进行了系统地评述, 着重介绍了这些方法的主要思想、实现过程及应用中的注意事项等, 并指出开展大规模全基因组范围互作检测面临的问题, 以期能为相关领域的研究者提供方法学参考。     

Epistatic interaction maps relative to multiple metabolic phenotypes

An epistatic interaction between two genes occurs when the phenotypic impact of one gene depends on another gene, often exposing a functional association between them. Due to experimental scalability and to evolutionary significance, abundant work has been focused on studying how epistasis affects cellular growth rate, most notably in yeast. However, epistasis likely influences many different phenotypes, affecting our capacity to understand cellular functions, biochemical networks adaptation, and genetic diseases. Despite its broad significance, the extent and nature of epistasis relative to different phenotypes remain fundamentally unexplored. Here we use genome-scale metabolic network modeling to investigate the extent and properties of epistatic interactions relative to multiple phenotypes. Specifically, using an experimentally refined stoichiometric model for Saccharomyces cerevisiae, we computed a three-dimensional matrix of epistatic interactions between any two enzyme gene deletions, with respect to all metabolic flux phenotypes. We found that the total number of epistatic interactions between enzymes increases rapidly as phenotypes are added, plateauing at approximately 80 phenotypes, to an overall connectivity that is roughly 8-fold larger than the one observed relative to growth alone. Looking at interactions across all phenotypes, we found that gene pairs interact incoherently relative to different phenotypes, i.e. antagonistically relative to some phenotypes and synergistically relative to others. Specific deletion-deletion-phenotype triplets can be explained metabolically, suggesting a highly informative role of multi-phenotype epistasis in mapping cellular functions. Finally, we found that genes involved in many interactions across multiple phenotypes are more highly expressed, evolve slower, and tend to be associated with diseases, indicating that the importance of genes is hidden in their total phenotypic impact. Our predictions indicate a pervasiveness of nonlinear effects in how genetic perturbations affect multiple metabolic phenotypes. The approaches and results reported could influence future efforts in understanding metabolic diseases and the role of biochemical regulation in the cell.