Homoclinic Solutions for a Class of Second Order Nonautonomous Singular Hamiltonian Systems

We are concerned with the existence of homoclinic solutions for the following second order nonautonomous singular Hamiltonian systems u¨+atWuu=0, (HS) where -∞<t<+∞, u=u1,u2, …,uN∈ℝNN≥3, a:ℝ→ℝ is a continuous bounded function, and the potential W:ℝN∖{ξ}→ℝ has a singularity at 0≠ξ∈ℝN, and Wuu is the gradient of W at u. The novelty of this paper is that, for the case that N≥3 and (HS) is nonautonomous (neither periodic nor almost periodic), we show that (HS) possesses at least one nontrivial homoclinic solution. Our main hypotheses are the strong force condition of Gordon and the uniqueness of a global maximum of W. Different from the cases that (HS) is autonomous at≡1 or (HS) is periodic or almost periodic, as far as we know, this is the first result concerning the case that (HS) is nonautonomous and N≥3. Besides the usual conditions on W, we need the assumption that a′t<0 for all t∈ℝ to guarantee the existence of homoclinic solution. Recent results in the literature are generalized and significantly improved

Dynamical Aspects of Initial/Boundary Value Problems for Ordinary Differential Equations

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Intraretinal signaling by ganglion cell photoreceptors to dopaminergic amacrine neurons

Retinal dopaminergic amacrine neurons (DA neurons) play a central role in reconfiguring retinal function according to prevailing illumination conditions, yet the mechanisms by which light regulates their activity are poorly understood. We investigated the means by which sustained light responses are evoked in DA neurons. Sustained light responses were driven by cationic currents and persisted in vitro and in vivo in the presence of L-AP4, a blocker of retinal ON-bipolar cells. Several characteristics of these L-AP4-resistant light responses suggested that they were driven by melanopsin-expressing intrinsically photosensitive retinal ganglion cells (ipRGCs), including long latencies, marked poststimulus persistence, and a peak spectral sensitivity of 478 nm. Furthermore, sustained DA neuron light responses, but not transient DA neuron responses, persisted in rod/cone degenerate retinas, in which ipRGCs account for virtually all remaining retinal phototransduction. Thus, ganglion-cell photoreceptors provide excitatory drive to DA neurons, most likely by way of the coramification of their dendrites and the processes of DA neurons in the inner plexiform layer. This unprecedented centrifugal outflow of ganglion-cell signals within the retina provides a novel basis for the restructuring of retinal circuits by light

Eigenvalues of higher order Sturm-Liouville boundary value problems with derivatives in nonlinear terms

We shall consider the Sturm-Liouville boundary value problem y(m)(t)+λF(t,y(t),y′(t),…,y(q)(t))=0, t∈(0,1), y(k)(0)=0, 0≤k≤m−3, ζy(m−2)(0)−θy(m−1)(0)=0, ρy(m−2)(1)+δy(m−1)(1)=0 where m≥3, 1≤q≤m−2, and λ>0. It is noted that the boundary value problem considered has a derivative-dependent nonlinear term, which makes the investigation much more challenging. In this paper we shall develop a new technique to characterize the eigenvalues λ so that the boundary value problem has a positive solution. Explicit eigenvalue intervals are also established. Some examples are included to dwell upon the usefulness of the results obtained.Published versio

Light-Induced Fos Expression in Intrinsically Photosensitive Retinal Ganglion Cells in Melanopsin Knockout (Opn4−/−) Mice

Retinal ganglion cells that express the photopigment melanopsin are intrinsically photosensitive (ipRGCs) and exhibit robust synaptically driven ON-responses to light, yet they will continue to depolarize in response to light when all synaptic input from rod and cone photoreceptors is removed. The light-evoked increase in firing of classical ganglion cells is determined by synaptic input from ON-bipolar cells in the proximal sublamina of the inner plexiform layer. OFF-bipolar cells synapse with ganglion cell dendrites in the distal sublamina of the inner plexiform layer. Of the several types of ipRGC that have been described, M1 ipRGCs send dendrites exclusively into the OFF region of the inner plexiform layer where they stratify near the border of the inner nuclear layer. We tested whether M1 ipRGCs with dendrites restricted to the OFF sublamina of the inner plexiform layer receive synaptic ON-bipolar input by examining light-induced gene expression in vivo using melanopsin knockout mice. Mice in which both copies of the melanopsin gene (opn4) have been replaced with the tau-lacZ gene (homozygous tau-lacZ+/+ knockin mice) are melanopsin knockouts (opn4−/−) but M1 ipRGCs are specifically identified by their expression of β-galactosidase. Approximately 60% of M1 ipRGCs in Opn4−/− mice exposed to 3 hrs of light expressed c-Fos; no β-galactosidase-positive RGCs expressed c-Fos in the dark. Intraocular application of L-AP4, a compound which blocks transmission of visual signals between photoreceptors and ON-bipolar cells significantly reduced light-evoked c-Fos expression in M1 ipRGCs compared to saline injected eyes (66% saline vs 27% L-AP4). The results are the first description of a light-evoked response in an ipRGC lacking melanopsin and provide in vivo confirmation of previous in vitro observations illustrating an unusual circuit in the retina in which ganglion cells sending dendrites to the OFF sublamina of the inner plexiform layer receive excitatory synaptic input from ON-bipolar cells

Manganese superoxide dismutase Ala-9Val polymorphism and risk of breast cancer in a population-based case–control study of African Americans and whites

INTRODUCTION: A polymorphism in the manganese superoxide dismutase (MnSOD) gene, Ala-9Val, has been examined in association with breast cancer risk in several epidemiologic studies. Results suggest that the Ala allele increases the risk of breast cancer and modifies the effects of environmental exposures that produce oxidative damage to DNA. METHODS: We examined the role of the MnSOD Ala-9Val polymorphism in a population-based case–control study of invasive and in situ breast cancer in North Carolina. Genotypes were evaluated for 2025 cases (760 African Americans and 1265 whites) and for 1812 controls (677 African Americans and 1135 whites). RESULTS: The odds ratio for MnSOD Ala/Ala versus any MnSOD Val genotypes was not elevated in African Americans (odds ratio = 0.9, 95% confidence interval = 0.7–1.2) or in whites (odds ratio = 1.0, 95% confidence interval = 0.8–1.2). Greater than additive joint effects were observed for the Ala/Ala genotype and smoking, radiation to the chest, and occupational exposure to ionizing radiation. Antagonism was observed between the Ala/Ala genotype and the use of nonsteroidal anti-inflammatory drugs. CONCLUSIONS: The MnSOD genotype may contribute to an increased risk of breast cancer in the presence of specific environmental exposures. These results provide further evidence for the importance of reactive oxygen species and of oxidative DNA damage in the etiology of breast cancer

Calcineurin Interacts with PERK and Dephosphorylates Calnexin to Relieve ER Stress in Mammals and Frogs

Background: The accumulation of misfolded proteins within the endoplasmic reticulum (ER) triggers a cellular process known as the Unfolded Protein Response (UPR). One of the earliest responses is the attenuation of protein translation. Little is known about the role that Ca 2+ mobilization plays in the early UPR. Work from our group has shown that cytosolic phosphorylation of calnexin (CLNX) controls Ca 2+ uptake into the ER via the sarco-endoplasmic reticulum Ca 2+-ATPase (SERCA) 2b. Methodology/Principal Findings: Here, we demonstrate that calcineurin (CN), a Ca 2+ dependent phosphatase, associates with the (PKR)-like ER kinase (PERK), and promotes PERK auto-phosphorylation. This association, in turn, increases the phosphorylation level of eukaryotic initiation factor-2 a (eIF2-a) and attenuates protein translation. Data supporting these conclusions were obtained from co-immunoprecipitations, pull-down assays, in-vitro kinase assays, siRNA treatments and [ 35 S]-methionine incorporation measurements. The interaction of CN with PERK was facilitated at elevated cytosolic Ca 2+ concentrations and involved the cytosolic domain of PERK. CN levels were rapidly increased by ER stressors, which could be blocked by siRNA treatments for CN-Aa in cultured astrocytes. Downregulation of CN blocked subsequent ER-stress-induced increases in phosphorylated elF2-a. CN knockdown in Xenopus oocytes predisposed them to induction of apoptosis. We also found that CLNX was dephosphorylated by CN when Ca 2+ increased. These data were obtained from [c 32 P]-CLN

A genome-wide association study identifies new susceptibility loci for esophageal adenocarcinoma and Barrett's esophagus.

Esophageal adenocarcinoma is a cancer with rising incidence and poor survival. Most such cancers arise in a specialized intestinal metaplastic epithelium, which is diagnostic of Barrett's esophagus. In a genome-wide association study, we compared esophageal adenocarcinoma cases (n = 2,390) and individuals with precancerous Barrett's esophagus (n = 3,175) with 10,120 controls in 2 phases. For the combined case group, we identified three new associations. The first is at 19p13 (rs10419226: P = 3.6 × 10(-10)) in CRTC1 (encoding CREB-regulated transcription coactivator), whose aberrant activation has been associated with oncogenic activity. A second is at 9q22 (rs11789015: P = 1.0 × 10(-9)) in BARX1, which encodes a transcription factor important in esophageal specification. A third is at 3p14 (rs2687201: P = 5.5 × 10(-9)) near the transcription factor FOXP1, which regulates esophageal development. We also refine a previously reported association with Barrett's esophagus near the putative tumor suppressor gene FOXF1 at 16q24 and extend our findings to now include esophageal adenocarcinoma