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.

Gene by environment interaction: effects of a single-gene and social-environment on reproductive phenotypes of fire ant queens

1. The gene Pgm-3 (or a closely linked gene) influences the phenotype and reproductive success of queens in multiple-queen (polygynous) colonies but not single-queen (monogynous) colonies of the Fire Ant Solenopsis invicta. 2. We investigated the mechanisms of differential phenotypic expression of Pgm-3 in these alternate social forms. Mature winged queens with the homozygous genotype Pgm-3(a/a) averaged 26% heavier than queens with the genotypes Pgm-3(a/b) and Pgm 3(b/b) in the polygynous form. Heterozygotes were slightly heavier (2%) than Pgm-3(b/b) queens in this form, demonstrating that the allele Pgm-3(a) is not completely recessive in its effects on weight. 3. There was no significant difference in weight among queens of the three Pgm-3 genotypes in the monogynous form, with the mean weight of monogynous queens slightly greater than that of polygynous Pgm-3(a/a) queens. Differences in weight between queens of the two social forms and among queens of the three genotypes in the polygynous form are not evident at the pupal stage and thus appear to develop during sexual maturation of the adults. This suggests that some component of the social environment of polygynous colonies inhibits weight gains during queen maturation and that Pgm-(3a/a) queens are relatively less sensitive to this factor. 4. To test whether the high cumulative queen pheromone level characteristic of polygynous colonies is the factor responsible for the differential queen maturation, we compared phenotypes of winged queens reared in split colonies in which pheromone levels were manipulated by adjusting queen number. Queens produced in colony fragments made monogynous were heavier than those produced in polygynous fragments, a finding consistent with the hypothesis that pheromone level affects the reproductive development of queens. However, genotype-specific differences in weights of queens were similar between the two treatments, suggesting that pheromone level was not the key factor of the social environment responsible for the gene-environment interaction. 5. To test whether limited food availability to winged queens associated with the high brood/worker ratios in polygynous colonies is the factor responsible for this interaction, similar split-colony experiments were performed. Elevated brood/worker ratios decreased the weight of winged queens but there was no evidence that this treatment intensified differential weight gains among queens with different Pgm-3 genotypes. Manipulation of the amount of food provided to colonies had no effect on queen weight. 6. The combined data indicate that cumulative pheromone level and brood/worker ratio are two of the factors responsible for the differences in reproductive phenotypes between monogynous and polygynous winged queens but that these factors are not directly responsible for inducing the phenotypic effects of Pgm-3 in polygynous colonies.

Gene by environment QTL mapping through multiple trait analyses in blood pressure salt-sensitivity: identification of a novel QTL in rat chromosome 5

Background The genetic mechanisms underlying interindividual blood pressure variation reflect the complex interplay of both genetic and environmental variables. The current standard statistical methods for detecting genes involved in the regulation mechanisms of complex traits are based on univariate analysis. Few studies have focused on the search for and understanding of quantitative trait loci responsible for gene × environmental interactions or multiple trait analysis. Composite interval mapping has been extended to multiple traits and may be an interesting approach to such a problem. Methods We used multiple-trait analysis for quantitative trait locus mapping of loci having different effects on systolic blood pressure with NaCl exposure. Animals studied were 188 rats, the progenies of an F2 rat intercross between the hypertensive and normotensive strain, genotyped in 179 polymorphic markers across the rat genome. To accommodate the correlational structure from measurements taken in the same animals, we applied univariate and multivariate strategies for analyzing the data. Results We detected a new quantitative train locus on a region close to marker R589 in chromosome 5 of the rat genome, not previously identified through serial analysis of individual traits. In addition, we were able to justify analytically the parametric restrictions in terms of regression coefficients responsible for the gain in precision with the adopted analytical approach. Conclusion Future work should focus on fine mapping and the identification of the causative variant responsible for this quantitative trait locus signal. The multivariable strategy might be valuable in the study of genetic determinants of interindividual variation of antihypertensive drug effectiveness.

A deleterious gene-by-environment interaction imposed by calcium channel blockers in Marfan syndrome.

Calcium channel blockers (CCBs) are prescribed to patients with Marfan syndrome for prophylaxis against aortic aneurysm progression, despite limited evidence for their efficacy and safety in the disorder. Unexpectedly, Marfan mice treated with CCBs show accelerated aneurysm expansion, rupture, and premature lethality. This effect is both extracellular signal-regulated kinase (ERK1/2) dependent and angiotensin-II type 1 receptor (AT1R) dependent. We have identified protein kinase C beta (PKCβ) as a critical mediator of this pathway and demonstrate that the PKCβ inhibitor enzastaurin, and the clinically available anti-hypertensive agent hydralazine, both normalize aortic growth in Marfan mice, in association with reduced PKCβ and ERK1/2 activation. Furthermore, patients with Marfan syndrome and other forms of inherited thoracic aortic aneurysm taking CCBs display increased risk of aortic dissection and need for aortic surgery, compared to patients on other antihypertensive agents.

Molecular Genetic Basis of Opposite Gene by Environment Interactions in Reading Disability and Attention Deficit/Hyperactivity Disorder

The goal of this study is to better understand the genetic basis of Reading Disability (RD) and Attention Deficit Hyperactivity Disorder (ADHD) by examining molecular G x E interactions with parental education for each disorder. Research indicates that despite sharing genetic risk factors, RD and ADHD are influenced by different types of G x E interactions with parental education - a diathesis stress interaction in the case of ADHD and a bioecological interaction in RD. In order to resolve this apparent paradox, we conducted a preliminary study using behavioral genetic methods to test for G x E interactions in RD and the inattentive subtype of ADHD (ADHD-I) in the same sample of monozygotic and dizygotic Colorado Learning Disabilities Research Center same-sex twin pairs (DeFries et al., 1997), and our findings were consistent with the literature. We posited a genetic hypothesis for this opposite pattern of interactions, which suggests that only genes specific to each disorder enter into these opposite interactions, not the shared genes underlying their comorbidity. This study sought to further investigate this paradox using molecular genetics methods. We examined multiple candidate genes identified for RD or related language phenotypes and those identified for ADHD for G x E interactions with parental education. The specific aims of this study were as follows: 1) partition known risk alleles for RD and/or related language phenotypes and ADHD-I into those which are pleiotropic and non-pleiotropic by testing each risk allele for association with both RD and ADHD-I, 2) explore the main effects of parental education on both RD and ADHD-I, 3) address G-E correlations, and 4) conduct exploratory G x E interaction analyses in order to test the genetic hypothesis. Analyses suggested a number of pleiotropic genes that influence both RD and ADHD; however, results did not remain after correcting for multiple comparisons. Although exploratory G x E interaction findings were not significant after multiple comparison correction, results suggested a G x E interaction in the bioecological direction with KIAA0319, parental education, and ADHD-I. Given the limited power in the current study, replication of these findings with larger samples is necessary.

Gene by smoking interaction in blood pressure

Hypertension (HT) is mediated by the interaction of many genetic and environmental factors. Previous genome-wide linkage analysis studies have found many loci that show linkage to HT or blood pressure (BP) regulation, but the results were generally inconsistent. Gene by environment interaction is among the reasons that potentially explain these inconsistencies between studies. Here we investigate influences of gene by smoking (GxS) interaction on HT and BP in European American (EA), African American (AA) and Mexican American (MA) families from the GENOA study. A variance component-based method was utilized to perform genome-wide linkage analysis of systolic blood pressure (SBP), diastolic blood pressure (DBP), and HT status, as well as bivariate analysis for SBP and DBP for smokers, non-smokers, and combined groups. The most significant results were found for SBP in MA. The strongest signal was for chromosome 17q24 (LOD = 4.2), increased to (LOD = 4.7) in bivariate analysis but there was no evidence of GxS interaction at this locus (p = 0.48). Two signals were identified only in one group: on chromosome 15q26.2 (LOD = 3.37) in non-smokers and chromosome 7q21.11 (LOD = 1.4) in smokers, both of which had strong evidence for GxS interaction (p = 0.00039 and 0.009 respectively). There were also two other signals, one on chromosome 20q12 (LOD = 2.45) in smokers, which became much higher in the combined sample (LOD = 3.53), and one on chromosome 6p22.2 (LOD = 2.06) in non-smokers. Neither peak had very strong evidence for GxS interaction (p = 0.08 and 0.06 respectively). A fine mapping association study was performed using 200 SNPs in 30 genes located under the linkage signals on chromosomes 15 and 17. Under the chromosome 15 peak, the association analysis identified 6 SNPs accounting for a 7 mmHg increase in SBP in MA non-smokers. For the chromosome 17 linkage peak, the association analysis identified 3 SNPs accounting for a 6 mmHg increase in SBP in MA. However, none of these SNPs was significant after correcting for multiple testing, and accounting for them in the linkage analysis produced very small reductions in the linkage signal. ^ The linkage analysis of BP traits considering the smoking status produced very interesting signals for SBP in the MA population. The fine mapping association analysis gave some insight into the contribution of some SNPs to two of the identified signals, but since these SNPs did not remain significant after multiple testing correction and did not explain the linkage peaks, more work is needed to confirm these exploratory results and identify the culprit variations under these linkage peaks. ^

Evaluating gene by sex and age interactions on cardiovascular risk factors in Brazilian families

Background: In family studies, it is important to evaluate the impact of genes and environmental factors on traits of interest. In particular, the relative influences of both genes and the environment may vary in different strata of the population of interest, such as young and old individuals, or males and females. Methods: In this paper, extensions of the variance components model are used to evaluate heterogeneity in the genetic and environmental variance components due to the effects of sex and age (the cutoff between young and old was 43 yrs). The data analyzed were from 81 Brazilian families (1,675 individuals) of the Baependi Family Heart Study. Results: The models allowing for heterogeneity of variance components by sex suggest that genetic and environmental variances are not different in males and females for diastolic blood pressure, LDL-cholesterol, and HDL-cholesterol, independent of the covariates included in the models. However, for systolic blood pressure, fasting glucose and triglycerides, the evidence for heterogeneity was dependent on the covariates in the model. For instance, in the presence of sex and age covariates, heterogeneity in the genetic variance component was suggested for fasting glucose. But, for systolic blood pressure, there was no evidence of heterogeneity in any of the two variance components. Except for the LDL-cholesterol, models allowing for heterogeneity by age provide evidence of heterogeneity in genetic variance for triglycerides and systolic and diastolic blood pressure. There was evidence of heterogeneity in environmental variance in fasting glucose and HDL-cholesterol. Conclusions: Our results suggest that heterogeneity in trait variances should not be ignored in the design and analyses of gene-finding studies involving these traits, as it may generate additional information about gene effects, and allow the investigation of more sophisticated models such as the model including sex-specific oligogenic variance components.

PPARGC1A sequence variation and cardiovascular risk-factor levels: a study of the main genetic effects and gene x environment interactions in children from the European Youth Heart Study.

AIMS/HYPOTHESIS: The PPARGC1A gene coactivates multiple nuclear transcription factors involved in cellular energy metabolism and vascular stasis. In the present study, we genotyped 35 tagging polymorphisms to capture all common PPARGC1A nucleotide sequence variations and tested for association with metabolic and cardiovascular traits in 2,101 Danish and Estonian boys and girls from the European Youth Heart Study, a multicentre school-based cross-sectional cohort study. METHODS: Fasting plasma glucose concentrations, anthropometric variables and blood pressure were measured. Habitual physical activity and aerobic fitness were objectively assessed using uniaxial accelerometry and a maximal aerobic exercise stress test on a bicycle ergometer, respectively. RESULTS: In adjusted models, nominally significant associations were observed for BMI (rs10018239, p = 0.039), waist circumference (rs7656250, p = 0.012; rs8192678 [Gly482Ser], p = 0.015; rs3755863, p = 0.02; rs10018239, beta = -0.01 cm per minor allele copy, p = 0.043), systolic blood pressure (rs2970869, p = 0.018) and fasting glucose concentrations (rs11724368, p = 0.045). Stronger associations were observed for aerobic fitness (rs7656250, p = 0.005; rs13117172, p = 0.008) and fasting glucose concentrations (rs7657071, p = 0.002). None remained significant after correcting for the number of statistical comparisons. We proceeded by testing for gene x physical activity interactions for the polymorphisms that showed nominal evidence of association in the main effect models. None of these tests was statistically significant. CONCLUSIONS/INTERPRETATION: Variants at PPARGC1A may influence several metabolic traits in this European paediatric cohort. However, variation at PPARGC1A is unlikely to have a major impact on cardiovascular or metabolic health in these children.

From nature versus nurture, via nature and nurture, to gene x environment interaction in mental disorders

It is now generally accepted that complex mental disorders are the results of interplay between genetic and environmental factors. This holds out the prospect that by studying G x E interplay we can explain individual variation in vulnerability and resilience to environmental hazards in the development of mental disorders. Furthermore studying G x E findings may give insights in neurobiological mechanisms of psychiatric disorder and so improve individualized treatment and potentially prevention. In this paper, we provide an overview of the state of field with regard to G x E in mental disorders. Strategies for G x E research are introduced. G x E findings from selected mental disorders with onset in childhood or adolescence are reviewed [such as depressive disorders, attention-deficit/hyperactivity disorder (ADHD), obesity, schizophrenia and substance use disorders]. Early seminal studies provided evidence for G x E in the pathogenesis of depression implicating 5-HTTLPR, and conduct problems implicating MAOA. Since then G x E effects have been seen across a wide range of mental disorders (e.g., ADHD, anxiety, schizophrenia, substance abuse disorder) implicating a wide range of measured genes and measured environments (e.g., pre-, peri- and postnatal influences of both a physical and a social nature). To date few of these G x E effects have been sufficiently replicated. Indeed meta-analyses have raised doubts about the robustness of even the most well studied findings. In future we need larger, sufficiently powered studies that include a detailed and sophisticated characterization of both phenotype and the environmental risk.

The effect of genotype-by-environment interaction on longitudinal triglyceride profiles in the Bogalusa Heart Study

Triglyceride levels are a component of plasma lipids that are thought to be an important risk factor for coronary heart disease and are influenced by genetic and environmental factors, such as single nucleotide polymorphisms (SNPs), alcohol intake, and smoking. This study used longitudinal data from the Bogalusa Heart Study, a biracial community-based survey of cardiovascular disease risk factors. A sample of 1191 individuals, 4 to 38 years of age, was measured multiple times from 1973 to 2000. The study sample consisted of 730 white and 461 African American participants. Individual growth models were developed in order to assess gene-environment interactions affecting plasma triglycerides over time. After testing for inclusion of significant covariates and interactions, final models, each accounting for the effects of a different SNP, were assessed for fit and normality. After adjustment for all other covariates and interactions, LIPC -514C/T was found to interact with age3, age2, and age and a non-significant interaction of CETP -971G/A genotype with smoking status was found (p = 0.0812). Ever-smokers had higher triglyceride levels than never smokers, but persons heterozygous at this locus, about half of both races, had higher triglyceride levels after smoking cessation compared to current smokers. Since tobacco products increase free fatty acids circulating in the bloodstream, smoking cessation programs have the potential to ultimately reduce triglyceride levels for many persons. However, due to the effect of smoking cessation on the triglyceride levels of CETP -971G/A heterozygotes, the need for smoking prevention programs is also demonstrated. Both smoking cessation and prevention programs would have a great public health impact on minimizing triglyceride levels and ultimately reducing heart disease. ^

BAYESIAN STATISTICAL METHODS IN GENE-ENVIRONMENT AND GENE-GENE INTERACTION STUDIES

Complex diseases such as cancer result from multiple genetic changes and environmental exposures. Due to the rapid development of genotyping and sequencing technologies, we are now able to more accurately assess causal effects of many genetic and environmental factors. Genome-wide association studies have been able to localize many causal genetic variants predisposing to certain diseases. However, these studies only explain a small portion of variations in the heritability of diseases. More advanced statistical models are urgently needed to identify and characterize some additional genetic and environmental factors and their interactions, which will enable us to better understand the causes of complex diseases. In the past decade, thanks to the increasing computational capabilities and novel statistical developments, Bayesian methods have been widely applied in the genetics/genomics researches and demonstrating superiority over some regular approaches in certain research areas. Gene-environment and gene-gene interaction studies are among the areas where Bayesian methods may fully exert its functionalities and advantages. This dissertation focuses on developing new Bayesian statistical methods for data analysis with complex gene-environment and gene-gene interactions, as well as extending some existing methods for gene-environment interactions to other related areas. It includes three sections: (1) Deriving the Bayesian variable selection framework for the hierarchical gene-environment and gene-gene interactions; (2) Developing the Bayesian Natural and Orthogonal Interaction (NOIA) models for gene-environment interactions; and (3) extending the applications of two Bayesian statistical methods which were developed for gene-environment interaction studies, to other related types of studies such as adaptive borrowing historical data. We propose a Bayesian hierarchical mixture model framework that allows us to investigate the genetic and environmental effects, gene by gene interactions (epistasis) and gene by environment interactions in the same model. It is well known that, in many practical situations, there exists a natural hierarchical structure between the main effects and interactions in the linear model. Here we propose a model that incorporates this hierarchical structure into the Bayesian mixture model, such that the irrelevant interaction effects can be removed more efficiently, resulting in more robust, parsimonious and powerful models. We evaluate both of the 'strong hierarchical' and 'weak hierarchical' models, which specify that both or one of the main effects between interacting factors must be present for the interactions to be included in the model. The extensive simulation results show that the proposed strong and weak hierarchical mixture models control the proportion of false positive discoveries and yield a powerful approach to identify the predisposing main effects and interactions in the studies with complex gene-environment and gene-gene interactions. We also compare these two models with the 'independent' model that does not impose this hierarchical constraint and observe their superior performances in most of the considered situations. The proposed models are implemented in the real data analysis of gene and environment interactions in the cases of lung cancer and cutaneous melanoma case-control studies. The Bayesian statistical models enjoy the properties of being allowed to incorporate useful prior information in the modeling process. Moreover, the Bayesian mixture model outperforms the multivariate logistic model in terms of the performances on the parameter estimation and variable selection in most cases. Our proposed models hold the hierarchical constraints, that further improve the Bayesian mixture model by reducing the proportion of false positive findings among the identified interactions and successfully identifying the reported associations. This is practically appealing for the study of investigating the causal factors from a moderate number of candidate genetic and environmental factors along with a relatively large number of interactions. The natural and orthogonal interaction (NOIA) models of genetic effects have previously been developed to provide an analysis framework, by which the estimates of effects for a quantitative trait are statistically orthogonal regardless of the existence of Hardy-Weinberg Equilibrium (HWE) within loci. Ma et al. (2012) recently developed a NOIA model for the gene-environment interaction studies and have shown the advantages of using the model for detecting the true main effects and interactions, compared with the usual functional model. In this project, we propose a novel Bayesian statistical model that combines the Bayesian hierarchical mixture model with the NOIA statistical model and the usual functional model. The proposed Bayesian NOIA model demonstrates more power at detecting the non-null effects with higher marginal posterior probabilities. Also, we review two Bayesian statistical models (Bayesian empirical shrinkage-type estimator and Bayesian model averaging), which were developed for the gene-environment interaction studies. Inspired by these Bayesian models, we develop two novel statistical methods that are able to handle the related problems such as borrowing data from historical studies. The proposed methods are analogous to the methods for the gene-environment interactions on behalf of the success on balancing the statistical efficiency and bias in a unified model. By extensive simulation studies, we compare the operating characteristics of the proposed models with the existing models including the hierarchical meta-analysis model. The results show that the proposed approaches adaptively borrow the historical data in a data-driven way. These novel models may have a broad range of statistical applications in both of genetic/genomic and clinical studies.

Transcription regulation of the PbGP43 gene by nitrogen in the human pathogen Paracoccidioides brasiliensis

We show indirect evidences for the possible involvement of NIT-2-like binding motifs in transcription modulation of the PbGP43 gene, which codes for an important antigen from the human fungal pathogen Paracoccidioides brasiliensis. This investigation was motivated by the finding of 23 NIT2-like sites within the proximal -2047 nucleotides of the PbGP43 5` intergenic region from the Pb339 isolate. They compose four clusters, two of them identical. We found four NIT2-containing probes that were positive in electrophoretic mobility shift assays and further analyzed them. PbGP43 could be modulated by nitrogen primary sources in Pb339, Pb3 and Pb18 isolates, as observed by reverse transcription (RT) real time-PCR. Gene reporter assays conducted in Aspergillus nidulans suggested that the minimal fragment responsible for nitrogen modulation lies within -480 bp of the PbGP43 gene. This is the first report on PbGP43 transcription modulation in response to nitrogen primary sources, which might help understand its regulation during infection. (C) 2008 Elsevier Inc. All rights reserved.

Using crop simulation to generate genotype by environment interaction effects for sorghum in water-limited environments

Multi-environment trials (METs) used to evaluate breeding lines vary in the number of years that they sample. We used a cropping systems model to simulate the target population of environments (TPE) for 6 locations over 108 years for 54 'near-isolines' of sorghum in north-eastern Australia. For a single reference genotype, each of 547 trials was clustered into 1 of 3 'drought environment types' (DETs) based on a seasonal water stress index. Within sequential METs of 2 years duration, the frequencies of these drought patterns often differed substantially from those derived for the entire TPE. This was reflected in variation in the mean yield of the reference genotype. For the TPE and for 2-year METs, restricted maximum likelihood methods were used to estimate components of genotypic and genotype by environment variance. These also varied substantially, although not in direct correlation with frequency of occurrence of different DETs over a 2-year period. Combined analysis over different numbers of seasons demonstrated the expected improvement in the correlation between MET estimates of genotype performance and the overall genotype averages as the number of seasons in the MET was increased.