Reduced Dynamics from the Unitary Group to Some Flag Manifolds : Interacting Matrix Riccati Equations

In this paper we treat the time evolution of unitary elements in the N level system and consider the reduced dynamics from the unitary group U(N) to flag manifolds of the second type (in our terminology). Then we derive a set of differential equations of matrix Riccati types interacting with one another and present an important problem on a nonlinear superposition formula that the Riccati equation satisfies. Our result is a natural generalization of the paper {\bf Chaturvedi et al} (arXiv : 0706.0964 [quant-ph]).Comment: Latex ; 13 pages ; no figur

Feeding Cues and Injected Nutrients Induce Acute Expression of Multiple Clock Genes in the Mouse Liver

The circadian clock is closely associated with energy metabolism. The liver clock can rapidly adapt to a new feeding cycle within a few days, whereas the lung clock is gradually entrained over one week. However, the mechanism underlying tissue-specific clock resetting is not fully understood. To characterize the rapid response to feeding cues in the liver clock, we examined the effects of a single time-delayed feeding on circadian rhythms in the liver and lungs of Per2::Luc reporter knockin mice. After adapting to a night-time restricted feeding schedule, the mice were fed according to a 4, 8, or 13 h delayed schedule on the last day. The phase of the liver clock was delayed in all groups with delayed feeding, whereas the lung clock remained unaffected. We then examined the acute response of clock and metabolism-related genes in the liver using focused DNA-microarrays. Clock mutant mice were bred under constant light to attenuate the endogenous circadian rhythm, and gene expression profiles were determined during 24 h of fasting followed by 8 h of feeding. Per2 and Dec1 were significantly increased within 1 h of feeding. Real-time RT-PCR analysis revealed a similarly acute response in hepatic clock gene expression caused by feeding wild type mice after an overnight fast. In addition to Per2 and Dec1, the expression of Per1 increased, and that of Rev-erbα decreased in the liver within 1 h of feeding after fasting, whereas none of these clock genes were affected in the lung. Moreover, an intraperitoneal injection of glucose combined with amino acids, but not either alone, reproduced a similar hepatic response. Our findings show that multiple clock genes respond to nutritional cues within 1 h in the liver but not in the lung

Effects of body weight and alcohol consumption on insulin sensitivity

<p>Abstract</p> <p>Background</p> <p>Obesity is a risk factor for the development of insulin resistance, which can eventually lead to type-2 diabetes. Alcohol consumption is a protective factor against insulin resistance, and thus protects against the development of type-2 diabetes. The mechanism by which alcohol protects against the development of type-2 diabetes is not well known. To determine the mechanism by which alcohol improves insulin sensitivity, we fed water or alcohol to lean, control, and obese mice. The aim of this study was to determine whether alcohol consumption and body weights affect overlapping metabolic pathways and to identify specific target genes that are regulated in these pathways.</p> <p>Method</p> <p>Adipose tissue dysfunction has been associated with the development of type-2 diabetes. We assessed possible gene expression alterations in epididymal white adipose tissue (WAT). We obtained WAT from mice fed a calorie restricted (CR), low fat (LF Control) or high fat (HF) diets and either water or 20% ethanol in the drinking water. We screened the expression of genes related to the regulation of energy homeostasis and insulin regulation using a gene array composed of 384 genes.</p> <p>Results</p> <p>Obesity induced insulin resistance and calorie restriction and alcohol improved insulin sensitivity. The insulin resistance in obese mice was associated with the increased expression of inflammatory markers Cd68, Il-6 and Il-1α; in contrast, most of these genes were down-regulated in CR mice. Anti-inflammatory factors such as Il-10 and adrenergic beta receptor kinase 1 (Adrbk1) were decreased in obese mice and increased by CR and alcohol. Also, we report a direct correlation between body weight and the expression of the following genes: Kcnj11 (potassium inwardly-rectifying channel, subfamily J, member 11), Lpin2 (lipin2), and Dusp9 (dual-specificity MAP kinase phosphatase 9).</p> <p>Conclusion</p> <p>We show that alcohol consumption increased insulin sensitivity. Additionally, alterations in insulin sensitivity related with obesity were coupled with alterations in inflammatory genes. We provide evidence that alcohol may improve insulin sensitivity by up-regulating anti-inflammatory genes. Moreover, we have indentified potential gene targets in energy metabolic pathways and signal transducers that may contribute to obesity-related insulin resistance as well as calorie restriction and alcohol-induced insulin sensitivity.</p