Norm estimates of complex symmetric operators applied to quantum systems

This paper communicates recent results in theory of complex symmetric operators and shows, through two non-trivial examples, their potential usefulness in the study of Schr\"odinger operators. In particular, we propose a formula for computing the norm of a compact complex symmetric operator. This observation is applied to two concrete problems related to quantum mechanical systems. First, we give sharp estimates on the exponential decay of the resolvent and the single-particle density matrix for Schr\"odinger operators with spectral gaps. Second, we provide new ways of evaluating the resolvent norm for Schr\"odinger operators appearing in the complex scaling theory of resonances

Association of the Asn306Ser variant of the SP4 transcription factor and an intronic variant in the β-subunit of transducin with digenic disease

Purpose SP4 is a transcription factor abundantly expressed in retina that binds to the GC promoter region of photoreceptor signal transduction genes. We have previously shown that SP4 may be involved in the transcriptional activation of these genes alone or together with other transcription factors such as SP1, neural retina leucine zipper protein (NRL), and cone-rod homeobox gene (CRX). Since mutations in NRL and CRX are involved in inherited retinal degenerations, SP4 was considered a good candidate for mutation screening in patients with this type of diseases. The purpose of this work, therefore, was to investigate possible mutations in SP4 in a cohort of patients affected with different forms of retinal degenerations. Methods 270 unrelated probands with various forms of retinal degeneration including autosomal dominant and autosomal recessive retinitis pigmentosa (RP), autosomal dominant and autosomal recessive cone-rod dystrophy (CRD), and Leber's congenital amaurosis (LCA), were screened for mutations in the SP4 gene. Single strand conformation polymorphism (SSCP) analysis was performed on the six SP4 gene exons including flanking regions followed by direct sequencing of SSCP variants. Results Nine different sequence variants were found in 29 patients, four in introns and five in exons. Many of the probands were previously screened for mutations in the genes encoding the α-, β- and γ-subunits of rod-specific cGMP phosphodiesterase (PDE6A, PDE6B, PDE6G), the β-subunit of rod-specific transducin (GNB1), and peripherin/rds (RDS). One group of seven probands of Hispanic background that included five with arRP, one with RP of unknown inheritance (isolate) and 1 with arCRD carried an Asn306Ser mutation in SP4. Of the seven, the isolate case was homozygous and the other 6 heterozygous for the variant. Two arRP and the arCRD probands carried an additional intronic GNB1 variant. DNA from the family members of the arCRD proband could not be obtained, but for the other two families, all affected members and none of the unaffected carried both the SP4 Asn306Ser allele and the GNB1 intronic variant. Conclusions If mutations in SP4 do cause retinal degenerative disease, their frequency would be low. While digenic disease with the SP4 Asn306Ser and the GNB1 intronic variant alleles has not been established, neither has it been ruled out. This leaves open the possibility of a cooperative involvement of SP4 and GNB1 in the normal function of the retina.PubMedWo

Cone rod dystrophies

Cone rod dystrophies (CRDs) (prevalence 1/40,000) are inherited retinal dystrophies that belong to the group of pigmentary retinopathies. CRDs are characterized by retinal pigment deposits visible on fundus examination, predominantly localized to the macular region. In contrast to typical retinitis pigmentosa (RP), also called the rod cone dystrophies (RCDs) resulting from the primary loss in rod photoreceptors and later followed by the secondary loss in cone photoreceptors, CRDs reflect the opposite sequence of events. CRD is characterized by primary cone involvement, or, sometimes, by concomitant loss of both cones and rods that explains the predominant symptoms of CRDs: decreased visual acuity, color vision defects, photoaversion and decreased sensitivity in the central visual field, later followed by progressive loss in peripheral vision and night blindness. The clinical course of CRDs is generally more severe and rapid than that of RCDs, leading to earlier legal blindness and disability. At end stage, however, CRDs do not differ from RCDs. CRDs are most frequently non syndromic, but they may also be part of several syndromes, such as Bardet Biedl syndrome and Spinocerebellar Ataxia Type 7 (SCA7). Non syndromic CRDs are genetically heterogeneous (ten cloned genes and three loci have been identified so far). The four major causative genes involved in the pathogenesis of CRDs are ABCA4 (which causes Stargardt disease and also 30 to 60% of autosomal recessive CRDs), CRX and GUCY2D (which are responsible for many reported cases of autosomal dominant CRDs), and RPGR (which causes about 2/3 of X-linked RP and also an undetermined percentage of X-linked CRDs). It is likely that highly deleterious mutations in genes that otherwise cause RP or macular dystrophy may also lead to CRDs. The diagnosis of CRDs is based on clinical history, fundus examination and electroretinogram. Molecular diagnosis can be made for some genes, genetic counseling is always advised. Currently, there is no therapy that stops the evolution of the disease or restores the vision, and the visual prognosis is poor. Management aims at slowing down the degenerative process, treating the complications and helping patients to cope with the social and psychological impact of blindness

Synchronizing Allelic Effects of Opposing Quantitative Trait Loci Confirmed a Major Epistatic Interaction Affecting Acute Lung Injury Survival in Mice

Increased oxygen (O2) levels help manage severely injured patients, but too much for too long can cause acute lung injury (ALI), acute respiratory distress syndrome (ARDS) and even death. In fact, continuous hyperoxia has become a prototype in rodents to mimic salient clinical and pathological characteristics of ALI/ARDS. To identify genes affecting hyperoxia-induced ALI (HALI), we previously established a mouse model of differential susceptibility. Genetic analysis of backcross and F2 populations derived from sensitive (C57BL/6J; B) and resistant (129X1/SvJ; X1) inbred strains identified five quantitative trait loci (QTLs; Shali1-5) linked to HALI survival time. Interestingly, analysis of these recombinant populations supported opposite within-strain effects on survival for the two major-effect QTLs. Whereas Shali1 alleles imparted the expected survival time effects (i.e., X1 alleles increased HALI resistance and B alleles increased sensitivity), the allelic effects of Shali2 were reversed (i.e., X1 alleles increased HALI sensitivity and B alleles increased resistance). For in vivo validation of these inverse allelic effects, we constructed reciprocal congenic lines to synchronize the sensitivity or resistance alleles of Shali1 and Shali2 within the same strain. Specifically, B-derived Shali1 or Shali2 QTL regions were transferred to X1 mice and X1-derived QTL segments were transferred to B mice. Our previous QTL results predicted that substituting Shali1 B alleles onto the resistant X1 background would add sensitivity. Surprisingly, not only were these mice more sensitive than the resistant X1 strain, they were more sensitive than the sensitive B strain. In stark contrast, substituting the Shali2 interval from the sensitive B strain onto the X1 background markedly increased the survival time. Reciprocal congenic lines confirmed the opposing allelic effects of Shali1 and Shali2 on HALI survival time and provide unique models to identify their respective quantitative trait genes and to critically assess the apparent bidirectional epistatic interactions between these major-effect loci

Q344ter Mutation Causes Mislocalization of Rhodopsin Molecules That Are Catalytically Active: A Mouse Model of Q344ter-Induced Retinal Degeneration

Q344ter is a naturally occurring rhodopsin mutation in humans that causes autosomal dominant retinal degeneration through mechanisms that are not fully understood, but are thought to involve an early termination that removed the trafficking signal, QVAPA, leading to its mislocalization in the rod photoreceptor cell. To better understand the disease mechanism(s), transgenic mice that express Q344ter were generated and crossed with rhodopsin knockout mice. Dark-reared Q344terrho+/− mice exhibited retinal degeneration, demonstrating that rhodopsin mislocalization caused photoreceptor cell death. This degeneration is exacerbated by light-exposure and is correlated with the activation of transducin as well as other G-protein signaling pathways. We observed numerous sub-micrometer sized vesicles in the inter-photoreceptor space of Q344terrho+/− and Q344terrho−/− retinas, similar to that seen in another rhodopsin mutant, P347S. Whereas light microscopy failed to reveal outer segment structures in Q344terrho−/− rods, shortened and disorganized rod outer segment structures were visible using electron microscopy. Thus, some Q344ter molecules trafficked to the outer segment and formed disc structures, albeit inefficiently, in the absence of full length wildtype rhodopsin. These findings helped to establish the in vivo role of the QVAPA domain as well as the pathways leading to Q344ter-induced retinal degeneration

Gap junctions in olfactory neurons modulate olfactory sensitivity

<p>Abstract</p> <p>Background</p> <p>One of the fundamental questions in olfaction is whether olfactory receptor neurons (ORNs) behave as independent entities within the olfactory epithelium. On the basis that mature ORNs express multiple connexins, I postulated that gap junctional communication modulates olfactory responses in the periphery and that disruption of gap junctions in ORNs reduces olfactory sensitivity. The data collected from characterizing connexin 43 (Cx43) dominant negative transgenic mice OlfDNCX, and from calcium imaging of wild type mice (WT) support my hypothesis.</p> <p>Results</p> <p>I generated OlfDNCX mice that express a dominant negative Cx43 protein, Cx43/β-gal, in mature ORNs to inactivate gap junctions and hemichannels composed of Cx43 or other structurally related connexins. Characterization of OlfDNCX revealed that Cx43/β-gal was exclusively expressed in areas where mature ORNs resided. Real time quantitative PCR indicated that cellular machineries of OlfDNCX were normal in comparison to WT. Electroolfactogram recordings showed decreased olfactory responses to octaldehyde, heptaldehyde and acetyl acetate in OlfDNCX compared to WT. Octaldehyde-elicited glomerular activity in the olfactory bulb, measured according to odor-elicited <it>c-fos </it>mRNA upregulation in juxtaglomerular cells, was confined to smaller areas of the glomerular layer in OlfDNCX compared to WT. In WT mice, octaldehyde sensitive neurons exhibited reduced response magnitudes after application of gap junction uncoupling reagents and the effects were specific to subsets of neurons.</p> <p>Conclusions</p> <p>My study has demonstrated that altered assembly of Cx43 or structurally related connexins in ORNs modulates olfactory responses and changes olfactory activation maps in the olfactory bulb. Furthermore, pharmacologically uncoupling of gap junctions reduces olfactory activity in subsets of ORNs. These data suggest that gap junctional communication or hemichannel activity plays a critical role in maintaining olfactory sensitivity and odor perception.</p

A glimpse into Thurston's work

We present an overview of some significant results of Thurston and their impact on mathematics. The final version of this paper will appear as Chapter 1 of the book "In the tradition of Thurston: Geometry and topology", edited by K. Ohshika and A. Papadopoulos (Springer, 2020)

Genetic Variations Strongly Influence Phenotypic Outcome in the Mouse Retina

Variation in genetic background can significantly influence the phenotypic outcome of both disease and non-disease associated traits. Additionally, differences in temporal and strain specific gene expression can also contribute to phenotypes in the mammalian retina. This is the first report of microarray based cross-strain analysis of gene expression in the retina investigating genetic background effects. Microarray analyses were performed on retinas from the following mouse strains: C57BL6/J, AKR/J, CAST/EiJ, and NOD.NON-H2-nb1 at embryonic day 18.5 (E18.5) and postnatal day 30.5 (P30.5). Over 3000 differentially expressed genes were identified between strains and developmental stages. Differential gene expression was confirmed by qRT-PCR, Western blot, and immunohistochemistry. Three major gene networks were identified that function to regulate retinal or photoreceptor development, visual perception, cellular transport, and signal transduction. Many of the genes in these networks are implicated in retinal diseases such as bradyopsia, night-blindness, and cone-rod dystrophy. Our analysis revealed strain specific variations in cone photoreceptor cell patterning and retinal function. This study highlights the substantial impact of genetic background on both development and function of the retina and the level of gene expression differences tolerated for normal retinal function. These strain specific genetic variations may also be present in other tissues. In addition, this study will provide valuable insight for the development of more accurate models for human retinal diseases

Hif1a inactivation rescues photoreceptor degeneration induced by a chronic hypoxia-like stress

Reduced choroidal blood flow and tissue changes in the ageing human eye impair oxygen delivery to photoreceptors and the retinal pigment epithelium. As a consequence, mild but chronic hypoxia may develop and disturb cell metabolism, function and ultimately survival, potentially contributing to retinal pathologies such as age-related macular degeneration (AMD). Here, we show that several hypoxia-inducible genes were expressed at higher levels in the aged human retina suggesting increased activity of hypoxia-inducible transcription factors (HIFs) during the physiological ageing process. To model chronically elevated HIF activity and investigate ensuing consequences for photoreceptors, we generated mice lacking von Hippel Lindau (VHL) protein in rods. This activated HIF transcription factors and led to a slowly progressing retinal degeneration in the ageing mouse retina. Importantly, this process depended mainly on HIF1 with only a minor contribution of HIF2. A gene therapy approach using AAV-mediated RNA interference through an anti-Hif1a shRNA significantly mitigated the degeneration suggesting a potential intervention strategy that may be applicable to human patients