Kiranmoy Das

A dynamic model for genome-wide association studies

Although genome-wide association studies (GWAS) are widely used to identify the genetic and environmental etiology of a trait, several key issues related to their statistical power and biological relevance have remained unexplored. Here, we describe a novel statistical approach, called functional GWAS or fGWAS, to analyze the genetic control of traits by integrating biological principles of trait formation into the GWAS framework through mathematical and statistical bridges. fGWAS can address many fundamental questions, such as the patterns of genetic control over development, the duration of genetic effects, as well as what causes developmental trajectories to change or stop changing. In statistics, fGWAS displays increased power for gene detection by capitalizing on cumulative phenotypic variation in a longitudinal trait over time and increased robustness for manipulating sparse longitudinal data.

A dynamic model for functional mapping of biological rhythms

Functional mapping is a statistical method for mapping quantitative trait loci (QTLs) that regulate the dynamic pattern of a biological trait. This method integrates mathematical aspects of biological complexity into a mixture model for genetic mapping and tests the genetic effects of QTLs by comparing genotype-specific curve parameters. As a way of quantitatively specifying the dynamic behaviour of a system, differential equations have proved to be powerful for modelling and unravelling the biochemical, molecular, and cellular mechanisms of a biological process, such as biological rhythms. The equipment of functional mapping with biologically meaningful differential equations provides new insights into the genetic control of any dynamic processes. We formulate a new functional mapping framework for a dynamic biological rhythm by incorporating a group of ordinary differential equations (ODE). The Runge–Kutta fourth-order algorithm was implemented to estimate the parameters that define the system of ODE. The new model will find its implications for understanding the interplay between gene interactions and developmental pathways in complex biological rhythms.

Functional mapping of human growth trajectories

Human height is an important trait from biological and social perspectives. Genes have been widely recognized to be involved in human body growth, but their detailed controlling mechanisms are poorly understood. Here, we present a computational model for functional mapping of quantitative trait loci (QTLs) that control trajectories of human height growth through an interactive network. The model integrates mathematical equations of human growth curves into the mixture model-based functional mapping framework, allowing the identification and mapping of individual QTLs responsible for the developmental pattern of human growth. The model was derived on a random sample of subjects from a natural population, for each of which molecular markers within candidate genes or throughout the entire genome are typed and height data from childhood to adulthood are collected. A series of testable hypotheses are formulated about the genetic control of developmental timing and duration at different stages. The model was used to characterize epistatic QTLs for height growth hidden in 548 Japanese girls which is a semi-real data set with simulated the marker genotypes. With an increasing availability of genetic polymorphic data, the model will have great implications for probing the genetic and developmental mechanisms of human body growth and its associated diseases.

Multilocus genomics of outcrossing plant populations.

The structure and organization of natural plant populations can be understood by estimating the genetic parameters related to mating behavior, recombination frequency, and gene associations with DNA-based markers typed throughout the genome. We developed a statistical and computational model for estimating and testing these parameters from multilocus data collected in a natural population. This model, constructed by a maximum likelihood approach and implemented within the EM algorithm, is shown to be robust for simultaneously estimating the outcrossing rate, recombination frequencies and linkage disequilibria. The algorithm built with three or more markers allows the characterization of crossover interference in meiosis and high-order disequilibria among different genes, thus providing a powerful tool for illustrating a detailed picture of genetic diversity and organization in natural populations. Computer simulations demonstrate the statistical properties of the proposed model. This multilocus model will be useful for studying the pattern and amount of genetic variation within and among populations to further infer the evolutionary history of a plant species.

Genome-Wide Association Studies for Bivariate Sparse Longitudinal Data

Objective: Longitudinal measurements with bivariate response have been analyzed by several authors using two separate models for each response. However, for most of the biological or medical experiments, the two responses are highly correlated and hence a separate model for each response might not be a desirable way to analyze such data. A single model considering a bivariate response provides a more powerful inference as the correlation between the responses is modeled appropriately. In this article, we propose a dynamic statistical model to detect the genes controlling human blood pressure (systolic and diastolic). Methods: By modeling the mean function with orthogonal Legendre polynomials and the covariance matrix with a stationary parametric structure, we incorporate the statistical ideas in functional genome-wide association studies to detect SNPs which have significant control on human blood pressure. The traditional false discovery rate is used for multiple comparisons. Results: We analyze the data from the Framingham Heart Study to detect such SNPs by appropriately considering gender-gene interaction. We detect 8 SNPs for males and 7 for females which are most significant in controlling blood pressure. The genotype-specific mean curves and additive and dominant effects over time are shown for each significant SNP for both genders. Simulation studies are performed to examine the statistical properties of our model. The current model will be extremely useful in detecting genes controlling different traits and diseases for humans or non-human subjects.

Functional mapping of reaction norms to multiple environmental signals through nonparametric covariance estimation

BackgroundThe identification of genes or quantitative trait loci that are expressed in response to different environmental factors such as temperature and light, through functional mapping, critically relies on precise modeling of the covariance structure. Previous work used separable parametric covariance structures, such as a Kronecker product of autoregressive one [AR(1)] matrices, that do not account for interaction effects of different environmental factors.ResultsWe implement a more robust nonparametric covariance estimator to model these interactions within the framework of functional mapping of reaction norms to two signals. Our results from Monte Carlo simulations show that this estimator can be useful in modeling interactions that exist between two environmental signals. The interactions are simulated using nonseparable covariance models with spatio-temporal structural forms that mimic interaction effects.ConclusionsThe nonparametric covariance estimator has an advantage over separable parametric covariance estimators in the detection of QTL location, thus extending the breadth of use of functional mapping in practical settings.

EM Algorithm for Mapping Quantitative Trait Loci in Multivalent Tetraploids

Multivalent tetraploids that include many plant species, such as potato, sugarcane, and rose, are of paramount importance to agricultural production and biological research. Quantitative trait locus (QTL) mapping in multivalent tetraploids is challenged by their unique cytogenetic properties, such as double reduction. We develop a statistical method for mapping multivalent tetraploid QTLs by considering these cytogenetic properties. This method is built in the mixture model-based framework and implemented with the EM algorithm. The method allows the simultaneous estimation of QTL positions, QTL effects, the chromosomal pairing factor, and the degree of double reduction as well as the assessment of the estimation precision of these parameters. We used simulated data to examine the statistical properties of the method and validate its utilization. The new method and its software will provide a useful tool for QTL mapping in multivalent tetraploids that undergo double reduction.

A statistical model for mapping morphological shape

BackgroundLiving things come in all shapes and sizes, from bacteria, plants, and animals to humans. Knowledge about the genetic mechanisms for biological shape has far-reaching implications for a range spectrum of scientific disciplines including anthropology, agriculture, developmental biology, evolution and biomedicine.ResultsWe derived a statistical model for mapping specific genes or quantitative trait loci (QTLs) that control morphological shape. The model was formulated within the mixture framework, in which different types of shape are thought to result from genotypic discrepancies at a QTL. The EM algorithm was implemented to estimate QTL genotype-specific shapes based on a shape correspondence analysis. Computer simulation was used to investigate the statistical property of the model.ConclusionBy identifying specific QTLs for morphological shape, the model developed will help to ask, disseminate and address many major integrative biological and genetic questions and challenges in the genetic control of biological shape and function.

A Bayesian Framework for Functional Mapping through Joint Modeling of Longitudinal and Time-to-Event Data.

The most powerful and comprehensive approach of study in modern biology is to understand the whole process of development and all events of importance to development which occur in the process. As a consequence, joint modeling of developmental processes and events has become one of the most demanding tasks in statistical research. Here, we propose a joint modeling framework for functional mapping of specific quantitative trait loci (QTLs) which controls developmental processes and the timing of development and their causal correlation over time. The joint model contains two submodels, one for a developmental process, known as a longitudinal trait, and the other for a developmental event, known as the time to event, which are connected through a QTL mapping framework. A nonparametric approach is used to model the mean and covariance function of the longitudinal trait while the traditional Cox proportional hazard (PH) model is used to model the event time. The joint model is applied to map QTLs that control whole-plant vegetative biomass growth and time to first flower in soybeans. Results show that this model should be broadly useful for detecting genes controlling physiological and pathological processes and other events of interest in biomedicine.

Statistical Models for Genetic Mapping in Polyploids: Challenges and Opportunities

Statistical methods for genetic mapping have well been developed for diploid species but are lagging in the more complex polyploids. The genetic mapping of polyploids, where genome number is higher than two, is complicated by uncertainty about the genotype-phenotype correspondence, inconsistent meiotic mechanisms, heterozygous genome structures, and increased allelic (action) and nonallelic (interaction) combinations. According to their meiotic configurations, polyploids can be classified as bivalent polyploids, in which only two chromosomes pair during meiosis at a time, and multivalent polyploids, where multiple chromosomes pair simultaneously. For some polyploids, these two types of pairing occur at the same time, leading to a mixed category. This chapter reviews several challenges due to the complexities of linkage analysis in polyploids and describes statistical models and algorithms that have been developed for linkage mapping based on their distinct meiotic characteristics. We discuss several issues that should be addressed to better understand the genome structure and organization of polyploids and the genetic architecture of complex traits for this unique group of plants.