A Model for Transgenerational Imprinting Variation in Complex Traits

Despite the fact that genetic imprinting, i.e., differential expression of the same allele due to its different parental origins, plays a pivotal role in controlling complex traits or diseases, the origin, action and transmission mode of imprinted genes have still remained largely unexplored. We present a new strategy for studying these properties of genetic imprinting with a two-stage reciprocal F mating design, initiated with two contrasting inbred lines. This strategy maps quantitative trait loci that are imprinted (i.e., iQTLs) based on their segregation and transmission across different generations. By incorporating the allelic configuration of an iQTL genotype into a mixture model framework, this strategy provides a path to trace the parental origin of alleles from previous generations. The imprinting effects of iQTLs and their interactions with other traditionally defined genetic effects, expressed in different generations, are estimated and tested by implementing the EM algorithm. The strategy was used to map iQTLs responsible for survival time with four reciprocal F populations and test whether and how the detected iQTLs inherit their imprinting effects into the next generation. The new strategy will provide a tool for quantifying the role of imprinting effects in the creation and maintenance of phenotypic diversity and elucidating a comprehensive picture of the genetic architecture of complex traits and diseases.     

A statistical model for estimating maternal-zygotic interactions and parent-of-origin effects of QTLs for seed development

Proper development of a seed requires coordinated exchanges of signals among the three components that develop side by side in the seed. One of these is the maternal integument that encloses the other two zygotic components, i.e., the diploid embryo and its nurturing annex, the triploid endosperm. Although the formation of the embryo and endosperm contains the contributions of both maternal and paternal parents, maternally and paternally derived alleles may be expressed differently, leading to a so-called parent-of-origin or imprinting effect. Currently, the nature of how genes from the maternal and zygotic genomes interact to affect seed development remains largely unknown. Here, we present a novel statistical model for estimating the main and interaction effects of quantitative trait loci (QTLs) that are derived from different genomes and further testing the imprinting effects of these QTLs on seed development. The experimental design used is based on reciprocal backcrosses toward both parents, so that the inheritance of parent-specific alleles could be traced. The computing model and algorithm were implemented with the maximum likelihood approach. The new strategy presented was applied to study the mode of inheritance for QTLs that control endoreduplication traits in maize endosperm. Monte Carlo simulation studies were performed to investigate the statistical properties of the new model with the data simulated under different imprinting degrees. The false positive rate of imprinting QTL discovery by the model was examined by analyzing the simulated data that contain no imprinting QTL. The reciprocal design and a series of analytical and testing strategies proposed provide a standard procedure for genomic mapping of QTLs involved in the genetic control of complex seed development traits in flowering plants.     

A statistical design for testing transgenerational genomic imprinting in natural human populations

Genomic imprinting is a phenomenon in which the same allele is expressed differently, depending on its parental origin. Such a phenomenon, also called the parent-of-origin effect, has been recognized to play a pivotal role in embryological development and pathogenesis in many species. Here we propose a statistical design for detecting imprinted loci that control quantitative traits based on a random set of three-generation families from a natural population in humans. This design provides a pathway for characterizing the effects of imprinted genes on a complex trait or disease at different generations and testing transgenerational changes of imprinted effects. The design is integrated with population and cytogenetic principles of gene segregation and transmission from a previous generation to next. The implementation of the EM algorithm within the design framework leads to the estimation of genetic parameters that define imprinted effects. A simulation study is used to investigate the statistical properties of the model and validate its utilization. This new design, coupled with increasingly used genome-wide association studies, should have an immediate implication for studying the genetic architecture of complex traits in humans.     

A framework for detecting and characterizing genetic background-dependent imprinting effects

Genomic imprinting, where the effects of alleles depend on their parent-of-origin, can be an important component of the genetic architecture of complex traits. Although there has been a rapidly increasing number of studies of genetic architecture that have examined imprinting effects, none have examined whether imprinting effects depend on genetic background. Such effects are critical for the evolution of genomic imprinting because they allow the imprinting state of a locus to evolve as a function of genetic background. Here we develop a two-locus model of epistasis that includes epistatic interactions involving imprinting effects and apply this model to scan the mouse genome for loci that modulate the imprinting effects of quantitative trait loci (QTL). The inclusion of imprinting leads to nine orthogonal forms of epistasis, five of which do not appear in the usual two-locus decomposition of epistasis. Each form represents a change in the imprinting status of one locus across different classes of genotypes at the other locus. Our genome scan identified two different locus pairs that show complex patterns of epistasis, where the imprinting effect at one locus changes across genetic backgrounds at the other locus. Thus, our model provides a framework for the detection of genetic background-dependent imprinting effects that should provide insights into the background dependence and evolution of genomic imprinting. Our application of the model to a genome scan supports this assertion by identifying pairs of loci that show reciprocal changes in their imprinting status as the background provided by the other locus changes.     

A statistical framework for genome-wide scanning and testing of imprinted quantitative trait loci

Non-equivalent expression of alleles at a locus results in genomic imprinting. In this article, a statistical framework for genome-wide scanning and testing of imprinted quantitative trait loci (iQTL) underlying complex traits is developed based on experimental crosses of inbred line species in backcross populations. The joint likelihood function is composed of four component likelihood functions with each of them derived from one of four backcross families. The proposed approach models genomic imprinting effect as a probability measure with which one can test the degree of imprinting. Simulation results show that the model is robust for identifying iQTL with various degree of imprinting ranging from no imprinting, partial imprinting to complete imprinting. Under various simulation scenarios, the proposed model shows consistent parameter estimation with reasonable precision and high power in testing iQTL. When a QTL shows Mendelian effect, the proposed model also outperforms traditional Mendelian model. Extension to incorporate maternal effect is also given. The developed model, built within the maximum likelihood framework and implemented with the EM algorithm, provides a quantitative framework for testing and estimating iQTL involved in the genetic control of complex traits.     

Influence of mom and dad: quantitative genetic models for maternal effects and genomic imprinting

The expression of an imprinted gene is dependent on the sex of the parent it was inherited from, and as a result reciprocal heterozygotes may display different phenotypes. In contrast, maternal genetic terms arise when the phenotype of an offspring is influenced by the phenotype of its mother beyond the direct inheritance of alleles. Both maternal effects and imprinting may contribute to resemblance between offspring of the same mother. We demonstrate that two standard quantitative genetic models for deriving breeding values, population variances and covariances between relatives, are not equivalent when maternal genetic effects and imprinting are acting. Maternal and imprinting effects introduce both sex-dependent and generation-dependent effects that result in differences in the way additive and dominance effects are defined for the two approaches. We use a simple example to demonstrate that both imprinting and maternal genetic effects add extra terms to covariances between relatives and that model misspecification may over- or underestimate true covariances or lead to extremely variable parameter estimation. Thus, an understanding of various forms of parental effects is essential in correctly estimating quantitative genetic variance components.     

A search for quantitative trait loci exhibiting imprinting effects on mouse mandible size and shape

Genomic imprinting refers to the pattern of monoallelic parent-of-origin-dependent gene expression where one of the two alleles at a locus is expressed and the other silenced. Although some genes in mice are known to be imprinted, the true scope of imprinting and its impact on the genetic architecture of a wide range of morphometric traits is mostly unknown. We therefore searched for quantitative trait loci (QTL) exhibiting imprinting effects on mandible size and shape traits in a large F(3) population of mice originating from an intercross of the LG/J (Large) and SM/J (Small) inbred strains. We discovered a total of 51 QTL affecting mandible size and shape, 6 of which exhibited differences between reciprocal heterozygotes, the usual signature of imprinting effects. However, our analysis showed that only one of these QTL (affecting mandible size) exhibited a pattern consistent with true imprinting effects, whereas reciprocal heterozygote differences in the other five all were due to maternal genetic effects. We concluded that genomic imprinting has a negligible effect on these specific morphometric traits, and that maternal genetic effects may account for many of the previously reported instances of apparent genomic imprinting.     

Bayesian mapping of genome-wide epistatic imprinted loci for quantitative traits

Genomic imprinting, an epigenetic phenomenon of parent-of-origin-specific gene expression, has been widely observed in plants, animals, and humans. To detect imprinting genes influencing quantitative traits, the least squares and maximum likelihood approaches for fitting a single quantitative trait locus (QTL) and Bayesian methods for simultaneously modeling multiple QTL have been adopted, respectively, in various studies. However, most of these studies have only estimated imprinting main effects and thus ignored imprinting epistatic effects. In the presence of extremely complex genomic imprinting architectures, we introduce a Bayesian model selection method to analyze the multiple interacting imprinted QTL (iQTL) model. This approach will greatly enhance the computational efficiency through setting the upper bound of the number of QTLs and performing selective sampling for QTL parameters. The imprinting types of detected main-effect QTLs can be estimated from the Bayes factor statistic formulated by the posterior probabilities for the genetic effects being compared. The performance of the proposed method is demonstrated by several simulation experiments. Moreover, this method is applied to dissect the imprinting genetic architecture for body weight in mouse and fruit weight in tomato. Matlab code for implementing this approach will be available from the authors upon request.     

Bayesian inference for genomic imprinting underlying developmental characteristics

The identification of imprinted genes is becoming a standard procedure in searching for quantitative trait loci (QTL) underlying complex traits. When a developmental characteristic such as growth or drug response is observed at multiple time points, understanding the dynamics of gene function governing the underlying feature should provide more biological information regarding the genetic control of an organism. Recognizing that differential imprinting can be development-specific, mapping imprinted genes considering the dynamic imprinting effect can provide additional biological insights into the epigenetic control of a complex trait. In this study, we proposed a Bayesian imprinted QTL (iQTL) mapping framework considering the dynamics of imprinting effects and model multiple iQTLs with an efficient Bayesian model selection procedure. The method overcomes the limitation of likelihood-based mapping procedure, and can simultaneously identify multiple iQTLs with different gene action modes across the whole genome with high computational efficiency. An inference procedure using Bayes factors to distinguish different imprinting patterns of iQTL was proposed. Monte Carlo simulations were conducted to evaluate the performance of the method. The utility of the approach was illustrated through an analysis of a body weight growth data set in an F(2) family derived from LG/J and SM/J mouse stains. The proposed Bayesian mapping method provides an efficient and computationally feasible framework for genome-wide multiple iQTL inference with complex developmental traits.     

A Unified Framework Integrating Parent-of-Origin Effects for Association Study

Genetic imprinting is the most well-known cause for parent-of-origin effect (POE) whereby a gene is differentially expressed depending on the parental origin of the same alleles. Genetic imprinting is related to several human disorders, including diabetes, breast cancer, alcoholism, and obesity. This phenomenon has been shown to be important for normal embryonic development in mammals. Traditional association approaches ignore this important genetic phenomenon. In this study, we generalize the natural and orthogonal interactions (NOIA) framework to allow for estimation of both main allelic effects and POEs. We develop a statistical (Stat-POE) model that has the orthogonal estimates of parameters including the POEs. We conducted simulation studies for both quantitative and qualitative traits to evaluate the performance of the statistical and functional models with different levels of POEs. Our results showed that the newly proposed Stat-POE model, which ensures orthogonality of variance components if Hardy-Weinberg Equilibrium (HWE) or equal minor and major allele frequencies is satisfied, had greater power for detecting the main allelic additive effect than a Func-POE model, which codes according to allelic substitutions, for both quantitative and qualitative traits. The power for detecting the POE was the same for the Stat-POE and Func-POE models under HWE for quantitative traits.     

A statistical model for dissecting genomic imprinting through genetic mapping

As a result of nonequivalent genetic contribution of maternal and paternal genomes to offsprings, genomic imprinting or called parent-of-origin effect, has been broadly identified in plants, animals and humans. Its role in shaping organism’s development has been unanimously recognized. However, statistical methods for identifying imprinted quantitative trait loci (iQTL) and estimating the imprinted effect have not been well developed. In this article, we propose an efficient statistical procedure for genomewide estimating and testing the effects of significant iQTL underlying the quantitative variation of interested traits. The developed model can be applied to two different genetic cross designs, backcross and F₂ families derived from inbred lines. The proposed procedure is built within the maximum likelihood framework and implemented with the EM algorithm. Extensive simulation studies show that the proposed model is well performed in a variety of situations. To demonstrate the usefulness of the proposed approach, we apply the model to a published data in an F₂ family derived from LG/S and SM/S mouse stains. Two partially maternal imprinting iQTL are identified which regulate the growth of body weight. Our approach provides a testable framework for identifying and estimating iQTL involved in the genetic control of complex traits.     

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 behavior of a system, differential equations have proven to be powerful for modeling and unraveling 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.     

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.     

Testing for genetic linkage in families by a variance-components approach in the presence of genomic imprinting

Some genes that affect development and behavior in mammals are known to be imprinted; and > or = 1% of all mammalian genes are imprinted. Hence, incorporating an imprinting parameter into linkage analysis may increase the power to detect linkage for these traits. Here we propose theoretical justifications for a recently developed model for testing of linkage, in the presence of genetic imprinting, between a quantitative-trait locus and a polymorphic marker; this is achieved in the variance-components framework. We also incorporate sex-specific recombination fractions into this model. We discuss the effects that imprinting and nonimprinting have on the power of the usual variance-components method and on the variance-components method that incorporates an imprinting parameter. We provide noncentrality parameters that can be used to determine the sample size necessary to attain a specified power for a given significance level, which is useful in the planning of a linkage study. Optimal strategies for a genome scan of potentially imprinted traits are discussed.     

A semiparametric approach for composite functional mapping of dynamic quantitative traits

Functional mapping has emerged as a powerful tool for mapping quantitative trait loci (QTL) that control developmental patterns of complex dynamic traits. Original functional mapping has been constructed within the context of simple interval mapping, without consideration of separate multiple linked QTL for a dynamic trait. In this article, we present a statistical framework for mapping QTL that affect dynamic traits by capitalizing on the strengths of functional mapping and composite interval mapping. Within this so-called composite functional-mapping framework, functional mapping models the time-dependent genetic effects of a QTL tested within a marker interval using a biologically meaningful parametric function, whereas composite interval mapping models the time-dependent genetic effects of the markers outside the test interval to control the genome background using a flexible nonparametric approach based on Legendre polynomials. Such a semiparametric framework was formulated by a maximum-likelihood model and implemented with the EM algorithm, allowing for the estimation and the test of the mathematical parameters that define the QTL effects and the regression coefficients of the Legendre polynomials that describe the marker effects. Simulation studies were performed to investigate the statistical behavior of composite functional mapping and compare its advantage in separating multiple linked QTL as compared to functional mapping. We used the new mapping approach to analyze a genetic mapping example in rice, leading to the identification of multiple QTL, some of which are linked on the same chromosome, that control the developmental trajectory of leaf age.     

Characterization of genomic imprinting effects and patterns with parametric accelerated failure time model

Genomic imprinting, a genetic phenomenon of non-equivalent allele expression that depends on parental origins, has been ubiquitously observed in nature. It does not only control the traits of growth and development but also may be responsible for survival traits. Based on the accelerated failure time model, we construct a general parametric model for mapping the imprinted QTL (iQTL). Within the framework of interval mapping, maximum likelihood estimation of iQTL parameters is implemented via EM algorithm. The imprinting patterns of the detected iQTL are statistically tested according to a series of null hypotheses. BIC model selection criterion is employed to choose an optimal baseline hazard function with maximum likelihood and parsimonious parameters. Simulations are used to validate the proposed mapping procedure. A published dataset from a mouse model system was used to illustrate the proposed framework. Results show that among the five commonly used survival distributions, Log-logistic distribution is the optimal baseline hazard function for mapping QTL of hyperoxic acute lung injury (HALI) survival; under the log-logistic distribution, four QTLs were identified, in which only one QTL was inherited in Mendelian fashion, whereas others were imprinted in different imprinting patterns.     

A Novel Statistical Model to Estimate Host Genetic Effects Affecting Disease Transmission

There is increasing recognition that genetic diversity can affect the spread of diseases, potentially affecting plant and livestock disease control as well as the emergence of human disease outbreaks. Nevertheless, even though computational tools can guide the control of infectious diseases, few epidemiological models can simultaneously accommodate the inherent individual heterogeneity in multiple infectious disease traits influencing disease transmission, such as the frequently modeled propensity to become infected and infectivity, which describes the host ability to transmit the infection to susceptible individuals. Furthermore, current quantitative genetic models fail to fully capture the heritable variation in host infectivity, mainly because they cannot accommodate the nonlinear infection dynamics underlying epidemiological data. We present in this article a novel statistical model and an inference method to estimate genetic parameters associated with both host susceptibility and infectivity. Our methodology combines quantitative genetic models of social interactions with stochastic processes to model the random, nonlinear, and dynamic nature of infections and uses adaptive Bayesian computational techniques to estimate the model parameters. Results using simulated epidemic data show that our model can accurately estimate heritabilities and genetic risks not only of susceptibility but also of infectivity, therefore exploring a trait whose heritable variation is currently ignored in disease genetics and can greatly influence the spread of infectious diseases. Our proposed methodology offers potential impacts in areas such as livestock disease control through selective breeding and also in predicting and controlling the emergence of disease outbreaks in human populations.     

A GWAS assessment of the contribution of genomic imprinting to the variation of body mass index in mice

Background

Genomic imprinting is an epigenetic mechanism that can lead to differential gene expression depending on the parent-of-origin of a received allele. While most studies on imprinting address its underlying molecular mechanisms or attempt at discovering genomic regions that might be subject to imprinting, few have focused on the amount of phenotypic variation contributed by such epigenetic process. In this report, we give a brief review of a one-locus imprinting model in a quantitative genetics framework, and provide a decomposition of the genetic variance according to this model. Analytical deductions from the proposed imprinting model indicated a non-negligible contribution of imprinting to genetic variation of complex traits. Also, we performed a whole-genome scan analysis on mouse body mass index (BMI) aiming at revealing potential consequences when existing imprinting effects are ignored in genetic analysis.

Results

10,021 SNP markers were used to perform a whole-genome single marker regression on mouse BMI using an additive and an imprinting model. Markers significant for imprinting indicated that BMI is subject to imprinting. Marked variance changed from 1.218 ×10⁻⁴ to 1.842 ×10⁻⁴ when imprinting was considered in the analysis, implying that one third of marked variance would be lost if existing imprinting effects were not accounted for. When both marker and pedigree information were used, estimated heritability increased from 0.176 to 0.195 when imprinting was considered.

Conclusions

When a complex trait is subject to imprinting, using an additive model that ignores this phenomenon may result in an underestimate of additive variability, potentially leading to wrong inferences about the underlying genetic architecture of that trait. This could be a possible factor explaining part of the missing heritability commonly observed in genome-wide association studies (GWAS).     

Bayesian adaptive Markov chain Monte Carlo estimation of genetic parameters

Accurate and fast estimation of genetic parameters that underlie quantitative traits using mixed linear models with additive and dominance effects is of great importance in both natural and breeding populations. Here, we propose a new fast adaptive Markov chain Monte Carlo (MCMC) sampling algorithm for the estimation of genetic parameters in the linear mixed model with several random effects. In the learning phase of our algorithm, we use the hybrid Gibbs sampler to learn the covariance structure of the variance components. In the second phase of the algorithm, we use this covariance structure to formulate an effective proposal distribution for a Metropolis-Hastings algorithm, which uses a likelihood function in which the random effects have been integrated out. Compared with the hybrid Gibbs sampler, the new algorithm had better mixing properties and was approximately twice as fast to run. Our new algorithm was able to detect different modes in the posterior distribution. In addition, the posterior mode estimates from the adaptive MCMC method were close to the REML (residual maximum likelihood) estimates. Moreover, our exponential prior for inverse variance components was vague and enabled the estimated mode of the posterior variance to be practically zero, which was in agreement with the support from the likelihood (in the case of no dominance). The method performance is illustrated using simulated data sets with replicates and field data in barley.