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

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

Multi-trait genome-wide association study identifies new loci associated with optic disc parameters

A new avenue of mining published genome-wide association studies includes the joint analysis of related traits. The power of this approach depends on the genetic correlation of traits, which reflects the number of pleiotropic loci, i.e. genetic loci influencing multiple traits. Here, we applied new meta-analyses of optic nerve head (ONH) related traits implicated in primary open-angle glaucoma (POAG); intraocular pressure and central corneal thickness using Haplotype reference consortium imputations. We performed a multi-trait analysis of ONH parameters cup area, disc area and vertical cup-disc ratio. We uncover new variants; rs11158547 in PPP1R36-PLEKHG3 and rs1028727 near SERPINE3 at genome-wide significance that replicate in independent Asian cohorts imputed to 1000 Genomes. At this point, validation of these variants in POAG cohorts is hampered by the high degree of heterogeneity. Our results show that multi-trait analysis is a valid approach to identify novel pleiotropic variants for ONH

Bound States of Energy Dependent Singular Potentials

We consider attractive power-law potentials depending on energy through their coupling constant. These potentials are proportional to 1/|x| m with m ≥ 1 in the D = 1 dimensional space, to 1/r m with m ≥ 2 in the D = 3 dimensional space. We study the ground state of such potentials. First, we show that all singular attractive potentials with an energy dependent coupling constant are bounded from below, contrarily to the usual case. In D = 1, a bound state of finite energy is found with a kind of universality for the eigenvalue and the eigenfunction, which become independent on m for m > 1. We prove the solution to be unique. A similar situation arises for D = 3 for m > 2, except that, in this case, the solution is not directly comparable to a bound state: the wave function, though square integrable, diverges at the origin