Two isoperimetric inequalities for the Sobolev constant

In this note we prove two isoperimetric inequalities for the sharp constant in the Sobolev embedding and its associated extremal function. The first such inequality is a variation on the classical Schwarz Lemma from complex analysis, similar to recent inequalities of Burckel, Marshall, Minda, Poggi-Corradini, and Ransford, while the second generalises an isoperimetric inequality for the first eigenfunction of the Laplacian due to Payne and Rayner.Comment: 11 page

Alterations in hippocampal serotonergic and INSR function in streptozotocin induced diabetic rats exposed to stress: neuroprotective role of pyridoxine and Aegle marmelose

Diabetes and stress stimulate hippocampal 5-HT synthesis, metabolism and release. The present study was carried out to find the effects of insulin, Aegle marmelose alone and in combination with pyridoxine on the hippocampal 5-HT, 5-HT2A receptor subtype, gene expression studies on 5-HT2A, 5-HTT, INSR, immunohistochemical studies and elevated plus maze in streptozotocin induced diabetic rats. 5-HT content showed a significant decrease (p < 0.001) and a significant increase (p < 0.001) in 5-HIAA in hippocampus of diabetic rats compared to control. 5-HT receptor binding parameters Bmax and Kd showed a significant decrease (p < 0.001) whereas 5-HT2A receptor binding parameters Bmax showed a significant decrease (p < 0.001) with a significant increase (p < 0.05) in Kd in hippocampus of diabetic rats compared to control. Gene expression studies of 5-HT2A, 5-HTT and INSR in hippocampus showed a significant down regulation (p < 0.001) in diabetic rats compared to control. Pyridoxine treated in combination with insulin and A. marmelose to diabetic rats reversed the 5-HT content, Bmax , Kd of 5-HT, 5-HT2A and gene expression of 5-HT2A, 5-HTT and INSR in hippocampus to near control. The gene expression of 5-HT2A and 5-HTT were confirmed by immunohistochemical studies. Behavioural studies using elevated plus maze showed that serotonin through its transporter significantly increased (p < 0.001) anxiety-related traits in diabetic rats which were corrected by combination therapy. Our results suggest that pyridoxine treated in combination with insulin and A. marmelose has a role in the regulation of insulin synthesis and release, normalising diabetic related stress and anxiety through hippocampal serotonergic function. This has clinical significance in the management of diabetes

Carbon star survey in the Local Group. VII. NGC 3109 a galaxy without a stellar halo

We present a CFH12K wide field survey of the carbon star population in and around NGC 3109. Carbon stars, the brightest members of the intermediate-age population, were found nearly exclusively in and near the disk of NGC 3109, ruling out the existence of an extensive intermediate-age halo like the one found in NGC 6822. Over 400 carbon stars identified have = -4.71, confirming the nearly universality of mean magnitude of C star populations in Local Group galaxies. Star counts over the field reveal that NGC 3109 is a truncated disk shaped galaxy without an extensive stellar halo. The minor axis star counts reach the foreground density between 4' and 5', a distance that can be explained by an inclined disk rather than a spheroidal halo. We calculate a global C/M ratio of 1.75 +/- 0.20, a value expected for such a metal poor galaxy.Comment: Accepted in Astronomy and Astrophysic

High-Fat Diet: Bacteria Interactions Promote Intestinal Inflammation Which Precedes and Correlates with Obesity and Insulin Resistance in Mouse

Obesity induced by high fat (HF) diet is associated with inflammation which contributes to development of insulin resistance. Most prior studies have focused on adipose tissue as the source of obesity-associated inflammation. Increasing evidence links intestinal bacteria to development of diet-induced obesity (DIO). This study tested the hypothesis that HF western diet and gut bacteria interact to promote intestinal inflammation, which contributes to the progression of obesity and insulin resistance.Conventionally raised specific-pathogen free (CONV) and germ-free (GF) mice were given HF or low fat (LF) diet for 2-16 weeks. Body weight and adiposity were measured. Intestinal inflammation was assessed by evaluation of TNF-alpha mRNA and activation of a NF-kappaB(EGFP) reporter gene. In CONV but not GF mice, HF diet induced increases in body weight and adiposity. HF diet induced ileal TNF-alpha mRNA in CONV but not GF mice and this increase preceded obesity and strongly and significantly correlated with diet induced weight gain, adiposity, plasma insulin and glucose. In CONV mice HF diet also resulted in activation of NF-kappaB(EGFP) in epithelial cells, immune cells and endothelial cells of small intestine. Further experiments demonstrated that fecal slurries from CONV mice fed HF diet are sufficient to activate NF-kappaB(EGFP) in GF NF-kappaB(EGFP) mice.Bacteria and HF diet interact to promote proinflammatory changes in the small intestine, which precede weight gain and obesity and show strong and significant associations with progression of obesity and development of insulin resistance. To our knowledge, this is the first evidence that intestinal inflammation is an early consequence of HF diet which may contribute to obesity and associated insulin resistance. Interventions which limit intestinal inflammation induced by HF diet and bacteria may protect against obesity and insulin resistance

Toll-Like Receptor 9-Dependent Macrophage Activation by Entamoeba histolytica DNA

Activation of the innate immune system by bacterial DNA and DNA of other invertebrates represents a pathogen recognition mechanism. In this study we investigated macrophage responses to DNA from the intestinal protozoan parasite Entamoeba histolytica. E. histolytica genomic DNA was purified from log-phase trophozoites and tested with the mouse macrophage cell line RAW 264.7. RAW cells treated with E. histolytica DNA demonstrated an increase in levels of tumor necrosis factor alpha (TNF-α) mRNA and protein production. TNF-α production was blocked by pretreatment with chloroquine or monensin. In fact, an NF-κB luciferase reporter assay in HEK cells transfected with human TLR9 demonstrated that E. histolytica DNA signaled through Toll-like receptor 9 (TLR9) in a manner similar to that seen with CpG-ODN. Immunofluorescence assays confirmed NF-κB activation in RAW cells, as seen by nuclear translocation of the p65 subunit. Western blot analysis demonstrated mitogen-activated protein kinase activation by E. histolytica DNA. E. histolytica DNA effects were abolished in MYD88−/− mouse-derived macrophages. In the context of disease, immunization with E. histolytica DNA protected gerbils from an E. histolytica challenge infection. Taken together, these results demonstrate that E. histolytica DNA is recognized by TLR9 to activate macrophages and may provide an innate defense mechanism characterized by the induction of the inflammatory mediator TNF-α

IKKβ and Phosphatidylinositol 3-Kinase/Akt Participate in Non-pathogenic Gram-negative Enteric Bacteria-induced RelA Phosphorylation and NF-κB Activation in Both Primary and Intestinal Epithelial Cell Lines

Pathogenic and enteroinvasive bacteria have been shown to trigger the I kappa B/NF-kappa B transcriptional system and proinflammatory gene expression in epithelial cells. In this study, we investigated the molecular mechanism of the commensal Gram-negative Bacteroides vulgatus-induced NF-kappa B signal transduction in intestinal epithelial cells (IEC). We report that B. vulgatus induced interleukin-1 receptor-associated kinase-1 degradation, I kappa B alpha phosphorylation/degradation, RelA and Akt phosphorylation, as well as NF-kappa B DNA binding and NF-kappa B transcriptional activity in rat non-transformed IEC-6 cells. B. vulgatus- but not interleukin-1 beta-mediated NF-kappa B transcriptional activity was inhibited by dominant negative (dn) toll-like receptor 4. Of importance, B. vulgatus induced I kappa B alpha phosphorylation/degradation and IKK alpha/beta and RelA phosphorylation in primary IEC derived from germ-free or mono-associated HLA-B27 transgenic and wild type rats, demonstrating the physiological relevance of non-pathogenic bacterial signaling in IEC. Adenoviral delivery of dn IKK beta or treatment with wortmannin inhibited B. vulgatus-induced endogenous RelA Ser-536 and GST-p65TAD (Ser-529/Ser-536) phosphorylation as well as NF-kappa B transcriptional activity in IEC-6 cells, suggesting a critical role of IKK beta and phosphatidylinositol 3-kinase/Akt in bacteria-induced RelA phosphorylation and NF-kappa B activation. Interestingly, B. vulgatus-induced I kappa B alpha degradation and NF-kappa B transcriptional activity in IEC transwell cultures were inhibited in the presence of lymphocytes. We propose that non-pathogenic B. vulgatus activates the NF-kappa B signaling pathway through both I kappa B degradation and RelA phosphorylation but that immune cells mediate tolerance of IEC to this commensal bacteria

Tumor Necrosis Factor (TNF) α Increases Collagen Accumulation and Proliferation in Intestinal Myofibroblasts via TNF Receptor 2

Intestinal fibrosis is an incurable complication of Crohn's disease involving increased numbers of collagen-producing myofibroblasts. Tumor necrosis factor (TNF) alpha has defined proinflammatory roles in Crohn's disease but its role in fibrosis is unclear. We tested the hypothesis that TNFalpha increases collagen accumulation and proliferation in intestinal myofibroblasts and has additive effects in combination with insulin-like growth factor (IGF) I. The mechanisms, TNF receptor isoform, and downstream signaling pathways were examined. Intestinal myofibroblasts from wild-type (WT) mice or mice homozygous for disruption of genes encoding TNFR1 (TNFR1-/-), TNFR2 (TNFR2-/-), or both (TNFR1/2-/-), were treated with TNFalpha, IGF-I, or both. In WT cells, TNFalpha and IGF-I stimulated type I collagen accumulation and DNA synthesis in an additive manner. IGF-I, but not TNFalpha, stimulated type I collagen gene activation. TNFalpha, but not IGF-I, induced tissue inhibitor of metalloproteinase-1 (TIMP-1) expression and reduced matrix metalloproteinases-2 activity and collagen degradation. TNFalpha also activated ERK1/2. These responses to TNFalpha were absent in TNFR2-/- and TNFR1/2-/- myofibroblasts, whereas TNFR1-/- cells showed similar responses to WT. Inhibition of ERK1/2 diminished TNFalpha induced DNA synthesis in WT and TNFR1-/- cells. Differences in TNFalpha-induced STAT3/DNA binding activity and not NFkappaB and AP-1 transcriptional activation correlated with impaired collagen accumulation/TIMP-1 induction in TNFR2(-/-) cells. Constitutively active STAT3 rescued TIMP-1 expression in TNFR2-/- cells. We conclude that TNFalpha and IGF-I may additively contribute to fibrosis during intestinal inflammation. TNFR2 is a primary mediator of fibrogenic actions of TNFalpha acting through ERK1/2 to stimulate proliferation and through STAT3 to stimulate TIMP-1 and inhibit collagen degradation