Exact 2-point function in Hermitian matrix model

J. Harer and D. Zagier have found a strikingly simple generating function for exact (all-genera) 1-point correlators in the Gaussian Hermitian matrix model. In this paper we generalize their result to 2-point correlators, using Toda integrability of the model. Remarkably, this exact 2-point correlation function turns out to be an elementary function - arctangent. Relation to the standard 2-point resolvents is pointed out. Some attempts of generalization to 3-point and higher functions are described.Comment: 31 pages, 1 figur

Nuclear Receptor Rev-erb Alpha (Nr1d1) Functions in Concert with Nr2e3 to Regulate Transcriptional Networks in the Retina

The majority of diseases in the retina are caused by genetic mutations affecting the development and function of photoreceptor cells. The transcriptional networks directing these processes are regulated by genes such as nuclear hormone receptors. The nuclear hormone receptor gene Rev-erb alpha/Nr1d1 has been widely studied for its role in the circadian cycle and cell metabolism, however its role in the retina is unknown. In order to understand the role of Rev-erb alpha/Nr1d1 in the retina, we evaluated the effects of loss of Nr1d1 to the developing retina and its co-regulation with the photoreceptor-specific nuclear receptor gene Nr2e3 in the developing and mature retina. Knock-down of Nr1d1 expression in the developing retina results in pan-retinal spotting and reduced retinal function by electroretinogram. Our studies show that NR1D1 protein is co-expressed with NR2E3 in the outer neuroblastic layer of the developing mouse retina. In the adult retina, NR1D1 is expressed in the ganglion cell layer and is co-expressed with NR2E3 in the outer nuclear layer, within rods and cones. Several genes co-targeted by NR2E3 and NR1D1 were identified that include: Nr2c1, Recoverin, Rgr, Rarres2, Pde8a, and Nupr1. We examined the cyclic expression of Nr1d1 and Nr2e3 over a twenty-four hour period and observed that both nuclear receptors cycle in a similar manner. Taken together, these studies reveal a novel role for Nr1d1, in conjunction with its cofactor Nr2e3, in regulating transcriptional networks critical for photoreceptor development and function

Nr2e3 is a Genetic Modifier That Rescues Retinal Degeneration and Promotes Homeostasis in Multiple Models of Retinitis Pigmentosa

Recent advances in viral vector engineering, as well as an increased understanding of the cellular and molecular mechanism of retinal diseases, have led to the development of novel gene therapy approaches. Furthermore, ease of accessibility and ocular immune privilege makes the retina an ideal target for gene therapies. In this study, the nuclear hormone receptor gene Nr2e3 was evaluated for efficacy as broad-spectrum therapy to attenuate early to intermediate stages of retinal degeneration in five unique mouse models of retinitis pigmentosa (RP). RP is a group of heterogenic inherited retinal diseases associated with over 150 gene mutations, affecting over 1.5 million individuals worldwide. RP varies in age of onset, severity, and rate of progression. In addition, ~40% of RP patients cannot be genetically diagnosed, confounding the ability to develop personalized RP therapies. Remarkably, Nr2e3 administered therapy resulted in reduced retinal degeneration as observed by increase in photoreceptor cells, improved electroretinogram, and a dramatic molecular reset of key transcription factors and associated gene networks. These therapeutic effects improved retinal homeostasis in diseased tissue. Results of this study provide evidence that Nr2e3 can serve as a broad-spectrum therapy to treat multiple forms of RP

Polymorphic variants of genes encoding Ca(2+)-transporting sarcoplasmic reticulum proteins in the progression of chronic heart failure

Aim. To study the association between polymorphic rs1860561 variants of Ca(2+)-ATPase SERCA2a (ATP2A2) gene and rs3766871 of ryanodine receptor (RYR2) gene and the severity of chronic heart failure (CHF).Material and methods. We determined rs1860561 and rs3766871 variants of the ATP2A2 and RYR2 genes, respectively, in 168 patients with coronary artery disease (CAD) and CHF using real-time polymerase chain reaction.Results. A statistically significant (p=0,046) decrease in the left ventricular ejection fraction in AA homozygotes of the ATP2A2 gene compared to carriers of the G allele was shown. But among GG homozygotes, patients with FC II CHF prevailed and participants with FC I CHF were less common than among patients with genotype GA (p=0,041).Conclusion. The association of the AA genotype carriage for the rs1860561 variant of the ATP2A2 gene encoding Ca(2+)-ATPase SERCA2a, with a decrease in the left ventricle ejection fraction in patients with CHF and CAD was revealed. At the same time, among the GG homozygotes, FC I CHF was the least prevalent. There was no association of the rY3766871 variant of the RYR2 gene with CHF severity