Topological transversals to a family of convex sets

Let $\mathcal F$ be a family of compact convex sets in $\mathbb R^d$. We say that $\mathcal F$ has a \emph{topological $\rho$-transversal of index $(m,k)$} ($\rho<m$, $0<k\leq d-m$) if there are, homologically, as many transversal $m$-planes to $\mathcal F$ as $m$-planes containing a fixed $\rho$-plane in $\mathbb R^{m+k}$. Clearly, if $\mathcal F$ has a $\rho$-transversal plane, then $\mathcal F$ has a topological $\rho$-transversal of index $(m,k),$ for $\rho<m$ and $k\leq d-m$. The converse is not true in general. We prove that for a family $\mathcal F$ of $\rho+k+1$ compact convex sets in $\mathbb R^d$ a topological $\rho$-transversal of index $(m,k)$ implies an ordinary $\rho$-transversal. We use this result, together with the multiplication formulas for Schubert cocycles, the Lusternik-Schnirelmann category of the Grassmannian, and different versions of the colorful Helly theorem by B\'ar\'any and Lov\'asz, to obtain some geometric consequences

Identification of common genetic risk variants for autism spectrum disorder

Autism spectrum disorder (ASD) is a highly heritable and heterogeneous group of neurodevelopmental phenotypes diagnosed in more than 1% of children. Common genetic variants contribute substantially to ASD susceptibility, but to date no individual variants have been robustly associated with ASD. With a marked sample-size increase from a unique Danish population resource, we report a genome-wide association meta-analysis of 18,381 individuals with ASD and 27,969 controls that identified five genome-wide-significant loci. Leveraging GWAS results from three phenotypes with significantly overlapping genetic architectures (schizophrenia, major depression, and educational attainment), we identified seven additional loci shared with other traits at equally strict significance levels. Dissecting the polygenic architecture, we found both quantitative and qualitative polygenic heterogeneity across ASD subtypes. These results highlight biological insights, particularly relating to neuronal function and corticogenesis, and establish that GWAS performed at scale will be much more productive in the near term in ASD.Peer reviewe

Associations of autozygosity with a broad range of human phenotypes

In many species, the offspring of related parents suffer reduced reproductive success, a phenomenon known as inbreeding depression. In humans, the importance of this effect has remained unclear, partly because reproduction between close relatives is both rare and frequently associated with confounding social factors. Here, using genomic inbreeding coefficients (F-ROH) for >1.4 million individuals, we show that F-ROH is significantly associated (p <0.0005) with apparently deleterious changes in 32 out of 100 traits analysed. These changes are associated with runs of homozygosity (ROH), but not with common variant homozygosity, suggesting that genetic variants associated with inbreeding depression are predominantly rare. The effect on fertility is striking: F-ROH equivalent to the offspring of first cousins is associated with a 55% decrease [95% CI 44-66%] in the odds of having children. Finally, the effects of F-ROH are confirmed within full-sibling pairs, where the variation in F-ROH is independent of all environmental confounding.Peer reviewe

Genome-Wide Association Study in BRCA1 Mutation Carriers Identifies Novel Loci Associated with Breast and Ovarian Cancer Risk

BRCA1-associated breast and ovarian cancer risks can be modified by common genetic variants. To identify further cancer risk-modifying loci, we performed a multi-stage GWAS of 11,705 BRCA1 carriers (of whom 5,920 were diagnosed with breast and 1,839 were diagnosed with ovarian cancer), with a further replication in an additional sample of 2,646 BRCA1 carriers. We identified a novel breast cancer risk modifier locus at 1q32 for BRCA1 carriers (rs2290854, P = 2.7×10-8, HR = 1.14, 95% CI: 1.09-1.20). In addition, we identified two novel ovarian cancer risk modifier loci: 17q21.31 (rs17631303, P = 1.4×10-8, HR = 1.27, 95% CI: 1.17-1.38) and 4q32.3 (rs4691139, P = 3.4×10-8, HR = 1.20, 95% CI: 1.17-1.38). The 4q32.3 locus was not associated with ovarian cancer risk in the general population or BRCA2 carriers, suggesting a BRCA1-specific associat

Genetic architecture of spatial electrical biomarkers for cardiac arrhythmia and relationship with cardiovascular disease

The 3-dimensional spatial and 2-dimensional frontal QRS-T angles are measures derived from the vectorcardiogram. They are independent risk predictors for arrhythmia, but the underlying biology is unknown. Using multi-ancestry genome-wide association studies we identify 61 (58 previously unreported) loci for the spatial QRS-T angle (N = 118,780) and 11 for the frontal QRS-T angle (N = 159,715). Seven out of the 61 spatial QRS-T angle loci have not been reported for other electrocardiographic measures. Enrichments are observed in pathways related to cardiac and vascular development, muscle contraction, and hypertrophy. Pairwise genome-wide association studies with classical ECG traits identify shared genetic influences with PR interval and QRS duration. Phenome-wide scanning indicate associations with atrial fibrillation, atrioventricular block and arterial embolism and genetically determined QRS-T angle measures are associated with fascicular and bundle branch block (and also atrioventricular block for the frontal QRS-T angle). We identify potential biology involved in the QRS-T angle and their genetic relationships with cardiovascular traits and diseases, may inform future research and risk prediction

Multi-ancestry GWAS of the electrocardiographic PR interval identifies 202 loci underlying cardiac conduction

The electrocardiographic PR interval reflects atrioventricular conduction, and is associated with conduction abnormalities, pacemaker implantation, atrial fibrillation (AF), and cardiovascular mortality. Here we report a multi-ancestry (N = 293,051) genome-wide association meta-analysis for the PR interval, discovering 202 loci of which 141 have not previously been reported. Variants at identified loci increase the percentage of heritability explained, from 33.5% to 62.6%. We observe enrichment for cardiac muscle developmental/contractile and cytoskeletal genes, highlighting key regulation processes for atrioventricular conduction. Additionally, 8 loci not previously reported harbor genes underlying inherited arrhythmic syndromes and/or cardiomyopathies suggesting a role for these genes in cardiovascular pathology in the general population. We show that polygenic predisposition to PR interval duration is an endophenotype for cardiovascular disease, including distal conduction disease, AF, and atrioventricular pre-excitation. These findings advance our understanding of the polygenic basis of cardiac conduction, and the genetic relationship between PR interval duration and cardiovascular disease

Genetic insights into resting heart rate and its role in cardiovascular disease.

Resting heart rate is associated with cardiovascular diseases and mortality in observational and Mendelian randomization studies. The aims of this study are to extend the number of resting heart rate associated genetic variants and to obtain further insights in resting heart rate biology and its clinical consequences. A genome-wide meta-analysis of 100 studies in up to 835,465 individuals reveals 493 independent genetic variants in 352 loci, including 68 genetic variants outside previously identified resting heart rate associated loci. We prioritize 670 genes and in silico annotations point to their enrichment in cardiomyocytes and provide insights in their ECG signature. Two-sample Mendelian randomization analyses indicate that higher genetically predicted resting heart rate increases risk of dilated cardiomyopathy, but decreases risk of developing atrial fibrillation, ischemic stroke, and cardio-embolic stroke. We do not find evidence for a linear or non-linear genetic association between resting heart rate and all-cause mortality in contrast to our previous Mendelian randomization study. Systematic alteration of key differences between the current and previous Mendelian randomization study indicates that the most likely cause of the discrepancy between these studies arises from false positive findings in previous one-sample MR analyses caused by weak-instrument bias at lower P-value thresholds. The results extend our understanding of resting heart rate biology and give additional insights in its role in cardiovascular disease development

Breast cancer risk genes: association analysis in more than 113,000 women

BACKGROUNDGenetic testing for breast cancer susceptibility is widely used, but for many genes, evidence of an association with breast cancer is weak, underlying risk estimates are imprecise, and reliable subtype-specific risk estimates are lacking.METHODSWe used a panel of 34 putative susceptibility genes to perform sequencing on samples from 60,466 women with breast cancer and 53,461 controls. In separate analyses for protein-truncating variants and rare missense variants in these genes, we estimated odds ratios for breast cancer overall and tumor subtypes. We evaluated missense-variant associations according to domain and classification of pathogenicity.RESULTSProtein-truncating variants in 5 genes (ATM, BRCA1, BRCA2, CHEK2, and PALB2) were associated with a risk of breast cancer overall with a P value of less than 0.0001. Protein-truncating variants in 4 other genes (BARD1, RAD51C, RAD51D, and TP53) were associated with a risk of breast cancer overall with a P value of less than 0.05 and a Bayesian false-discovery probability of less than 0.05. For protein-truncating variants in 19 of the remaining 25 genes, the upper limit of the 95% confidence interval of the odds ratio for breast cancer overall was less than 2.0. For protein-truncating variants in ATM and CHEK2, odds ratios were higher for estrogen receptor (ER)-positive disease than for ER-negative disease; for protein-truncating variants in BARD1, BRCA1, BRCA2, PALB2, RAD51C, and RAD51D, odds ratios were higher for ER-negative disease than for ER-positive disease. Rare missense variants (in aggregate) in ATM, CHEK2, and TP53 were associated with a risk of breast cancer overall with a P value of less than 0.001. For BRCA1, BRCA2, and TP53, missense variants (in aggregate) that would be classified as pathogenic according to standard criteria were associated with a risk of breast cancer overall, with the risk being similar to that of protein-truncating variants.CONCLUSIONSThe results of this study define the genes that are most clinically useful for inclusion on panels for the prediction of breast cancer risk, as well as provide estimates of the risks associated with protein-truncating variants, to guide genetic counseling. (Funded by European Union Horizon 2020 programs and others.)Molecular tumour pathology - and tumour geneticsMTG1 - Moleculaire genetica en pathologie van borstkanke

Genome-wide by Environment Interaction Studies of Depressive Symptoms and Psychosocial Stress in UK Biobank and Generation Scotland

Stress is associated with poorer physical and mental health. To improve our understanding of this link, we performed genome-wide association studies (GWAS) of depressive symptoms and genome-wide by environment interaction studies (GWEIS) of depressive symptoms and stressful life events (SLE) in two UK population-based cohorts (Generation Scotland and UK Biobank). No SNP was individually significant in either GWAS, but gene-based tests identified six genes associated with depressive symptoms in UK Biobank (DCC, ACSS3, DRD2, STAG1, FOXP2 and KYNU; p < 2.77 x 10(-6)). Two SNPs with genome-wide significant GxE effects were identified by GWEIS in Generation Scotland: rs12789145 (53-kb downstream PIWIL4; p = 4.95 x 10(-9); total SLE) and rs17070072 (intronic to ZCCHC2; p = 1.46 x 10(-8); dependent SLE). A third locus upstream CYLC2 (rs12000047 and rs12005200, p < 2.00 x 10(-8); dependent SLE) when the joint effect of the SNP main and GxE effects was considered. GWEIS gene-based tests identified: MTNR1B with GxE effect with dependent SLE in Generation Scotland; and PHF2 with the joint effect in UK Biobank (p < 2.77 x 10(-6)). Polygenic risk scores (PRSs) analyses incorporating GxE effects improved the prediction of depressive symptom scores, when using weights derived from either the UK Biobank GWAS of depressive symptoms (p = 0.01) or the PGC GWAS of major depressive disorder (p = 5.91 x 10(-3)). Using an independent sample, PRS derived using GWEIS GxE effects provided evidence of shared aetiologies between depressive symptoms and schizotypal personality, heart disease and COPD. Further such studies are required and may result in improved treatments for depression and other stress-related conditions

The Influence of Number and Timing of Pregnancies on Breast Cancer Risk for Women With BRCA1 or BRCA2 Mutations

Background: Full-term pregnancy (FTP) is associated with a reduced breast cancer (BC) risk over time, but women are at increased BC risk in the immediate years following an FTP. No large prospective studies, however, have examined whether the number and timing of pregnancies are associated with BC risk for BRCA1 and BRCA2 mutation carriers. Methods: Using weighted and time-varying Cox proportional hazards models, we investigated whether reproductive events are associated with BC risk for mutation carriers using a retrospective cohort (5707 BRCA1 and 3525 BRCA2 mutation carriers) and a prospective cohort (2276 BRCA1 and 1610 BRCA2 mutation carriers), separately for each cohort and the combined prospective and retrospective cohort. Results: For BRCA1 mutation carriers, there was no overall association with parity compared with nulliparity (combined hazard ratio [HRc] ¼ 0.99, 95% confidence interval [CI] ¼ 0.83 to 1.18). Relative to being uniparous, an increased number of FTPs was associated with decreased BC risk (HRc¼ 0.79, 95% CI ¼ 0.69 to 0.91; HRc¼ 0.70, 95% CI ¼ 0.59 to 0.82; HRc¼ 0.50, 95% CI ¼ 0.40 to 0.63, for 2, 3, and 4 FTPs, respectively, Ptrend < .0001) and increasing duration of breastfeeding was associated with decreased BC risk (combined cohort Ptrend ¼ .0003). Relative to being nulliparous, uniparous BRCA1 mutation carriers were at increased BC risk in the prospective analysis (prospective hazard ration [HRp] ¼ 1.69, 95% CI ¼ 1.09 to 2.62). For BRCA2 mutation carriers, being parous was associated with a 30% increase in BC risk (HRc ¼ 1.33, 95% CI ¼ 1.05 to 1.69), and there was no apparent decrease in risk associated with multiparity except for having at least 4 FTPs vs. 1 FTP (HRc¼ 0.72, 95% CI ¼ 0.54 to 0.98). Conclusions: These findings suggest differential associations with parity between BRCA1 and BRCA2 mutation carriers with higher risk for uniparous BRCA1 carriers and parous BRCA2 carriers