A note on the union-closed sets conjecture

A collection A of finite sets is closed under union if A, B ∈ A implies that A ∪ B ∈ A. The Union-Closed Sets Conjecture states that if A is a union-closed collection of sets, containing at least one non-empty set, then there is an element which belongs to at least half of the sets in A. We show that if q is the minimum cardinality of ∪A taken over allcounterexamples A, then any counterexample A has cardinality at least 4q − 1

IMI - Myopia Genetics Report

The knowledge on the genetic background of refractive error and myopia has expanded dramatically in the past few years. This white paper aims to provide a concise summary of current genetic findings and defines the direction where development is needed. We performed an extensive literature search and conducted informal discussions with key stakeholders. Specific topics reviewed included common refractive error, any and high myopia, and myopia related to syndromes. To date, almost 200 genetic loci have been identified for refractive error and myopia, and risk variants mostly carry low risk but are highly prevalent in the general population. Several genes for secondary syndromic myopia overlap with those for common myopia. Polygenic risk scores show overrepresentation of high myopia in the higher deciles of risk. Annotated genes have a wide variety of functions, and all retinal layers appear to be sites of expression. The current genetic findings offer a world of new molecules involved in myopiagenesis. As the missing heritability is still large, further genetic advances are needed. This Committee recommends expanding large-scale, in-depth genetic studies using complementary big data analytics, consideration of gene-environment effects by thorough measurement of environmental exposures, and focus on subgroups with extreme phenotypes and high familial occurrence. Functional characterization of associated variants is simultaneously needed to bridge the knowledge gap between sequence variance and consequence for eye growth

Case Reports1. A Late Presentation of Loeys-Dietz Syndrome: Beware of TGFβ Receptor Mutations in Benign Joint Hypermobility

Background: Thoracic aortic aneurysms (TAA) and dissections are not uncommon causes of sudden death in young adults. Loeys-Dietz syndrome (LDS) is a rare, recently described, autosomal dominant, connective tissue disease characterized by aggressive arterial aneurysms, resulting from mutations in the transforming growth factor beta (TGFβ) receptor genes TGFBR1 and TGFBR2. Mean age at death is 26.1 years, most often due to aortic dissection. We report an unusually late presentation of LDS, diagnosed following elective surgery in a female with a long history of joint hypermobility. Methods: A 51-year-old Caucasian lady complained of chest pain and headache following a dural leak from spinal anaesthesia for an elective ankle arthroscopy. CT scan and echocardiography demonstrated a dilated aortic root and significant aortic regurgitation. MRA demonstrated aortic tortuosity, an infrarenal aortic aneurysm and aneurysms in the left renal and right internal mammary arteries. She underwent aortic root repair and aortic valve replacement. She had a background of long-standing joint pains secondary to hypermobility, easy bruising, unusual fracture susceptibility and mild bronchiectasis. She had one healthy child age 32, after which she suffered a uterine prolapse. Examination revealed mild Marfanoid features. Uvula, skin and ophthalmological examination was normal. Results: Fibrillin-1 testing for Marfan syndrome (MFS) was negative. Detection of a c.1270G > C (p.Gly424Arg) TGFBR2 mutation confirmed the diagnosis of LDS. Losartan was started for vascular protection. Conclusions: LDS is a severe inherited vasculopathy that usually presents in childhood. It is characterized by aortic root dilatation and ascending aneurysms. There is a higher risk of aortic dissection compared with MFS. Clinical features overlap with MFS and Ehlers Danlos syndrome Type IV, but differentiating dysmorphogenic features include ocular hypertelorism, bifid uvula and cleft palate. Echocardiography and MRA or CT scanning from head to pelvis is recommended to establish the extent of vascular involvement. Management involves early surgical intervention, including early valve-sparing aortic root replacement, genetic counselling and close monitoring in pregnancy. Despite being caused by loss of function mutations in either TGFβ receptor, paradoxical activation of TGFβ signalling is seen, suggesting that TGFβ antagonism may confer disease modifying effects similar to those observed in MFS. TGFβ antagonism can be achieved with angiotensin antagonists, such as Losartan, which is able to delay aortic aneurysm development in preclinical models and in patients with MFS. Our case emphasizes the importance of timely recognition of vasculopathy syndromes in patients with hypermobility and the need for early surgical intervention. It also highlights their heterogeneity and the potential for late presentation. Disclosures: The authors have declared no conflicts of interes

Evaluating the Effects of SARS-CoV-2 Spike Mutation D614G on Transmissibility and Pathogenicity.

Global dispersal and increasing frequency of the SARS-CoV-2 spike protein variant D614G are suggestive of a selective advantage but may also be due to a random founder effect. We investigate the hypothesis for positive selection of spike D614G in the United Kingdom using more than 25,000 whole genome SARS-CoV-2 sequences. Despite the availability of a large dataset, well represented by both spike 614 variants, not all approaches showed a conclusive signal of positive selection. Population genetic analysis indicates that 614G increases in frequency relative to 614D in a manner consistent with a selective advantage. We do not find any indication that patients infected with the spike 614G variant have higher COVID-19 mortality or clinical severity, but 614G is associated with higher viral load and younger age of patients. Significant differences in growth and size of 614G phylogenetic clusters indicate a need for continued study of this variant

Socioeconomic and urban-rural differentials in exposure to air pollution and mortality burden in England

BACKGROUND: Socioeconomically disadvantaged populations often have higher exposures to particulate air pollution, which can be expected to contribute to differentials in life expectancy. We examined socioeconomic differentials in exposure and air pollution-related mortality relating to larger scale (5 km resolution) variations in background concentrations of selected pollutants across England. METHODS: Ozone and particulate matter (sub-divided into PM10, PM2.5, PM2.5-10, primary, nitrate and sulphate PM2.5) were simulated at 5 km horizontal resolution using an atmospheric chemistry transport model (EMEP4UK). Annual mean concentrations of these pollutants were assigned to all 1,202,578 residential postcodes in England, which were classified by urban-rural status and socioeconomic deprivation based on the income and employment domains of the 2010 English Index of Multiple Deprivation for the Lower-level Super Output Area of residence. We used life table methods to estimate PM2.5-attributable life years (LYs) lost in both relative and absolute terms. RESULTS: Concentrations of the most particulate fractions, but not of nitrate PM2.5 or ozone, were modestly higher in areas of greater socioeconomic deprivation. Relationships between pollution level and socioeconomic deprivation were non-linear and varied by urban-rural status. The pattern of PM2.5 concentrations made only a small contribution to the steep socioeconomic gradient in LYs lost due to PM2.5 per 103 population, which primarily was driven by the steep socioeconomic gradient in underlying mortality rates. In rural areas, the absolute burden of air pollution-related LYs lost was lowest in the most deprived deciles. CONCLUSIONS: Air pollution shows modest socioeconomic patterning at 5 km resolution in England, but absolute attributable mortality burdens are strongly related to area-level deprivation because of underlying mortality rates. Measures that cause a general reduction in background concentrations of air pollution may modestly help narrow socioeconomic differences in health

A new polygenic score for refractive error improves detection of children at risk of high myopia but not the prediction of those at risk of myopic macular degeneration

Background High myopia (HM), defined as a spherical equivalent refractive error (SER) ≤ −6.00 diopters (D), is a leading cause of sight impairment, through myopic macular degeneration (MMD). We aimed to derive an improved polygenic score (PGS) for predicting children at risk of HM and to test if a PGS is predictive of MMD after accounting for SER. Methods The PGS was derived from genome-wide association studies in participants of UK Biobank, CREAM Consortium, and Genetic Epidemiology Research on Adult Health and Aging. MMD severity was quantified by a deep learning algorithm. Prediction of HM was quantified as the area under the receiver operating curve (AUROC). Prediction of severe MMD was assessed by logistic regression. Findings In independent samples of European, African, South Asian and East Asian ancestry, the PGS explained 19% (95% confidence interval 17–21%), 2% (1–3%), 8% (7–10%) and 6% (3–9%) of the variation in SER, respectively. The AUROC for HM in these samples was 0.78 (0.75–0.81), 0.58 (0.53–0.64), 0.71 (0.69–0.74) and 0.67 (0.62–0.72), respectively. The PGS was not associated with the risk of MMD after accounting for SER: OR = 1.07 (0.92–1.24). Interpretation Performance of the PGS approached the level required for clinical utility in Europeans but not in other ancestries. A PGS for refractive error was not predictive of MMD risk once SER was accounted fo

Genome-wide association meta-analysis of corneal curvature identifies novel loci and shared genetic influences across axial length and refractive error

Abstract: Corneal curvature, a highly heritable trait, is a key clinical endophenotype for myopia - a major cause of visual impairment and blindness in the world. Here we present a trans-ethnic meta-analysis of corneal curvature GWAS in 44,042 individuals of Caucasian and Asian with replication in 88,218 UK Biobank data. We identified 47 loci (of which 26 are novel), with population-specific signals as well as shared signals across ethnicities. Some identified variants showed precise scaling in corneal curvature and eye elongation (i.e. axial length) to maintain eyes in emmetropia (i.e. HDAC11/FBLN2 rs2630445, RBP3 rs11204213); others exhibited association with myopia with little pleiotropic effects on eye elongation. Implicated genes are involved in extracellular matrix organization, developmental process for body and eye, connective tissue cartilage and glycosylation protein activities. Our study provides insights into population-specific novel genes for corneal curvature, and their pleiotropic effect in regulating eye size or conferring susceptibility to myopia

Subcortical brain volume, regional cortical thickness, and cortical surface area across disorders: findings from the ENIGMA ADHD, ASD, and OCD Working Groups

Objective Attention-deficit/hyperactivity disorder (ADHD), autism spectrum disorder (ASD), and obsessive-compulsive disorder (OCD) are common neurodevelopmental disorders that frequently co-occur. We aimed to directly compare all three disorders. The ENIGMA consortium is ideally positioned to investigate structural brain alterations across these disorders. Methods Structural T1-weighted whole-brain MRI of controls (n=5,827) and patients with ADHD (n=2,271), ASD (n=1,777), and OCD (n=2,323) from 151 cohorts worldwide were analyzed using standardized processing protocols. We examined subcortical volume, cortical thickness and surface area differences within a mega-analytical framework, pooling measures extracted from each cohort. Analyses were performed separately for children, adolescents, and adults using linear mixed-effects models adjusting for age, sex and site (and ICV for subcortical and surface area measures). Results We found no shared alterations among all three disorders, while shared alterations between any two disorders did not survive multiple comparisons correction. Children with ADHD compared to those with OCD had smaller hippocampal volumes, possibly influenced by IQ. Children and adolescents with ADHD also had smaller ICV than controls and those with OCD or ASD. Adults with ASD showed thicker frontal cortices compared to adult controls and other clinical groups. No OCD-specific alterations across different age-groups and surface area alterations among all disorders in childhood and adulthood were observed. Conclusion Our findings suggest robust but subtle alterations across different age-groups among ADHD, ASD, and OCD. ADHD-specific ICV and hippocampal alterations in children and adolescents, and ASD-specific cortical thickness alterations in the frontal cortex in adults support previous work emphasizing neurodevelopmental alterations in these disorders