Heritability, defined as the proportion of phenotypic variation attributable to genetic variation, provides important information about the genetic basis of a trait. Existing heritability analysis methods do not discriminate between stable effects (e.g., due to the subject’s unique environment) and transient effects, such as measurement error. This can lead to misleading assessments, particularly when comparing the heritability of traits that exhibit different levels of reliability. Here, we present a linear mixed effects model to conduct heritability analyses that explicitly accounts for intrasubject fluctuations (e.g., due to measurement noise or biological transients) using repeat measurements. We apply the proposed strategy to the analysis of resting-state fMRI measurements—a prototypic data modality that exhibits variable levels of test–retest reliability across space. Our results reveal that the stable components of functional connectivity within and across well-established large-scale brain networks can be considerably heritable. Furthermore, we demonstrate that dissociating intra- and intersubject variation can reveal genetic influence on a phenotype that is not fully captured by conventional heritability analyses.
Heritability estimation provides important information about the relative contribution of genetic and environmental factors to phenotypic variation, and provides an upper bound for the utility of genetic risk prediction models. Recent technological and statistical advances have enabled the estimation of additive heritability attributable to common genetic variants (SNP heritability) across a broad phenotypic spectrum. Here, we present a computationally and memory efficient heritability estimation method that can handle large sample sizes, and report the SNP heritability for 551 complex traits derived from the interim data release (152,736 subjects) of the large-scale, population-based UK Biobank, comprising both quantitative phenotypes and disease codes. We demonstrate that common genetic variation contributes to a broad array of quantitative traits and human diseases in the UK population, and identify phenotypes whose heritability is moderated by age (e.g., a majority of physical measures including height and body mass index), sex (e.g., blood pressure related traits) and socioeconomic status (education). Our study represents the first comprehensive phenome-wide heritability analysis in the UK Biobank, and underscores the importance of considering population characteristics in interpreting heritability.
In the dawning era of large-scale biomedical data, multidimensional phenotype vectors will play an increasing role in examining the genetic underpinnings of brain features, behaviour and disease. For example, shape measurements derived from brain MRI scans are multidimensional geometric descriptions of brain structure and provide an alternate class of phenotypes that remains largely unexplored in genetic studies. Here we extend the concept of heritability to multidimensional traits, and present the first comprehensive analysis of the heritability of neuroanatomical shape measurements across an ensemble of brain structures based on genome-wide SNP and MRI data from 1,320 unrelated, young and healthy individuals. We replicate our findings in an extended twin sample from the Human Connectome Project (HCP). Our results demonstrate that neuroanatomical shape can be significantly heritable, above and beyond volume, and can serve as a complementary phenotype to study the genetic determinants and clinical relevance of brain structure.
Complex physiological and behavioral traits, including neurological and psychiatric disorders, often associate with distributed anatomical variation. This paper introduces a global metric, called morphometricity, as a measure of the anatomical signature of different traits. Morphometricity is defined as the proportion of phenotypic variation that can be explained by macroscopic brain morphology. We estimate morphometricity via a linear mixed-effects model that uses an anatomical similarity matrix computed based on measurements derived from structural brain MRI scans. We examined over 3,800 unique MRI scans from nine large-scale studies to estimate the morphometricity of a range of phenotypes, including clinical diagnoses such as Alzheimer’s disease, and non-clinical traits such as measures of cognition. Our results demonstrate that morphometricity can provide novel insights about the neuroanatomical correlates of a diverse set of traits, revealing associations that might not be detectable through traditional statistical techniques.
The human brain is patterned with disproportionately large, distributed cerebral networks that connect multiple association zones in the frontal, temporal, and parietal lobes. The expansion of the cortical surface, along with the emergence of long-range connectivity networks, may be reflected in changes to the underlying molecular architecture. Using the Allen Institute’s human brain transcriptional atlas, we demonstrate that genes particularly enriched in supragranular layers of the human cerebral cortex relative to mouse distinguish major cortical classes. The topography of transcriptional expression reflects large-scale brain network organization consistent with estimates from functional connectivity MRI and anatomical tracing in nonhuman primates. Microarray expression data for genes preferentially expressed in human upper layers (II/III), but enriched only in lower layers (V/VI) of mouse, were cross-correlated to identify molecular profiles across the cerebral cortex of postmortem human brains (n = 6). Unimodal sensory and motor zones have similar molecular profiles, despite being distributed across the cortical mantle. Sensory/motor profiles were anticorrelated with paralimbic and certain distributed association network profiles. Tests of alternative gene sets did not consistently distinguish sensory and motor regions from paralimbic and association regions: (i) genes enriched in supragranular layers in both humans and mice, (ii) genes cortically enriched in humans relative to nonhuman primates, (iii) genes related to connectivity in rodents, (iv) genes associated with human and mouse connectivity, and (v) 1,454 gene sets curated from known gene ontologies. Molecular innovations of upper cortical layers may be an important component in the evolution of long-range corticocortical projections.
The discovery and prioritization of heritable phenotypes is a computational challenge in a variety of settings, including neuroimaging genetics and analyses of the vast phenotypic repositories in electronic health record systems and population-based biobanks. Classical estimates of heritability require twin or pedigree data, which can be costly and difficult to acquire. Genome-wide complex trait analysis is an alternative tool to compute heritability estimates from unrelated individuals, using genome-wide data that are increasingly ubiquitous, but is computationally demanding and becomes difficult to apply in evaluating very large numbers of phenotypes. Here we present a fast and accurate statistical method for high-dimensional heritability analysis using genome-wide SNP data from unrelated individuals, termed massively expedited genome-wide heritability analysis (MEGHA) and accompanying nonparametric sampling techniques that enable flexible inferences for arbitrary statistics of interest. MEGHA produces estimates and significance measures of heritability with several orders of magnitude less computational time than existing methods, making heritability-based prioritization of millions of phenotypes based on data from unrelated individuals tractable for the first time to our knowledge. As a demonstration of application, we conducted heritability analyses on global and local morphometric measurements derived from brain structural MRI scans, using genome-wide SNP data from 1,320 unrelated young healthy adults of non-Hispanic European ancestry. We also computed surface maps of heritability for cortical thickness measures and empirically localized cortical regions where thickness measures were significantly heritable. Our analyses demonstrate the unique capability of MEGHA for large-scale heritability-based screening and high-dimensional heritability profile construction.
Measurements derived from neuroimaging data can serve as markers of disease and/or healthy development, are largely heritable, and have been increasingly utilized as (intermediate) phenotypes in genetic association studies. To date, imaging genetic studies have mostly focused on discovering isolated genetic effects, typically ignoring potential interactions with non-genetic variables such as disease risk factors, environmental exposures, and epigenetic markers. However, identifying significant interaction effects is critical for revealing the true relationship between genetic and phenotypic variables, and shedding light on disease mechanisms. In this paper, we present a general kernel machine based method for detecting effects of the interaction between multidimensional variable sets. This method can model the joint and epistatic effect of a collection of single nucleotide polymorphisms (SNPs), accommodate multiple factors that potentially moderate genetic influences, and test for nonlinear interactions between sets of variables in a flexible framework. As a demonstration of application, we applied the method to the data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) to detect the effects of the interactions between candidate Alzheimer's disease (AD) risk genes and a collection of cardiovascular disease (CVD) risk factors, on hippocampal volume measurements derived from structural brain magnetic resonance imaging (MRI) scans. Our method identified that two genes, CR1 and EPHA1, demonstrate significant interactions with CVD risk factors on hippocampal volume, suggesting that CR1 and EPHA1 may play a role in influencing AD-related neurodegeneration in the presence of CVD risks.
Magnetic resonance imaging (MRI) plays a vital role in the scientific investigation and clinical management of multiple sclerosis. Analyses of binary multiple sclerosis lesion maps are typically "mass univariate" and conducted with standard linear models that are ill suited to the binary nature of the data and ignore the spatial dependence between nearby voxels (volume elements). Smoothing the lesion maps does not entirely eliminate the non-Gaussian nature of the data and requires an arbitrary choice of the smoothing parameter. Here we present a Bayesian spatial model to accurately model binary lesion maps and to determine if there is spatial dependence between lesion location and subject specific covariates such as MS subtype, age, gender, disease duration and disease severity measures. We apply our model to binary lesion maps derived from T2-weighted MRI images from 250 multiple sclerosis patients classified into five clinical subtypes, and demonstrate unique modeling and predictive capabilities over existing methods.
In this paper, we develop an approach to achieve either frequency or amplitude modulation of an oscillator merely through feedback control. We present and implement a unified theory of our approach for any finite-dimensional continuous dynamical system that exhibits oscillatory behavior. The approach is illustrated not only for the normal forms of dynamical systems but also for representative biological models, such as the isolated and coupled FitzHugh-Nagumo model. We demonstrate the potential usefulness of our approach to uncover the mechanisms of frequency and amplitude modulations experimentally observed in a wide range of real systems.
Connectome genetics attempts to discover how genetic factors affect brain connectivity. Here we review a variety of genetic analysis methods — such as genome-wide association studies (GWAS), linkage and candidate gene studies — that have been fruitfully adapted to imaging data to implicate specific variants in the genome for brain-related traits. Studies that emphasized the genetic influences on brain connectivity. Some of these analyses of brain integrity and connectivity using diffusion MRI, and others have mapped genetic effects on functional networks using resting state functional MRI. Connectome-wide genome-wide scans have also been conducted, and we review the multivariate methods required to handle the extremely high dimension of the genomic and network data. We also review some consortium efforts, such as ENIGMA, that offer the power to detect robust common genetic associations using phenotypic harmonization procedures and meta-analysis. Current work on connectome genetics is advancing on many fronts and promises to shed light on how disease risk genes affect the brain. It is already discovering new genetic loci and even entire genetic networks that affect brain organization and connectivity.
We show, for the first time, that in cortical areas, for example the insular, orbitofrontal, and lateral prefrontal cortex, there is signal-dependent noise in the fMRI blood-oxygen level dependent (BOLD) time series, with the variance of the noise increasing approximately linearly with the square of the signal. Classical Granger causal models are based on autoregressive models with time invariant covariance structure, and thus do not take this signal-dependent noise into account. To address this limitation, here we describe a Granger causal model with signal-dependent noise, and a novel, likelihood ratio test for causal inferences. We apply this approach to the data from an fMRI study to investigate the source of the top-down attentional control of taste intensity and taste pleasantness processing. The Granger causality with signal-dependent noise analysis reveals effects not identified by classical Granger causal analysis. In particular, there is a top-down effect from the posterior lateral prefrontal cortex to the insular taste cortex during attention to intensity but not to pleasantness, and there is a top-down effect from the anterior and posterior lateral prefrontal cortex to the orbitofrontal cortex during attention to pleasantness but not to intensity. In addition, there is stronger forward effective connectivity from the insular taste cortex to the orbitofrontal cortex during attention to pleasantness than during attention to intensity. These findings indicate the importance of explicitly modeling signal-dependent noise in functional neuroimaging, and reveal some of the processes involved in a biased activation theory of selective attention.
Imaging traits are thought to have more direct links to genetic variation than diagnostic measures based on cognitive or clinical assessments and provide a powerful substrate to examine the influence of genetics on human brains. Although imaging genetics has attracted growing attention and interest, most brain-wide genome-wide association studies focus on voxel-wise single-locus approaches, without taking advantage of the spatial information in images or combining the effect of multiple genetic variants. In this paper we present a fast implementation of voxel- and cluster-wise inferences based on the random field theory to fully use the spatial information in images. The approach is combined with a multi-locus model based on least square kernel machines to associate the joint effect of several single nucleotide polymorphisms (SNP) with imaging traits. A fast permutation procedure is also proposed which significantly reduces the number of permutations needed relative to the standard empirical method and provides accurate small p-value estimates based on parametric tail approximation. We explored the relation between 448,294 single nucleotide polymorphisms and 18,043 genes in 31,662 voxels of the entire brain across 740 elderly subjects from the Alzheimer's Disease Neuroimaging Initiative (ADNI). Structural MRI scans were analyzed using tensor-based morphometry (TBM) to compute 3D maps of regional brain volume differences compared to an average template image based on healthy elderly subjects. We find method to be more sensitive compared with voxel-wise single-locus approaches. A number of genes were identified as having significant associations with volumetric changes. The most associated gene was GRIN2B, which encodes the N-methyl-D-aspartate (NMDA) glutamate receptor NR2B subunit and affects both the parietal and temporal lobes in human brains. Its role in Alzheimer's disease has been widely acknowledged and studied, suggesting the validity of the approach. The various advantages over existing approaches indicate a great potential offered by this novel framework to detect genetic influences on human brains.
This technical note establishes several versions of invariance principles for describing the eventual dynamical behaviors of discrete dynamical systems. Instead of the requirement of the so-called Lyapunov functions in the classical LaSalle invariance principle, some more relaxed conditions are imported. The established invariance principles thus can be applied to a more general class of discrete dynamical systems for classifying their orbits into two categories based on the eventual dynamical behaviors, and the proposed classification scheme is suitable for theoretically and numerically estimating the local or global attractors produced by the discrete dynamical systems. The practical usefulness of the analytical results is verified by systematically investigating several representative discrete systems.