Appearance of vertices of infinite order in a model of random trees

We study an equilibrium statistical mechanical model of tree graphs which are made up of a linear subgraph (the spine) to which leaves are attached. We prove that the model has two phases, a generic phase where the spine becomes infinitely long in the thermodynamic limit and all vertices have finite order and a condensed phase where the spine is finite with probability one and a single vertex of infinite order appears in the thermodynamic limit. We calculate the spectral dimension of the graphs in both phases and prove the existence of a Gibbs measure. We discuss generalizations of this model and the relationship with models of nongeneric random trees.Comment: 22 pages, 5 figure

De novo CNV analysis implicates specific abnormalities of postsynaptic signalling complexes in the pathogenesis of schizophrenia

A small number of rare, recurrent genomic copy number variants (CNVs) are known to substantially increase susceptibility to schizophrenia. As a consequence of the low fecundity in people with schizophrenia and other neurodevelopmental phenotypes to which these CNVs contribute, CNVs with large effects on risk are likely to be rapidly removed from the population by natural selection. Accordingly, such CNVs must frequently occur as recurrent de novo mutations. In a sample of 662 schizophrenia proband–parent trios, we found that rare de novo CNV mutations were significantly more frequent in cases (5.1% all cases, 5.5% family history negative) compared with 2.2% among 2623 controls, confirming the involvement of de novo CNVs in the pathogenesis of schizophrenia. Eight de novo CNVs occurred at four known schizophrenia loci (3q29, 15q11.2, 15q13.3 and 16p11.2). De novo CNVs of known pathogenic significance in other genomic disorders were also observed, including deletion at the TAR (thrombocytopenia absent radius) region on 1q21.1 and duplication at the WBS (Williams–Beuren syndrome) region at 7q11.23. Multiple de novos spanned genes encoding members of the DLG (discs large) family of membrane-associated guanylate kinases (MAGUKs) that are components of the postsynaptic density (PSD). Two de novos also affected EHMT1, a histone methyl transferase known to directly regulate DLG family members. Using a systems biology approach and merging novel CNV and proteomics data sets, systematic analysis of synaptic protein complexes showed that, compared with control CNVs, case de novos were significantly enriched for the PSD proteome (P=1.72 × 10−6). This was largely explained by enrichment for members of the N-methyl-D-aspartate receptor (NMDAR) (P=4.24 × 10−6) and neuronal activity-regulated cytoskeleton-associated protein (ARC) (P=3.78 × 10−8) postsynaptic signalling complexes. In an analysis of 18 492 subjects (7907 cases and 10 585 controls), case CNVs were enriched for members of the NMDAR complex (P=0.0015) but not ARC (P=0.14). Our data indicate that defects in NMDAR postsynaptic signalling and, possibly, ARC complexes, which are known to be important in synaptic plasticity and cognition, play a significant role in the pathogenesis of schizophrenia

Genome-wide study of association and interaction with maternal cytomegalovirus infection suggests new schizophrenia loci.

Genetic and environmental components as well as their interaction contribute to the risk of schizophrenia, making it highly relevant to include environmental factors in genetic studies of schizophrenia. This study comprises genome-wide association (GWA) and follow-up analyses of all individuals born in Denmark since 1981 and diagnosed with schizophrenia as well as controls from the same birth cohort. Furthermore, we present the first genome-wide interaction survey of single nucleotide polymorphisms (SNPs) and maternal cytomegalovirus (CMV) infection. The GWA analysis included 888 cases and 882 controls, and the follow-up investigation of the top GWA results was performed in independent Danish (1396 cases and 1803 controls) and German-Dutch (1169 cases, 3714 controls) samples. The SNPs most strongly associated in the single-marker analysis of the combined Danish samples were rs4757144 in ARNTL (P=3.78 × 10(-6)) and rs8057927 in CDH13 (P=1.39 × 10(-5)). Both genes have previously been linked to schizophrenia or other psychiatric disorders. The strongest associated SNP in the combined analysis, including Danish and German-Dutch samples, was rs12922317 in RUNDC2A (P=9.04 × 10(-7)). A region-based analysis summarizing independent signals in segments of 100 kb identified a new region-based genome-wide significant locus overlapping the gene ZEB1 (P=7.0 × 10(-7)). This signal was replicated in the follow-up analysis (P=2.3 × 10(-2)). Significant interaction with maternal CMV infection was found for rs7902091 (P(SNP × CMV)=7.3 × 10(-7)) in CTNNA3, a gene not previously implicated in schizophrenia, stressing the importance of including environmental factors in genetic studies

Low BMI-1 expression is associated with an activated BMI-1-driven signature, vascular invasion, and hormone receptor loss in endometrial carcinoma

We studied the expression of polycomb group (PcG) protein BMI-1 in a large population-based patient series of endometrial carcinomas in relation to clinical and molecular phenotype. Also, 57 fresh frozen endometrial carcinomas were studied for the relationship between BMI-1 protein expression, BMI-1 mRNA level, and activation of an 11-gene signature reported to represent a BMI-1-driven pathway. BMI-1 protein expression was significantly weaker in tumours with vascular invasion (P<0.0001), deep myometrial infiltration (P=0.004), and loss of oestrogen receptor (ER) (P<0.0001) and progesterone receptors (PR) (P=0.03). Low BMI-1 protein expression was highly associated with low BMI-1 mRNA expression (P=0.002), and similarly low BMI-1 mRNA expression correlated significantly with vascular invasion, ER and PR loss, and histologic grade 3. In contrast, activation of the reported 11-gene signature, supposed to represent a BMI-1-driven pathway, correlated with low mRNA expression of BMI-1 (P<0.001), hormone receptor loss, presence of vascular invasion, and poor prognosis. We conclude that BMI-1 protein and mRNA expression are significantly correlated and that BMI-1 expression is inversely associated with activation of the 11-gene signature. Loss of BMI-1 seems to be associated with an aggressive phenotype in endometrial carcinomas

Genetic variability in the absorption of dietary sterols affects the risk of coronary artery disease

AIMS: To explore whether variability in dietary cholesterol and phytosterol absorption impacts the risk of coronary artery disease (CAD) using as instruments sequence variants in the ABCG5/8 genes, key regulators of intestinal absorption of dietary sterols. METHODS AND RESULTS: We examined the effects of ABCG5/8 variants on non-high-density lipoprotein (non-HDL) cholesterol (N up to 610 532) and phytosterol levels (N = 3039) and the risk of CAD in Iceland, Denmark, and the UK Biobank (105 490 cases and 844 025 controls). We used genetic scores for non-HDL cholesterol to determine whether ABCG5/8 variants confer greater risk of CAD than predicted by their effect on non-HDL cholesterol. We identified nine rare ABCG5/8 coding variants with substantial impact on non-HDL cholesterol. Carriers have elevated phytosterol levels and are at increased risk of CAD. Consistent with impact on ABCG5/8 transporter function in hepatocytes, eight rare ABCG5/8 variants associate with gallstones. A genetic score of ABCG5/8 variants predicting 1 mmol/L increase in non-HDL cholesterol associates with two-fold increase in CAD risk [odds ratio (OR) = 2.01, 95% confidence interval (CI) 1.75-2.31, P = 9.8 × 10-23] compared with a 54% increase in CAD risk (OR = 1.54, 95% CI 1.49-1.59, P = 1.1 × 10-154) associated with a score of other non-HDL cholesterol variants predicting the same increase in non-HDL cholesterol (P for difference in effects = 2.4 × 10-4). CONCLUSIONS: Genetic variation in cholesterol absorption affects levels of circulating non-HDL cholesterol and risk of CAD. Our results indicate that both dietary cholesterol and phytosterols contribute directly to atherogenesis

Roadmap for a precision-medicine initiative in the Nordic region

The Nordic region, comprising primarily Denmark, Estonia, Finland, Iceland, Norway and Sweden, has many of the necessary characteristics for being at the forefront of genome-based precision medicine. These include egalitarian and universal healthcare, expertly curated patient and population registries, biobanks, large population-based prospective cohorts linked to registries and biobanks, and a widely embraced sense of social responsibility that motivates public engagement in biomedical research. However, genome-based precision medicine can be achieved only through coordinated action involving all actors in the healthcare sector. Now is an opportune time to organize scientists in the Nordic region, together with other stakeholders including patient representatives, governments, pharmaceutical companies, academic institutions and funding agencies, to initiate a Nordic Precision Medicine Initiative. We present a roadmap for how this organization can be created. The Initiative should facilitate research, clinical trials and knowledge transfer to meet regional and global health challenges.Non peer reviewe

Henoch-Schönlein nephritis associated with streptococcal infection and persistent hypocomplementemia: a case report

<p>Abstract</p> <p>Introduction</p> <p>Henoch-Schönlein purpura is a systemic disease with frequent renal involvement, characterized by IgA mesangial deposits. Streptococcal infection can induce an abnormal IgA immune response like Henoch-Schönlein purpura, quite similar to typical acute post-infectious glomerulonephritis. Indeed, hypocomplementemia that is typical of acute glomerulonephritis has also been described in Henoch-Schönlein purpura.</p> <p>Case presentation</p> <p>We describe a 14-year-old Caucasian Spanish girl who developed urinary abnormalities and cutaneous purpura after streptococcal infection. Renal biopsy showed typical findings from Henoch-Schönlein purpura nephritis. In addition, she had low serum levels of complement (C4 fraction) that persisted during follow-up, in spite of her clinical evolution. She responded to treatment with enalapril and steroids.</p> <p>Conclusion</p> <p>The case described has, at least, three points of interest in Henoch-Schönlein purpura: 1) Initial presentation was preceded by streptococcal infection; 2) There was a persistence of low serum levels of complement; and 3) There was response to steroids and angiotensin-converting enzyme inhibitor in the presence of nephrotic syndrome. There are not many cases described in the literature with these characteristics. We conclude that Henoch-Schönlein purpura could appear after streptococcal infection in patients with abnormal complement levels, and that steroids and angiotensin-converting enzyme inhibitor could be successful treatment for the disease.</p

Rare and Common Variants Conferring Risk of Tooth Agenesis

We present association results from a large genome-wide association study of tooth agenesis (TA) as well as selective TA, including 1,944 subjects with congenitally missing teeth, excluding third molars, and 338,554 controls, all of European ancestry. We also tested the association of previously identified risk variants, for timing of tooth eruption and orofacial clefts, with TA. We report associations between TA and 9 novel risk variants. Five of these variants associate with selective TA, including a variant conferring risk of orofacial clefts. These results contribute to a deeper understanding of the genetic architecture of tooth development and disease. The few variants previously associated with TA were uncovered through candidate gene studies guided by mouse knockouts. Knowing the etiology and clinical features of TA is important for planning oral rehabilitation that often involves an interdisciplinary approach

Common Variants at 10 Genomic Loci Influence Hemoglobin A(1C) Levels via Glycemic and Nonglycemic Pathways

OBJECTIVE-Glycated hemoglobin (HbA(1c)), used to monitor and diagnose diabetes, is influenced by average glycemia over a 2- to 3-month period. Genetic factors affecting expression, turnover, and abnormal glycation of hemoglobin could also be associated with increased levels of HbA(1c). We aimed to identify such genetic factors and investigate the extent to which they influence diabetes classification based on HbA(1c) levels.RESEARCH DESIGN AND METHODS-We studied associations with HbA(1c) in up to 46,368 nondiabetic adults of European descent from 23 genome-wide association studies (GWAS) and 8 cohorts with de novo genotyped single nucleotide polymorphisms (SNPs). We combined studies using inverse-variance meta-analysis and tested mediation by glycemia using conditional analyses. We estimated the global effect of HbA(1c) loci using a multilocus risk score, and used net reclassification to estimate genetic effects on diabetes screening.RESULTS-Ten loci reached genome-wide significant association with HbA(1c), including six new loci near FN3K (lead SNP/P value, rs1046896/P = 1.6 x 10(-26)), HFE (rs1800562/P = 2.6 x 10(-20)), TMPRSS6 (rs855791/P = 2.7 x 10(-14)), ANK1 (rs4737009/P = 6.1 x 10(-12)), SPTA1 (rs2779116/P = 2.8 x 10(-9)) and ATP11A/TUBGCP3 (rs7998202/P = 5.2 x 10(-9)), and four known HbA(1c) loci: HK1 (rs16926246/P = 3.1 x 10(-54)), MTNR1B (rs1387153/P = 4.0 X 10(-11)), GCK (rs1799884/P = 1.5 x 10(-20)) and G6PC2/ABCB11 (rs552976/P = 8.2 x 10(-18)). We show that associations with HbA(1c) are partly a function of hyperglycemia associated with 3 of the 10 loci (GCK, G6PC2 and MTNR1B). The seven nonglycemic loci accounted for a 0.19 (%HbA(1c)) difference between the extreme 10% tails of the risk score, and would reclassify similar to 2% of a general white population screened for diabetes with HbA(1c).CONCLUSIONS-GWAS identified 10 genetic loci reproducibly associated with HbA(1c). Six are novel and seven map to loci where rarer variants cause hereditary anemias and iron storage disorders. Common variants at these loci likely influence HbA(1c) levels via erythrocyte biology, and confer a small but detectable reclassification of diabetes diagnosis by HbA(1c) Diabetes 59: 3229-3239, 201