The Schmidt rank for the commuting operator framework

In quantum information theory, the Schmidt rank is a fundamental measure for the entanglement dimension of a pure bipartite state. Its natural definition uses the Schmidt decomposition of vectors on bipartite Hilbert spaces, which does not exist (or at least is not canonically given) if the observable algebras of the local systems are allowed to be general C*-algebras. In this work, we generalize the Schmidt rank to the commuting operator framework where the joint system is not necessarily described by the minimal tensor product but by a general bipartite algebra. We give algebraic and operational definitions for the Schmidt rank and show their equivalence. We analyze bipartite states and compute the Schmidt rank in several examples: The vacuum in quantum field theory, Araki-Woods-Powers states, as well as ground states and translation invariant states on spin chains which are viewed as bipartite systems for the left and right half chains. We conclude with a list of open problems for the commuting operator framework.Comment: 44 pages, 3 figure

DNA methylation as a mediator of the association between prenatal adversity and risk factors for metabolic disease in adulthood

Although it is assumed that epigenetic mechanisms, such as changes in DNA methylation (DNAm), underlie the relationship between adverse intrauterine conditions and adult metabolic health, evidence from human studies remains scarce. Therefore, we evaluated whether DNAm in whole blood mediated the association between prenatal famine exposure and metabolic health in 422 individuals exposed to famine in utero and 463 (sibling) controls. We implemented a two-step analysis, namely, a genome-wide exploration across 342,596 cytosine-phosphate-guanine dinucleotides (CpGs) for potential mediators of the association between prenatal famine exposure and adult body mass index (BMI), serum triglycerides (TG), or glucose concentrations, which was followed by formal mediation analysis. DNAm mediated the association of prenatal famine exposure with adult BMI and TG but not with glucose. DNAm at PIM3 (cg09349128), a gene involved in energy metabolism, mediated 13.4% [95% confidence interval (CI), 5 to 28%] of the association between famine exposure and BMI. DNAm at six CpGs, including TXNIP (cg19693031), influencing β cell function, and ABCG1 (cg07397296), affecting lipid metabolism, together mediated 80% (95% CI, 38.5 to 100%) of the association between famine exposure and TG. Analyses restricted to those exposed to famine during early gestation identified additional CpGs mediating the relationship with TG near PFKFB3 (glycolysis) and METTL8 (adipogenesis). DNAm at the CpGs involved was associated with gene expression in an external data set and correlated with DNAm levels in fat depots in additional postmortem data. Our data are consistent with the hypothesis that epigenetic mechanisms mediate the influence of transient adverse environmental factors in early life on long-term metabolic health. The specific mechanism awaits elucidation

DNA methylation as a mediator of the association between prenatal adversity and risk factors for metabolic disease in adulthood

Although it is assumed that epigenetic mechanisms, such as changes in DNA methylation (DNAm), underlie the relationship between adverse intrauterine conditions and adult metabolic health, evidence from human studies remains scarce. Therefore, we evaluated whether DNAm in whole blood mediated the association between prenatal famine exposure and metabolic health in 422 individuals exposed to famine in utero and 463 (sibling) controls. We implemented a two-step analysis, namely, a genome-wide exploration across 342, 596 cytosine-phosphate-guanine dinucleotides (CpGs) for potential mediators of the association between prenatal famine exposure and adult body mass index (BMI), serum triglycerides (TG), or glucose concentrations, which was followed by formalmediation analysis.DNAm mediated the association of prenatal famine exposure with adult BMI and TG but not with glucose. DNAm at PIM3 (cg09349128), a gene involved in energy metabolism, mediated 13.4% [95% confidence interval (CI), 5 to 28%] of the association between famine exposure and BMI. DNAm at six CpGs, including TXNIP (cg19693031), influencing b cell function, and ABCG1 (cg07397296), affecting lipid metabolism, together mediated 80% (95% CI, 38.5 to 100%) of the association between famine exposure and TG. Analyses restricted to those exposed to famine during early gestation identified additional CpGs mediating the relationship with TG near PFKFB3 (glycolysis) and METTL8 (adipogenesis). DNAm at the CpGs involved was associated with gene expression in an external data set and correlated with DNAm levels in fat depots in additional postmortem data. Our data are consistent with the hypothesis that epigenetic mechanisms mediate the influence of transient adverse environmental factors in early life on long-termmetabolic health. The specific mechanism awaits elucidation.</p

Genome-wide identification of genes regulating DNA methylation using genetic anchors for causal inference

BACKGROUND: DNA methylation is a key epigenetic modification in human development and disease, yet there is limited understanding of its highly coordinated regulation. Here, we identify 818 genes that affect DNA methylation patterns in blood using large-scale population genomics data. RESULTS: By employing genetic instruments as causal anchors, we establish directed associations between gene expression and distant DNA methylation levels, while ensuring specificity of the associations by correcting for linkage disequilibrium and pleiotropy among neighboring genes. The identified genes are enriched for transcription factors, of which many consistently increased or decreased DNA methylation levels at multiple CpG sites. In addition, we show that a substantial number of transcription factors affected DNA methylation at their experimentally determined binding sites. We also observe genes encoding proteins with heterogenous functions that have widespread effects on DNA methylation, e.g., NFKBIE, CDCA7(L), and NLRC5, and for several examples, we suggest plausible mechanisms underlying their effect on DNA methylation. CONCLUSION: We report hundreds of genes that affect DNA methylation and provide key insights in the principles underlying epigenetic regulation

Age-related accrual of methylomic variability is linked to fundamental ageing mechanisms

Background: Epigenetic change is a hallmark of ageing but its link to ageing mechanisms in humans remains poorly understood. While DNA methylation at many CpG sites closely tracks chronological age, DNA methylation changes relevant to biological age are expected to gradually dissociate from chronological age, mirroring the increased heterogeneity in health status at older ages. Results: Here, we report on the large-scale identification of 6366 age-related variably methylated positions (aVMPs) identified in 3295 whole blood DNA methylation profiles, 2044 of which have a matching RNA-seq gene expression profile. aVMPs are enriched at polycomb repressed regions and, accordingly, methylation at those positions is associated with the expression of genes encoding components of polycomb repressive complex 2 (PRC2) in trans. Further analysis revealed trans-associations for 1816 aVMPs with an additional 854 genes. These trans-associated aVMPs are characterized by either an age-related

Genomic and phenotypic insights from an atlas of genetic effects on DNA methylation

Characterizing genetic influences on DNA methylation (DNAm) provides an opportunity to understand mechanisms underpinning gene regulation and disease. In the present study, we describe results of DNAm quantitative trait locus (mQTL) analyses on 32,851 participants, identifying genetic variants associated with DNAm at 420,509 DNAm sites in blood. We present a database of >270,000 independent mQTLs, of which 8.5% comprise long-range (trans) associations. Identified mQTL associations explain 15–17% of the additive genetic variance of DNAm. We show that the genetic architecture of DNAm levels is highly polygenic. Using shared genetic control between distal DNAm sites, we constructed networks, identifying 405 discrete genomic communities enriched for genomic annotations and complex traits. Shared genetic variants are associated with both DNAm levels and complex diseases, but only in a minority of cases do these associations reflect causal relationships from DNAm to trait or vice versa, indicating a more complex genotype–phenotype map than previously anticipated

Genomic and phenotypic insights from an atlas of genetic effects on DNA methylation.

Characterizing genetic influences on DNA methylation (DNAm) provides an opportunity to understand mechanisms underpinning gene regulation and disease. In the present study, we describe results of DNAm quantitative trait locus (mQTL) analyses on 32,851 participants, identifying genetic variants associated with DNAm at 420,509 DNAm sites in blood. We present a database of >270,000 independent mQTLs, of which 8.5% comprise long-range (trans) associations. Identified mQTL associations explain 15–17% of the additive genetic variance of DNAm. We show that the genetic architecture of DNAm levels is highly polygenic. Using shared genetic control between distal DNAm sites, we constructed networks, identifying 405 discrete genomic communities enriched for genomic annotations and complex traits. Shared genetic variants are associated with both DNAm levels and complex diseases, but only in a minority of cases do these associations reflect causal relationships from DNAm to trait or vice versa, indicating a more complex genotype–phenotype map than previously anticipated.C.L.R., G.D.S., G.S., J.L.M., K.B., M. Suderman, T.G.R. and T.R.G. are supported by the UK Medical Research Council (MRC) Integrative Epidemiology Unit at the University of Bristol (MC_UU_00011/1, MC_UU_00011/4, MC_UU_00011/5). C.L.R. receives support from a Cancer Research UK Programme grant (no. C18281/A191169). G.H. is funded by the Wellcome Trust and the Royal Society (208806/Z/17/Z). E.H. and J.M. were supported by MRC project grants (nos. MR/K013807/1 and MR/R005176/1 to J.M.) and an MRC Clinical Infrastructure award (no. MR/M008924/1 to J.M.). B.T.H. is supported by the Netherlands CardioVascular Research Initiative (the Dutch Heart Foundation, Dutch Federation of University Medical Centres, the Netherlands Organisation for Health Research and Development, and the Royal Netherlands Academy of Sciences) for the GENIUS project ‘Generating the best evidence-based pharmaceutical targets for atherosclerosis’ (CVON2011-19, CVON2017-20). J.T.B. was supported by the Economic and Social Research Council (grant no. ES/N000404/1). The present study was also supported by JPI HDHL-funded DIMENSION project (administered by the BBSRC UK, grant no. BB/S020845/1 to J.T.B., and by ZonMW the Netherlands, grant no. 529051021 to B.T.H). A.D.B. has been supported by a Wellcome Trust PhD Training Fellowship for Clinicians and the Edinburgh Clinical Academic Track programme (204979/Z/16/Z). J. Klughammer was supported by a DOC fellowship of the Austrian Academy of Sciences. Cohort-specific acknowledgements and funding are presented in the Supplementary Note

Controlling bias and inflation in epigenome- and transcriptome-wide association studies using the empirical null distribution

We show that epigenome- and transcriptome-wide association studies (EWAS and TWAS) are prone to significant inflation and bias of test statistics, an unrecognized phenomenon introducing spurious findings if left unaddressed. Neither GWAS-based methodology nor state-of-the-art confounder adjustment methods completely remove bias and inflation. We propose a Bayesian method to control bias and inflation in EWAS and TWAS based on estimation of the empirical null distribution. Using simulations and real data, we demonstrate that our method maximizes power while properly controlling the false positive rate. We illustrate the utility of our method in large-scale EWAS and TWAS meta-analyses of age and smoking

Refining Attention-Deficit/Hyperactivity Disorder and Autism Spectrum Disorder Genetic Loci by Integrating Summary Data From Genome-wide Association, Gene Expression, and DNA Methylation Studies

Background: Recent genome-wide association studies (GWASs) identified the first genetic loci associated with attention-deficit/hyperactivity disorder (ADHD) and autism spectrum disorder (ASD). The next step is to use these results to increase our understanding of the biological mechanisms involved. Most of the identified variants likely influence gene regulation. The aim of the current study is to shed light on the mechanisms underlying the genetic signals and prioritize genes by integrating GWAS results with gene expression and DNA methylation (DNAm) levels. Methods: We applied summary-data–based Mendelian randomization to integrate ADHD and ASD GWAS data with fetal brain expression and methylation quantitative trait loci, given the early onset of these disorders. We also analyzed expression and methylation quantitative trait loci datasets of adult brain and blood, as these provide increased statistical power. We subsequently used summary-data–based Mendelian randomization to investigate if the same variant influences both DNAm and gene expression levels. Results: We identified multiple gene expression and DNAm levels in fetal brain at chromosomes 1 and 17 that were associated with ADHD and ASD, respectively, through pleiotropy at shared genetic variants. The analyses in brain and blood showed additional associated gene expression and DNAm levels at the same and additional loci, likely because of increased statistical power. Several of the associated genes have not been identified in ADHD and ASD GWASs before. Conclusions: Our findings identified the genetic variants associated with ADHD and ASD that likely act through gene regulation. This facilitates prioritization of candidate genes for functional follow-up studies