Pure infiniteness, stability and C*-algebras of graphs and dynamical systems

Pure infiniteness (in sense of E.Kirchberg and M.R{\o}rdam) is considered for C*-algebras arising from singly generated dynamical systems. In particular, Cuntz-Krieger algebras and their generalizations, i.e., graph-algebras and O_A of an infinite matrix A, admit characterizations of pure infiniteness. As a consequence, these generalized Cuntz-Krieger algebras are traceless if and only if they are purely infinite. Also, a characterization of AF-algebras among these C*-algebras is given. In the case of graph-algebras of locally finite graphs, characterizations of stability are obtained.Comment: 31 page

The Liability Threshold Model for Censored Twin Data

Family studies provide an important tool for understanding etiology of diseases, with the key aim of discovering evidence of family aggregation and to determine if such aggregation can be attributed to genetic components. Heritability and concordance estimates are routinely calculated in twin studies of diseases, as a way of quantifying such genetic contribution. The endpoint in these studies are typically defined as occurrence of a disease versus death without the disease. However, a large fraction of the subjects may still be alive at the time of follow-up without having experienced the disease thus still being at risk. Ignoring this right-censoring can lead to severely biased estimates. We propose to extend the classical liability threshold model with inverse probability of censoring weighting of complete observations. This leads to a flexible way of modeling twin concordance and obtaining consistent estimates of heritability. We apply the method in simulations and to data from the population based Danish twin cohort where we describe the dependence in prostate cancer occurrence in twins

The heritability of BMI varies across the range of BMI-a heritability curve analysis in a twin cohort

Background The heritability of traits such as body mass index (BMI), a measure of obesity, is generally estimated using family and twin studies, and increasingly by molecular genetic approaches. These studies generally assume that genetic effects are uniform across all trait values, yet there is emerging evidence that this may not always be the case. Method/Subjects This paper analyzes twin data using a recently developed measure of heritability called the heritability curve. Under the assumption that trait values in twin pairs are governed by a flexible Gaussian mixture distribution, heritability curves may vary across trait values. The data consist of repeated measures of BMI on 1506 monozygotic (MZ) and 2843 like-sexed dizygotic (DZ) adult twin pairs, gathered from multiple surveys in older Finnish Twin Cohorts. Results The heritability curve and BMI value-specific MZ and DZ pairwise correlations were estimated, and these varied across the range of BMI. MZ correlations were highest at BMI values from 21 to 24, with a stronger decrease for women than for men at higher values. Models with additive and dominance effects fit best at low and high BMI values, while models with additive genetic and common environmental effects fit best in the normal range of BMI. Conclusions We demonstrate that twin and molecular genetic studies need to consider how genetic effects vary across trait values. Such variation may reconcile findings of traits with high heritability and major differences in mean values between countries or over time.Peer reviewe

Theory and Practice in Quantitative Genetics

With the rapid advances in molecular biology, the near completion of the human genome, the development of appropriate statistical genetic methods and the availability of the necessary computing power, the identification of quantitative trait loci has now become a realistic prospect for quantitative geneticists. We briefly describe the theoretical biometrical foundations underlying quantitative genetics. These theoretical underpinnings are translated into mathematical equations that allow the assessment of the contribution of observed (using DNA samples) and unobserved (using known genetic relationships) genetic variation to population variance in quantitative traits. Several statistical models for quantitative genetic analyses are described, such as models for the classical twin design, multivariate and longitudinal genetic analyses, extended twin analyses, and linkage and association analyses. For each, we show how the theoretical biometrical model can be translated into algebraic equations that may be used to generate scripts for statistical genetic software packages, such as Mx, Lisrel, SOLAR, or MERLIN. For using the former program a web-library (available from http://www.psy.vu.nl/mxbib) has been developed of freely available scripts that can be used to conduct all genetic analyses described in this paper

A Growth Curve Model with Fractional Polynomials for Analysing Incomplete Time-Course Data in Microarray Gene Expression Studies

Identifying the various gene expression response patterns is a challenging issue in expression microarray time-course experiments. Due to heterogeneity in the regulatory reaction among thousands of genes tested, it is impossible to manually characterize a parametric form for each of the time-course pattern in a gene by gene manner. We introduce a growth curve model with fractional polynomials to automatically capture the various time-dependent expression patterns and meanwhile efficiently handle missing values due to incomplete observations. For each gene, our procedure compares the performances among fractional polynomial models with power terms from a set of fixed values that offer a wide range of curve shapes and suggests a best fitting model. After a limited simulation study, the model has been applied to our human in vivo irritated epidermis data with missing observations to investigate time-dependent transcriptional responses to a chemical irritant. Our method was able to identify the various nonlinear time-course expression trajectories. The integration of growth curves with fractional polynomials provides a flexible way to model different time-course patterns together with model selection and significant gene identification strategies that can be applied in microarray-based time-course gene expression experiments with missing observations

Global Gene Expression Profiling of Body-Mass Index in Middle-Aged Danish Twins

Objective: The body mass index (BMI) measured as weight in relation to height is an important monitor for obesity and diabetes, with individual variation under control by genetic and environmental factors. In transcriptome-wide association studies on BMI, the genetic contribution calls for controlling of genetic confounding that affects both BMI and gene expression. We performed a global gene expression profiling of BMI on peripheral blood cells using monozygotic twins for efficient handling of genetic make-ups. Methods: We applied a generalized association method to genome-wide gene expression data on 229 pairs of monozygotic twins (age 56-80 years) for detecting diverse patterns of correlation between BMI and gene expression. Results: We detected seven probes associated with BMI with p<1e-04, among them two probes with p<1e-05 (p=2.83e-06 AAK1; p=7.83e-06 LILRA3). In total, the analysis found 1579 probes with nominal p<0.05. Biological pathway analysis of enriched pathways found 50 KEGG and 45 Reactome pathways (FDR<0.05). The identified top functional pathways included immune function, JAK-STAT signalling, insulin signalling and regulation of energy metabolism. Conclusion: This transcriptome-wide association study using monozygotic twins and generalized correlation identified differentially expressed genes and a broad spectrum of enriched biological pathways that may implicate metabolic health

Novel DNA methylation marker discovery by assumption-free genome-wide association analysis of cognitive function in twins

Privileged by rapid increase in available epigenomic data, epigenome-wide association studies (EWAS) are to make a profound contribution to understand the molecular mechanism of DNA methylation in cognitive aging. Current statistical methods used in EWAS are dominated by models based on multiple assumptions, for example, linear relationship between molecular profiles and phenotype, normal distribution for the methylation data and phenotype. In this study, we applied an assumption-free method, the generalized correlation coefficient (GCC), and compare it to linear models, namely the linear mixed model and kinship model. We use DNA methylation associated with a cognitive score in 400 and 206 twins as discovery and replication samples respectively. DNA methylation associated with cognitive function using GCC, linear mixed model, and kinship model, identified 65 CpGs (p < 1e-04) from discovery sample displaying both nonlinear and linear correlations. Replication analysis successfully replicated 9 of these top CpGs. When combining results of GCC and linear models to cover diverse patterns of relationships, we identified genes like KLHDC4, PAPSS2, and MRPS18B as well as pathways including focal adhesion, axon guidance, and some neurological signaling. Genomic region-based analysis found 15 methylated regions harboring 11 genes, with three verified in gene expression analysis, also the 11 genes were related to top functional clusters including neurohypophyseal hormone and maternal aggressive behaviors. The GCC approach detects valuable methylation sites missed by traditional linear models. A combination of methylation markers from GCC and linear models enriched biological pathways sensible in neurological function that could implicate cognitive performance and cognitive aging.Peer reviewe

Perceived age as clinically useful biomarker of ageing: cohort study

Objective To determine whether perceived age correlates with survival and important age related phenotypes

Genetic and environmental determinants of O6-methylguanine DNA-methyltransferase (MGMT) gene methylation: a 10-year longitudinal study of Danish twins

Background: Epigenetic inactivation of O6-methylguanine DNA-methyltransferase (MGMT) is associated with increased sensitivity to alkylating chemotherapeutic agents in glioblastoma patients. The genetic background underlying MGMT gene methylation may explain individual differences in treatment response and provide a clue to a personalized treatment strategy. Making use of the longitudinal twin design, we aimed, for the first time, to estimate the genetic contributions to MGMT methylation in a Danish twin cohort. Methods: DNA-methylation from whole blood (18 monozygotic (MZ) and 25 dizygotic (DZ) twin pairs) repeated 10 years apart from the Longitudinal Study of Aging Danish Twins (LSADT) were used to search for genetic and environmental contributions to DNA-methylation at 170 CpG sites of across the MGMT gene. Both univariate and bivariate twin models were applied. The intraclass correlations, performed on cross-sectional data (246 MZ twin pairs) from an independent study population, the Middle-Aged Danish Twins (MADT), were used to assess the genetic influence at each CpG site of MGMT for replication. Results: Univariate twin model revealed twelve CpG sites showing significantly high heritability at intake (wave 1, h2 > 0.43), and seven CpG sites with significant heritability estimates at end of follow-up (wave 2, h2 > 0.5). There were six significant CpG sites, located at the gene body region, that overlapped among the two waves (h2 > 0.5), of which five remained significant in the bivariate twin model, which was applied to both waves. Within MZ pair correlation in these six CpGs from MADT demarks top level of genetic influence. There were 11 CpGs constantly have substantial common environmental component over the 10 years. Conclusions: We have identified 6 CpG sites linked to the MGMT gene with strong and persistent genetic control based on their DNA methylation levels. The genetic basis of MGMT gene methylation could help to explain individual differences in glioblastoma treatment response and most importantly, provide references for mapping the methylation Quantitative Trait Loci (meQTL) underlying the genetic regulation.Peer reviewe