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.

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.

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.

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.

New strategies to detect and understand genotype-by-environment interactions and QTL-by-environment interactions

Dissertação para obtenção do Grau de Doutor em Estatística e Gestão do Risco, especialidade em Estatística

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 BMI Interactions Influencing C-Reactive Protein Levels in European-Americans

C-Reactive Protein (CRP) is a biomarker indicating tissue damage, inflammation, and infection. High-sensitivity CRP (hsCRP) is an emerging biomarker often used to estimate an individual’s risk for future coronary heart disease (CHD). hsCRP levels falling below 1.00 mg/l indicate a low risk for developing CHD, levels ranging between 1.00 mg/l and 3.00 mg/l indicate an elevated risk, and levels exceeding 3.00 mg/l indicate high risk. Multiple Genome-Wide Association Studies (GWAS) have identified a number of genetic polymorphisms which influence CRP levels. SNPs implicated in such studies have been found in or near genes of interest including: CRP, APOE, APOC, IL-6, HNF1A, LEPR, and GCKR. A strong positive correlation has also been found to exist between CRP levels and BMI, a known risk factor for CHD and a state of chronic inflammation. We conducted a series of analyses designed to identify loci which interact with BMI to influence CRP levels in a subsample of European-Americans in the ARIC cohort. In a stratified GWA analysis, 15 genetic regions were identified as having significantly (p-value < 2.00*10-3) distinct effects on hsCRP levels between the two obesity strata: lean (18.50 kg/m2 < BMI < 24.99 kg/m2) and obese (BMI ≥ 30.00 kg/m2). A GWA analysis performed on all individuals combined (i.e. not a priori stratified for obesity status) with the inclusion of an additional parameter for BMI by gene interaction, identified 11 regions which interact with BMI to influence hsCRP levels. Two regions containing the genes GJA5 and GJA8 (on chromosome 1) and FBXO11 (on chromosome 2) were identified in both methods of analysis suggesting that these genes possibly interact with BMI to influence hsCRP levels. We speculate that atrial fibrillation (AF), age-related cataracts and the TGF-β pathway may be the biological processes influenced by the interaction of GJA5, GJA8 and FBXO11, respectively, with BMI to cause changes in hsCRP levels. Future studies should focus on the influence of gene x bmi interaction on AF, age-related cataracts and TGF-β.

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.

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.

Genotype by environment interaction for 450-day weight of Nelore cattle analyzed by reaction norm models

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Factors that cause genotype by environment interaction and use of a multiple-trait herd-cluster model for milk yield of Holstein cattle from Brazil and Colombia

Descriptive herd variables (DVHE) were used to explain genotype by environment interactions (G x E) for milk yield (MY) in Brazilian and Colombian production environments and to develop a herd-cluster model to estimate covariance components and genetic parameters for each herd environment group. Data consisted of 180,522 lactation records of 94,558 Holstein cows from 937 Brazilian and 400 Colombian herds. Herds in both countries were jointly grouped in thirds according to 8 DVHE: production level, phenotypic variability, age at first calving, calving interval, percentage of imported semen, lactation length, and herd size. For each DVHE, REML bivariate animal model analyses were used to estimate genetic correlations for MY between upper and lower thirds of the data. Based on estimates of genetic correlations, weights were assigned to each DVHE to group herds in a cluster analysis using the FASTCLUS procedure in SAS. Three clusters were defined, and genetic and residual variance components were heterogeneous among herd clusters. Estimates of heritability in clusters 1 and 3 were 0.28 and 0.29, respectively, but the estimate was larger (0.39) in Cluster 2. The genetic correlations of MY from different clusters ranged from 0.89 to 0.97. The herd-cluster model based on DVHE properly takes into account G x E by grouping similar environments accordingly and seems to be an alternative to simply considering country borders to distinguish between environments.

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. ^

Alcohol dehydrogenase activities and ethanol tolerance in Anastrepha (Diptera, Tephritidae) fruit-fly species and their hybrids

The ADH (alcohol dehydrogenase) system is one of the earliest known models of molecular evolution, and is still the most studied in Drosophila. Herein, we studied this model in the genus Anastrepha (Diptera, Tephritidae). Due to the remarkable advantages it presents, it is possible to cross species with different Adh genotypes and with different phenotype traits related to ethanol tolerance. The two species studied here each have a different number of Adh gene copies, whereby crosses generate polymorphisms in gene number and in composition of the genetic background. We measured certain traits related to ethanol metabolism and tolerance. ADH specific enzyme activity presented gene by environment interactions, and the larval protein content showed an additive pattern of inheritance, whilst ADH enzyme activity per larva presented a complex behavior that may be explained by epistatic effects. Regression models suggest that there are heritable factors acting on ethanol tolerance, which may be related to enzymatic activity of the ADHs and to larval mass, although a pronounced environmental effect on ethanol tolerance was also observed. By using these data, we speculated on the mechanisms of ethanol tolerance and its inheritance as well as of associated traits.

Pheomelanin-based coloration and the ability to cope with variation in food supply and parasitism.

Although gene by environment interactions may play a key role in the maintenance of genetic polymorphisms, little is known about the ecological factors involved in these interactions. We investigated whether food supply and parasites can mediate covariation between the degree of adult pheomelanin-based coloration, a heritable trait, and offspring body mass in the tawny owl (Strix aluco). We swapped clutches between nests to allocate genotypes randomly among environments. Three weeks after hatching, we challenged the immune system of 80 unrelated nestlings with either a phytohemagglutinin (PHA) or a lipopolysaccharide, surrogates of alternative parasites, and then fed them ad lib. or food-restricted them during the following 6 days in the laboratory. Whatever the immune challenge, nestlings fed ad lib. converted food more efficiently into body mass when their biological mother was dark pheomelanic. In contrast, food-restricted nestlings challenged with PHA lost less body mass when their biological mother was pale pheomelanic. Nestling tawny owls born from differently melanic mothers thus show differing reaction norms relative to food availability and parasitism. This suggests that dark and pale pheomelanic owls reflect alternative adaptations to food availability and parasites, factors known to vary in space and time.