The Polynomial Carathéodory—Fejér Approximation Method for Jordan Regions

We propose a method for the approximation of analytic functions on Jordan regions that is based on a Carathéodory—Fejér type of economization of the Faber series. The method turns out to be very effective if the boundary of the region is analytic. It often still works when the region degenerates to a Jordan arc. We also derive related lower and upper bounds for the error of the best approximatio

The Carathéodory—Fejér Extension of a Finite Geometric Series

It is shown that the Caratheodory—Fejer extension of a finite geometric series can be given explicitly up to a simple polynomial equation in an auxiliary variable. This result allows us to analyse the Caratheodory-Fejer approximation method in the case where the quotients of successive Maclaurin coefficients of the given function tend to a limi

Neurochemical Characterization of Body Weight-Regulating Leptin Receptor Neurons in the Nucleus of the Solitary Tract

The action of peripherally released leptin at long-form leptin receptors (LepRb) within the brain represents a fundamental axis in the regulation of energy homeostasis and body weight. Efforts to delineate the neuronal mediators of leptin action have recently focused on extrahypothalamic populations and have revealed that leptin action within the nucleus of the solitary tract (NTS) is critical for normal appetite and body weight regulation. To elucidate the neuronal circuits that mediate leptin action within the NTS, we employed multiple transgenic reporter lines to characterize the neurochemical identity of LepRb-expressing NTS neurons. LepRb expression was not detected in energy balance-associated NTS neurons that express cocaine- and amphetamine-regulated transcript, brain-derived neurotrophic factor, neuropeptide Y, nesfatin, catecholamines, γ-aminobutyric acid, prolactin-releasing peptide, or nitric oxide synthase. The population of LepRb-expressing NTS neurons was comprised of subpopulations marked by a proopiomelanocortin-enhanced green fluorescent protein (EGFP) transgene and distinct populations that express proglucagon and/or cholecystokinin. The significance of leptin action on these three populations of NTS neurons was assessed in leptin-deficient Ob/Ob mice, revealing increased NTS proglucagon and cholecystokinin, but not proopiomelanocortin, expression. These data provide new insight into the appetitive brainstem circuits engaged by leptin

Unraveling the Genetics of Human Obesity

The use of modern molecular biology tools in deciphering the perturbed biochemistry and physiology underlying the obese state has proven invaluable. Identifying the hypothalamic leptin/melanocortin pathway as critical in many cases of monogenic obesity has permitted targeted, hypothesis-driven experiments to be performed, and has implicated new candidates as causative for previously uncharacterized clinical cases of obesity. Meanwhile, the effects of mutations in the melanocortin-4 receptor gene, for which the obese phenotype varies in the degree of severity among individuals, are now thought to be influenced by one's environmental surroundings. Molecular approaches have revealed that syndromes (Prader-Willi and Bardet-Biedl) previously assumed to be controlled by a single gene are, conversely, regulated by multiple elements. Finally, the application of comprehensive profiling technologies coupled with creative statistical analyses has revealed that interactions between genetic and environmental factors are responsible for the common obesity currently challenging many Westernized societies. As such, an improved understanding of the different “types” of obesity not only permits the development of potential therapies, but also proposes novel and often unexpected directions in deciphering the dysfunctional state of obesity

The Number of X Chromosomes Causes Sex Differences in Adiposity in Mice

Sexual dimorphism in body weight, fat distribution, and metabolic disease has been attributed largely to differential effects of male and female gonadal hormones. Here, we report that the number of X chromosomes within cells also contributes to these sex differences. We employed a unique mouse model, known as the “four core genotypes,” to distinguish between effects of gonadal sex (testes or ovaries) and sex chromosomes (XX or XY). With this model, we produced gonadal male and female mice carrying XX or XY sex chromosome complements. Mice were gonadectomized to remove the acute effects of gonadal hormones and to uncover effects of sex chromosome complement on obesity. Mice with XX sex chromosomes (relative to XY), regardless of their type of gonad, had up to 2-fold increased adiposity and greater food intake during daylight hours, when mice are normally inactive. Mice with two X chromosomes also had accelerated weight gain on a high fat diet and developed fatty liver and elevated lipid and insulin levels. Further genetic studies with mice carrying XO and XXY chromosome complements revealed that the differences between XX and XY mice are attributable to dosage of the X chromosome, rather than effects of the Y chromosome. A subset of genes that escape X chromosome inactivation exhibited higher expression levels in adipose tissue and liver of XX compared to XY mice, and may contribute to the sex differences in obesity. Overall, our study is the first to identify sex chromosome complement, a factor distinguishing all male and female cells, as a cause of sex differences in obesity and metabolism

NPY Neuron-Specific Y2 Receptors Regulate Adipose Tissue and Trabecular Bone but Not Cortical Bone Homeostasis in Mice

BACKGROUND: Y2 receptor signalling is known to be important in neuropeptide Y (NPY)-mediated effects on energy homeostasis and bone physiology. Y2 receptors are located post-synaptically as well as acting as auto receptors on NPY-expressing neurons, and the different roles of these two populations of Y2 receptors in the regulation of energy homeostasis and body composition are unclear. METHODOLOGY/PRINCIPAL FINDINGS: We thus generated two conditional knockout mouse models, Y2(lox/lox) and NPYCre/+;Y2(lox/lox), in which Y2 receptors can be selectively ablated either in the hypothalamus or specifically in hypothalamic NPY-producing neurons of adult mice. Specific deletion of hypothalamic Y2 receptors increases food intake and body weight compared to controls. Importantly, specific ablation of hypothalamic Y2 receptors on NPY-containing neurons results in a significantly greater adiposity in female but not male mice, accompanied by increased hepatic triglyceride levels, decreased expression of liver carnitine palmitoyltransferase (CPT1) and increased expression of muscle phosphorylated acetyl-CoA carboxylase (ACC). While food intake, body weight, femur length, bone mineral content, density and cortical bone volume and thickness are not significantly altered, trabecular bone volume and number were significantly increased by hypothalamic Y2 deletion on NPY-expressing neurons. Interestingly, in situ hybridisation reveals increased NPY and decreased proopiomelanocortin (POMC) mRNA expression in the arcuate nucleus of mice with hypothalamus-specific deletion of Y2 receptors in NPY neurons, consistent with a negative feedback mechanism between NPY expression and Y2 receptors on NPY-ergic neurons. CONCLUSIONS/SIGNIFICANCE: Taken together these data demonstrate the anti-obesogenic role of Y2 receptors in the brain, notably on NPY-ergic neurons, possibly via inhibition of NPY neurons and concomitant stimulation of POMC-expressing neurons in the arcuate nucleus of the hypothalamus, reducing lipogenic pathways in liver and/or skeletal muscle in females. These data also reveal as an anti-osteogenic effect of Y2 receptors on hypothalamic NPY-expressing neurons on trabecular but not on cortical bone

Intraperitoneal drain placement and outcomes after elective colorectal surgery: international matched, prospective, cohort study

Despite current guidelines, intraperitoneal drain placement after elective colorectal surgery remains widespread. Drains were not associated with earlier detection of intraperitoneal collections, but were associated with prolonged hospital stay and increased risk of surgical-site infections.Background Many surgeons routinely place intraperitoneal drains after elective colorectal surgery. However, enhanced recovery after surgery guidelines recommend against their routine use owing to a lack of clear clinical benefit. This study aimed to describe international variation in intraperitoneal drain placement and the safety of this practice. Methods COMPASS (COMPlicAted intra-abdominal collectionS after colorectal Surgery) was a prospective, international, cohort study which enrolled consecutive adults undergoing elective colorectal surgery (February to March 2020). The primary outcome was the rate of intraperitoneal drain placement. Secondary outcomes included: rate and time to diagnosis of postoperative intraperitoneal collections; rate of surgical site infections (SSIs); time to discharge; and 30-day major postoperative complications (Clavien-Dindo grade at least III). After propensity score matching, multivariable logistic regression and Cox proportional hazards regression were used to estimate the independent association of the secondary outcomes with drain placement. Results Overall, 1805 patients from 22 countries were included (798 women, 44.2 per cent; median age 67.0 years). The drain insertion rate was 51.9 per cent (937 patients). After matching, drains were not associated with reduced rates (odds ratio (OR) 1.33, 95 per cent c.i. 0.79 to 2.23; P = 0.287) or earlier detection (hazard ratio (HR) 0.87, 0.33 to 2.31; P = 0.780) of collections. Although not associated with worse major postoperative complications (OR 1.09, 0.68 to 1.75; P = 0.709), drains were associated with delayed hospital discharge (HR 0.58, 0.52 to 0.66; P < 0.001) and an increased risk of SSIs (OR 2.47, 1.50 to 4.05; P < 0.001). Conclusion Intraperitoneal drain placement after elective colorectal surgery is not associated with earlier detection of postoperative collections, but prolongs hospital stay and increases SSI risk

Pathogenesis of adolescent idiopathic scoliosis in girls - a double neuro-osseous theory involving disharmony between two nervous systems, somatic and autonomic expressed in the spine and trunk: possible dependency on sympathetic nervous system and hormones with implications for medical therapy

Anthropometric data from three groups of adolescent girls - preoperative adolescent idiopathic scoliosis (AIS), screened for scoliosis and normals were analysed by comparing skeletal data between higher and lower body mass index subsets. Unexpected findings for each of skeletal maturation, asymmetries and overgrowth are not explained by prevailing theories of AIS pathogenesis. A speculative pathogenetic theory for girls is formulated after surveying evidence including: (1) the thoracospinal concept for right thoracic AIS in girls; (2) the new neuroskeletal biology relating the sympathetic nervous system to bone formation/resorption and bone growth; (3) white adipose tissue storing triglycerides and the adiposity hormone leptin which functions as satiety hormone and sentinel of energy balance to the hypothalamus for long-term adiposity; and (4) central leptin resistance in obesity and possibly in healthy females. The new theory states that AIS in girls results from developmental disharmony expressed in spine and trunk between autonomic and somatic nervous systems. The autonomic component of this double neuro-osseous theory for AIS pathogenesis in girls involves selectively increased sensitivity of the hypothalamus to circulating leptin (genetically-determined up-regulation possibly involving inhibitory or sensitizing intracellular molecules, such as SOC3, PTP-1B and SH2B1 respectively), with asymmetry as an adverse response (hormesis); this asymmetry is routed bilaterally via the sympathetic nervous system to the growing axial skeleton where it may initiate the scoliosis deformity (leptin-hypothalamic-sympathetic nervous system concept = LHS concept). In some younger preoperative AIS girls, the hypothalamic up-regulation to circulating leptin also involves the somatotropic (growth hormone/IGF) axis which exaggerates the sympathetically-induced asymmetric skeletal effects and contributes to curve progression, a concept with therapeutic implications. In the somatic nervous system, dysfunction of a postural mechanism involving the CNS body schema fails to control, or may induce, the spinal deformity of AIS in girls (escalator concept). Biomechanical factors affecting ribs and/or vertebrae and spinal cord during growth may localize AIS to the thoracic spine and contribute to sagittal spinal shape alterations. The developmental disharmony in spine and trunk is compounded by any osteopenia, biomechanical spinal growth modulation, disc degeneration and platelet calmodulin dysfunction. Methods for testing the theory are outlined. Implications are discussed for neuroendocrine dysfunctions, osteopontin, sympathoactivation, medical therapy, Rett and Prader-Willi syndromes, infantile idiopathic scoliosis, and human evolution. AIS pathogenesis in girls is predicated on two putative normal mechanisms involved in trunk growth, each acquired in evolution and unique to humans

Basal fatty acid oxidation increases after recurrent low glucose in human primary astrocytes

YesAims/hypothesis Hypoglycaemia is a major barrier to good glucose control in type 1 diabetes. Frequent hypoglycaemic episodes impair awareness of subsequent hypoglycaemic bouts. Neural changes underpinning awareness of hypoglycaemia are poorly defined and molecular mechanisms by which glial cells contribute to hypoglycaemia sensing and glucose counterregulation require further investigation. The aim of the current study was to examine whether, and by what mechanism, human primary astrocyte (HPA) function was altered by acute and recurrent low glucose (RLG). Methods To test whether glia, specifically astrocytes, could detect changes in glucose, we utilised HPA and U373 astrocytoma cells and exposed them to RLG in vitro. This allowed measurement, with high specificity and sensitivity, of RLG-associated changes in cellular metabolism. We examined changes in protein phosphorylation/expression using western blotting. Metabolic function was assessed using a Seahorse extracellular flux analyser. Immunofluorescent imaging was used to examine cell morphology and enzymatic assays were used to measure lactate release, glycogen content, intracellular ATP and nucleotide ratios. Results AMP-activated protein kinase (AMPK) was activated over a pathophysiologically relevant glucose concentration range. RLG produced an increased dependency on fatty acid oxidation for basal mitochondrial metabolism and exhibited hallmarks of mitochondrial stress, including increased proton leak and reduced coupling efficiency. Relative to glucose availability, lactate release increased during low glucose but this was not modified by RLG. Basal glucose uptake was not modified by RLG and glycogen levels were similar in control and RLG-treated cells. Mitochondrial adaptations to RLG were partially recovered by maintaining euglycaemic levels of glucose following RLG exposure. Conclusions/interpretation Taken together, these data indicate that HPA mitochondria are altered following RLG, with a metabolic switch towards increased fatty acid oxidation, suggesting glial adaptations to RLG involve altered mitochondrial metabolism that could contribute to defective glucose counterregulation to hypoglycaemia in diabetes.Diabetes UK (RD Lawrence Fellowship to CB; 13/0004647); the Medical Research Council (MR/N012763/1) to KLJE, ADR and CB; and a Mary Kinross Charitable Trust PhD studentship to CB, ADR and RW to support PGWP. Additional support for this work came from awards from the British Society for Neuroendocrinology (to CB and KLJE), the Society for Endocrinology (CB), Tenovus Scotland (CB) and the University of Exeter Medical School (CB and KLJE). AR was also supported by a Royal Society Industry Fellowship