On the use of blow up to study regularizations of singularities of piecewise smooth dynamical systems in R3\mathbb{R}^3

In this paper we use the blow up method of Dumortier and Roussarie \cite{dumortier_1991,dumortier_1993,dumortier_1996}, in the formulation due to Krupa and Szmolyan \cite{krupa_extending_2001}, to study the regularization of singularities of piecewise smooth dynamical systems \cite{filippov1988differential} in $\mathbb R^3$. Using the regularization method of Sotomayor and Teixeira \cite{Sotomayor96}, first we demonstrate the power of our approach by considering the case of a fold line. We quickly recover a main result of Bonet and Seara \cite{reves_regularization_2014} in a simple manner. Then, for the two-fold singularity, we show that the regularized system only fully retains the features of the singular canards in the piecewise smooth system in the cases when the sliding region does not include a full sector of singular canards. In particular, we show that every locally unique primary singular canard persists the regularizing perturbation. For the case of a sector of primary singular canards, we show that the regularized system contains a canard, provided a certain non-resonance condition holds. Finally, we provide numerical evidence for the existence of secondary canards near resonance.Comment: To appear in SIAM Journal of Applied Dynamical System

Leukocyte telomere length is associated with elevated plasma glucose and HbA1c in young healthy men independent of birth weight.

Telomeres are protein-bound regions of repetitive nucleotide sequences (TTAGGG) at the end of human chromosomes, and their length is a marker of cellular aging. Intrauterine growth restriction is associated with shorter blood cell telomeres at birth and individuals with type 2 diabetes have shorter telomeres. Individuals with a low birth weight (LBW) have an increased risk of metabolic disease and type 2 diabetes. Therefore, we aimed to investigate the relationship between birth weight and telomere length and the association between birth weight, telomere length and cardiometabolic phenotype in adulthood. Young, healthy men with LBW (n = 55) and normal birth weight (NBW) (n = 65) were examined including blood pressure, blood samples and body composition. Leukocyte telomere length was determined using a high-throughput qPCR method. The LBW men were more insulin resistant as determined by the HOMA-IR index. There was no difference in telomere length between LBW and NBW subjects. When adjusting for birth weight and cohort effect, significant negative associations between telomere length and fasting glucose (P = 0.003) and HbA1c (P = 0.0008) were found. In conclusion, no significant difference in telomere length was found between LBW and NBW men. The telomere length was negatively associated with glucose concentrations and HbA1c levels within the normal non-diabetic range independent of birth weight

Epigenetics and obesity: the devil is in the details

Obesity is a complex disease with multiple well-defined risk factors. Nevertheless, susceptibility to obesity and its sequelae within obesogenic environments varies greatly from one person to the next, suggesting a role for gene × environment interactions in the etiology of the disorder. Epigenetic regulation of the human genome provides a putative mechanism by which specific environmental exposures convey risk for obesity and other human diseases and is one possible mechanism that underlies the gene × environment/treatment interactions observed in epidemiological studies and clinical trials. A study published in BMC Medicine this month by Wang et al. reports on an examination of DNA methylation in peripheral blood leukocytes of lean and obese adolescents, comparing methylation patterns between the two groups. The authors identified two genes that were differentially methylated, both of which have roles in immune function. Here we overview the findings from this study in the context of those emerging from other recent genetic and epigenetic studies, discuss the strengths and weaknesses of the study and speculate on the future of epigenetics in chronic disease research

Gene Expression in Skeletal Muscle Biopsies from People with Type 2 Diabetes and Relatives: Differential Regulation of Insulin Signaling Pathways

BACKGROUND:Gene expression alterations have previously been associated with type 2 diabetes, however whether these changes are primary causes or secondary effects of type 2 diabetes is not known. As healthy first degree relatives of people with type 2 diabetes have an increased risk of developing type 2 diabetes, they provide a good model in the search for primary causes of the disease. METHODS/PRINCIPAL FINDINGS:We determined gene expression profiles in skeletal muscle biopsies from Caucasian males with type 2 diabetes, healthy first degree relatives, and healthy controls. Gene expression was measured using Affymetrix Human Genome U133 Plus 2.0 Arrays covering the entire human genome. These arrays have not previously been used for this type of study. We show for the first time that genes involved in insulin signaling are significantly upregulated in first degree relatives and significantly downregulated in people with type 2 diabetes. On the individual gene level, 11 genes showed altered expression levels in first degree relatives compared to controls, among others KIF1B and GDF8 (myostatin). LDHB was found to have a decreased expression in both groups compared to controls. CONCLUSIONS/SIGNIFICANCE:We hypothesize that increased expression of insulin signaling molecules in first degree relatives of people with type 2 diabetes, work in concert with increased levels of insulin as a compensatory mechanism, counter-acting otherwise reduced insulin signaling activity, protecting these individuals from severe insulin resistance. This compensation is lost in people with type 2 diabetes where expression of insulin signaling molecules is reduced

Programming of adipose tissue miR-483-3p and GDF-3 expression by maternal diet in type 2 diabetes.

Nutrition during early mammalian development permanently influences health of the adult, including increasing the risk of type 2 diabetes and coronary heart disease. However, the molecular mechanisms underlying such programming are poorly defined. Here we demonstrate that programmed changes in miRNA expression link early-life nutrition to long-term health. Specifically, we show that miR-483-3p is upregulated in adipose tissue from low-birth-weight adult humans and prediabetic adult rats exposed to suboptimal nutrition in early life. We demonstrate that manipulation of miR-483-3p levels in vitro substantially modulates the capacity of adipocytes to differentiate and store lipids. We show that some of these effects are mediated by translational repression of growth/differentiation factor-3, a target of miR-483-3p. We propose that increased miR-483-3p expression in vivo, programmed by early-life nutrition, limits storage of lipids in adipose tissue, causing lipotoxicity and insulin resistance and thus increasing susceptibility to metabolic disease.This work was funded by the BBSRC (project grants BB/F-15364/1 and BB/F-14279/1). SEO is a British Heart Foundation Senior Fellow (FS/09/029/27902), MB is an MRC Senior Fellow and AEW is a BBSRC Professorial Fellow. KS and SEO are members of the MRC Centre for Obesity and Related Metabolic Diseases (MRC-CORD), which also provided a studentship for MW. KS is a member of the European Union COST Action BM0602