Functional dynamic genetic effects on gene regulation are specific to particular cell types and environmental conditions

Genetic effects on gene expression and splicing can be modulated by cellular and environmental factors; yet interactions between genotypes, cell type and treatment have not been comprehensively studied together. We used an induced pluripotent stem cell system to study multiple cell types derived from the same individuals and exposed them to a large panel of treatments. Cellular responses involved different genes and pathways for gene expression and splicing, and were highly variable across contexts. For thousands of genes, we identified variable allelic expression across contexts and characterized different types of gene-environment interactions, many of which are associated with complex traits. Promoter functional and evolutionary features distinguished genes with elevated allelic imbalance mean and variance. On average half of the genes with dynamic regulatory interactions were missed by large eQTL mapping studies, indicating the importance of exploring multiple treatments to reveal previously unrecognized regulatory loci that may be important for disease

Functional dynamic genetic effects on gene regulation are specific to particular cell types and environmental conditions

Genetic effects on gene expression and splicing can be modulated by cellular and environmental factors; yet interactions between genotypes, cell type and treatment have not been comprehensively studied together. We used an induced pluripotent stem cell system to study multiple cell types derived from the same individuals and exposed them to a large panel of treatments. Cellular responses involved different genes and pathways for gene expression and splicing, and were highly variable across contexts. For thousands of genes, we identified variable allelic expression across contexts and characterized different types of gene-environment interactions, many of which are associated with complex traits. Promoter functional and evolutionary features distinguished genes with elevated allelic imbalance mean and variance. On average half of the genes with dynamic regulatory interactions were missed by large eQTL mapping studies, indicating the importance of exploring multiple treatments to reveal previously unrecognized regulatory loci that may be important for disease

List homomorphism to irreflexive oriented trees

Min ordering of a digraph $H$ plays an important role in deciding the existence of a list homomorphism to $H$. For reflexive oriented trees $T$, there exists a concrete forbidden induced subgraph characterization to have a min ordering. For irreflexive oriented trees $T$, the existence of a min-ordering turned out to be somewhat harder, as there are many types of obstructions to its existence. In this thesis, we first review the existing results for list homomorphism problems $LHOM(H)$ for digraphs and graphs. Second, for a specific subclass of irreflexive oriented trees, we present a concrete forbidden induced subgraph characterization to have a min ordering and to have an obstruction called invertible pair ($I$-$pair$) and digraph asteroidal triple ($DAT$). Moreover, for this subclass of irreflexive oriented trees $T$, we show that if $T$ contains one of the forbidden obstructions, then the problem $LHOM(T)$ is $NP$-complete, and is polynomial otherwise. Third, we discuss general trees, and present some approaches to find the minimal forbidden obstructions in the general case

Scalable and Robust Statistical Inference Algorithms for Linking Genotypes to Phenotypes

With the advancements in DNA sequencing technology and the decreasing cost of sequencing, there has been exponential growth in the amount of genomic data generated. This growth provides an unprecedented opportunity to access the genotypes of a large population, including millions of genetic variants, and to collect hundreds of thousands of phenotypic measurements from the same individuals. This opens doors to systematically studying the genetic architecture underlying complex traits and diseases. Genetic architecture refers broadly to a complete understanding of all genetic contributions to a given trait as well as to an awareness of the characteristics of this contribution. During the past decade, variance components analysis has emerged as a robust statistical framework for investigating the genetic architectures of complex traits. To gain accurate and innovative insights into genetic architecture, applying flexible variance component models to large-scale datasets is crucial. However, fitting such models necessitates the use of scalable algorithms. Common approaches for estimating variance components involve searching for parameter values that maximize the likelihood or the restricted maximum likelihood (REML). Despite several algorithmic advancements, computing REML estimates of variance components on extensive datasets like the UK Biobank, which consists of approximately 500,000 genotyped individuals, millions of single nucleotide polymorphisms (SNPs), and hundreds of thousands of phenotypes, remains challenging. This thesis introduces a set of scalable and robust statistical inference algorithms rooted in variance component analysis. These algorithms are designed to estimate the variation in a trait that can be explained by linear and non-linear functions of the genotype, such as the interaction between alleles at a single genetic variant (dominance), the interaction between genetic variants (epistasis), and the interaction between environmental factors and genetic variants (GxE). Furthermore, these algorithms aim to estimate the distribution of these effects across the genome. By applying our methods to the UK Biobank dataset, we uncover valuable insights into the genetic architecture of complex traits. Notable observations are as follows. First, we observe that both per-allele squared additive and GxE effect size increase with decreasing minor allele frequency (MAF) and linkage disequilibrium (LD). Second, testing whether GxE heritability is enriched around genes that are highly expressed in specific tissues, we find significant tissue-specific enrichments that include brain-specific enrichment for BMI and Basal Metabolic Rate in the context of smoking, adipose-specific enrichment for WHR in the context of sex, and cardiovascular tissue-specific enrichment for total cholesterol in the context of age. Third, we detect epistasis effects between SNPs located on the same chromosome and between SNPs located on different chromosomes. Fourth, our analyses indicate a limited contribution of dominance heritability to complex trait variation

Fast kernel-based association testing of non-linear genetic effects for biobank-scale data

Abstract Our knowledge of non-linear genetic effects on complex traits remains limited, in part, due to the modest power to detect such effects. While kernel-based tests offer a versatile approach to test for non-linear relationships between sets of genetic variants and traits, current approaches cannot be applied to Biobank-scale datasets containing hundreds of thousands of individuals. We propose, FastKAST, a kernel-based approach that can test for non-linear effects of a set of variants on a quantitative trait. FastKAST provides calibrated hypothesis tests while enabling analysis of Biobank-scale datasets with hundreds of thousands of unrelated individuals from a homogeneous population. We apply FastKAST to 53 quantitative traits measured across ≈ 300 K unrelated white British individuals in the UK Biobank to detect sets of variants with non-linear effects at genome-wide significance

Quantifying the contribution of dominance deviation effects to complex trait variation in biobank-scale data.

The proportion of variation in complex traits that can be attributed to non-additive genetic effects has been a topic of intense debate. The availability of biobank-scale datasets of genotype and trait data from unrelated individuals opens up the possibility of obtaining precise estimates of the contribution of non-additive genetic effects. We present an efficient method to estimate the variation in a complex trait that can be attributed to additive (additive heritability) and dominance deviation (dominance heritability) effects across all genotyped SNPs in a large collection of unrelated individuals. Over a wide range of genetic architectures, our method yields unbiased estimates of additive and dominance heritability. We applied our method, in turn, to array genotypes as well as imputed genotypes (at common SNPs with minor allele frequency [MAF] > 1%) and 50 quantitative traits measured in 291,273 unrelated white British individuals in the UK Biobank. Averaged across these 50 traits, we find that additive heritability on array SNPs is 21.86% while dominance heritability is 0.13% (about 0.48% of the additive heritability) with qualitatively similar results for imputed genotypes. We find no statistically significant evidence for dominance heritability (p<0.05/50 accounting for the number of traits tested) and estimate that dominance heritability is unlikely to exceed 1% for the traits analyzed. Our analyses indicate a limited contribution of dominance heritability to complex trait variation

Fast kernel-based association testing of non-linear genetic effects for biobank-scale data.

Our knowledge of non-linear genetic effects on complex traits remains limited, in part, due to the modest power to detect such effects. While kernel-based tests offer a versatile approach to test for non-linear relationships between sets of genetic variants and traits, current approaches cannot be applied to Biobank-scale datasets containing hundreds of thousands of individuals. We propose, FastKAST, a kernel-based approach that can test for non-linear effects of a set of variants on a quantitative trait. FastKAST provides calibrated hypothesis tests while enabling analysis of Biobank-scale datasets with hundreds of thousands of unrelated individuals from a homogeneous population. We apply FastKAST to 53 quantitative traits measured across ≈ 300 K unrelated white British individuals in the UK Biobank to detect sets of variants with non-linear effects at genome-wide significance