Lower bounds for the first eigenvalue of the magnetic Laplacian

We consider a Riemannian cylinder endowed with a closed potential 1-form A and study the magnetic Laplacian with magnetic Neumann boundary conditions associated with those data. We establish a sharp lower bound for the first eigenvalue and show that the equality characterizes the situation where the metric is a product. We then look at the case of a planar domain bounded by two closed curves and obtain an explicit lower bound in terms of the geometry of the domain. We finally discuss sharpness of this last estimate.Comment: Replaces in part arXiv:1611.0193

Cross-ancestry genome-wide association analysis of corneal thickness strengthens link between complex and Mendelian eye diseases

Central corneal thickness (CCT) is a highly heritable trait associated with complex eye diseases such as keratoconus and glaucoma. We perform a genome-wide association meta-analysis of CCT and identify 19 novel regions. In addition to adding support for known connective tissue-related pathways, pathway analyses uncover previously unreported gene sets. Remarkably, >20% of the CCT-loci are near or within Mendelian disorder genes. These included FBN1, ADAMTS2 and TGFB2 which associate with connective tissue disorders (Marfan, Ehlers-Danlos and Loeys-Dietz syndromes), and the LUM-DCN-KERA gene complex involved in myopia, corneal dystrophies and cornea plana. Using index CCT-increasing variants, we find a significant inverse correlation in effect sizes between CCT and keratoconus (r =-0.62, P = 5.30 × 10-5) but not between CCT and primary open-angle glaucoma (r =-0.17, P = 0.2). Our findings provide evidence for shared genetic influences between CCT and keratoconus, and implicate candidate genes acting in collagen and extracellular matrix regulation

Probing the Conformational Dynamics of Affinity-Enhanced T Cell Receptor Variants upon Binding the Peptide-Bound Major Histocompatibility Complex by Hydrogen/Deuterium Exchange Mass Spectrometry.

Binding of the T cell receptor (TCR) to its cognate, peptide antigen-loaded major histocompatibility complex (pMHC) is a key interaction for triggering T cell activation and ultimately elimination of the target cell. Despite the importance of this interaction for cellular immunity, a comprehensive molecular understanding of TCR specificity and affinity is lacking. We conducted hydrogen/deuterium exchange mass spectrometry (HDX-MS) analyses of individual affinity-enhanced TCR variants and clinically relevant pMHC class I molecules (HLA-A*0201/NY-ESO-1 <sub>157-165</sub> ) to investigate the causality between increased binding affinity and conformational dynamics in TCR-pMHC complexes. Differential HDX-MS analyses of TCR variants revealed that mutations for affinity enhancement in TCR CDRs altered the conformational response of TCR to pMHC ligation. Improved pMHC binding affinity was in general observed to correlate with greater differences in HDX upon pMHC binding in modified TCR CDR loops, thereby providing new insights into the TCR-pMHC interaction. Furthermore, a specific point mutation in the β-CDR3 loop of the NY-ESO-1 TCR associated with a substantial increase in binding affinity resulted in a substantial change in pMHC binding kinetics (i.e., very slow k <sub>on</sub> , revealed by the detection of EX1 HDX kinetics), thus providing experimental evidence for a slow induced-fit binding mode. We also examined the conformational impact of pMHC binding on an unrelated TRAV12-2 gene-encoded TCR directed against the immunodominant MART-1 <sub>26-35</sub> cancer antigen restricted by HLA-A*0201. Our findings provide a molecular basis for the observed TRAV12-2 gene bias in natural CD8 <sup>+</sup> T cell-based immune responses against the MART-1 antigen, with potential implications for general ligand discrimination and TCR cross-reactivity processes

Variation in sex ratio and evolutionary rate of hemiclonal Rana esculenta populations.

In many plant and animal taxa mutation rates are higher in males than in females. As a result, the evolutionary speed of genes depends on how much time they spend in either sex. Usually, this time differs between genes located on sex chromosomes but not between those on autosomes. Here we present an unusual system with a partially sex-linked inheritance of autosomes: the hemiclonal frog Rana esculenta (E) which is originally a hybrid between the sexual species R. lessonae (L) and R. ridibunda (R). Rana esculenta excludes the L genome prior to meiosis, produces eggs or sperm containing an unrecombined R genome and restores hybridity by mating with R. lessonae (‘hybridogenesis’). Matings between L males and E females result in offspring with an even sex ratio, whereas the reverse combination produces only daughters. The extent of the resulting female bias and the proportion that R alleles have spent in either sex depend on the relative survival (b) and the relative reproductive contribution (a) of E males vs. E females. In this paper, we analyze mathematically how different combinations of a and b influence the sex ratio in R. esculenta populations and, combined with the male/female mutation rate ratio (α), the evolutionary rate of the clonally transmitted R genome. We find that this rate is higher than in an asexual population and lower than in a sexual one. Hence, clonal diversity through new mutations is more easily achievable than in purely asexual species. In contrast, the occurrence and accumulation of deleterious mutations is lower than in a comparable sexual species. We conclude that these intermediate mutation rates improve the ecological and evolutionary potential of hemiclonal organisms, and we draw attention to the implications for the use of microsatellites