Discrete Integrable Systems and Hodograph Transformations Arising from Motions of Discrete Plane Curves

We consider integrable discretizations of some soliton equations associated with the motions of plane curves: the Wadati-Konno-Ichikawa elastic beam equation, the complex Dym equation, and the short pulse equation. They are related to the modified KdV or the sine-Gordon equations by the hodograph transformations. Based on the observation that the hodograph transformations are regarded as the Euler-Lagrange transformations of the curve motions, we construct the discrete analogues of the hodograph transformations, which yield integrable discretizations of those soliton equations.Comment: 19 page

Endothelial Cell and Platelet Bioenergetics: Effect of Glucose and Nutrient Composition

It has been suggested that cells that are independent of insulin for glucose uptake, when exposed to high glucose or other nutrient concentrations, manifest enhanced mitochondrial substrate oxidation with consequent enhanced potential and generation of reactive oxygen species (ROS); a paradigm that could predispose to vascular complications of diabetes. Here we exposed bovine aortic endothelial (BAE) cells and human platelets to variable glucose and fatty acid concentrations. We then examined oxygen consumption and acidification rates using recently available technology in the form of an extracellular oxygen and proton flux analyzer. Acute or overnight exposure of confluent BAE cells to glucose concentrations from 5.5 to 25 mM did not enhance or change the rate of oxygen consumption (OCR) under basal conditions, during ATP synthesis, or under uncoupled conditions. Glucose also did not alter OCR in sub-confluent cells, in cells exposed to low serum, or in cells treated with added pyruvate. Likewise, overnight exposure to fatty acids of varying saturation had no such effects. Overnight exposure of BAE cells to low glucose concentration decreased maximal uncoupled respiration, but not basal or ATP related oxygen consumption. Labeled glucose oxidation to CO2 increased, but only marginally after high glucose exposure while oleate oxidation to CO2 decreased. Overnight exposure to linolenic acid, but not oleic or linoleic acid increased extracellular acidification consistent with enhanced glycolytic metabolism. We were unable to detect an increase in production of reactive oxygen species (ROS) from BAE cells exposed to high medium glucose. Like BAE cells, exposure of human platelets to glucose did not increase oxygen consumption. As opposed to BAE cells, platelet mitochondria demonstrate less respiratory reserve capacity (beyond that needed for basal metabolism). Our data do not support the concept that exposure to high glucose or fatty acids accelerates mitochondrial oxidative metabolism in endothelial cells or platelets

Mind the gap: connexins and cell–cell communication in the diabetic kidney

Connexins, assembled as a hexameric connexon, form a transmembrane hemichannel that provides a conduit for paracrine signalling of small molecules and ions to regulate the activity and function of adjacent cells. When hemichannels align and associate with similar channels on opposing cells, they form a continuous aqueous pore or gap junction, allowing the direct transmission of metabolic and electrical signals between coupled cells. Regulation of gap junction synthesis and channel activity is critical for cell function, and a number of diseases can be attributed to changes in the expression/function of these important proteins. Diabetic nephropathy is associated with several complex metabolic and inflammatory responses characterised by defects at the molecular, cellular and tissue level. In both type 1 and type 2 diabetes, glycaemic injury of the kidney is the leading cause of end-stage renal failure, a consequence of multiple aetiologies, including increased deposition of extracellular matrix, glomerular hyperfiltration, albuminuria and tubulointerstitial fibrosis. In diabetic nephropathy, loss of connexin mediated cell–cell communication within the nephron may represent an early sign of disease; however, our current knowledge of the role of connexins in the diabetic kidney is sparse. This review highlights recent evidence demonstrating that maintenance of connexin-mediated cell–cell communication could benefit region-specific renal function in diabetic nephropathy and suggests that these proteins should be viewed as a tantalising novel target for therapeutic intervention

Investigating the Role of Islet Cytoarchitecture in Its Oscillation Using a New β-Cell Cluster Model

The oscillatory insulin release is fundamental to normal glycemic control. The basis of the oscillation is the intercellular coupling and bursting synchronization of β cells in each islet. The functional role of islet β cell mass organization with respect to its oscillatory bursting is not well understood. This is of special interest in view of the recent finding of islet cytoarchitectural differences between human and animal models. In this study we developed a new hexagonal closest packing (HCP) cell cluster model. The model captures more accurately the real islet cell organization than the simple cubic packing (SCP) cluster that is conventionally used. Using our new model we investigated the functional characteristics of β-cell clusters, including the fraction of cells able to burst fb, the synchronization index λ of the bursting β cells, the bursting period Tb, the plateau fraction pf, and the amplitude of intracellular calcium oscillation [Ca]. We determined their dependence on cluster architectural parameters including number of cells nβ, number of inter-β cell couplings of each β cell nc, and the coupling strength gc. We found that at low values of nβ, nc and gc, the oscillation regularity improves with their increasing values. This functional gain plateaus around their physiological values in real islets, at nβ∼100, nc∼6 and gc∼200 pS. In addition, normal β-cell clusters are robust against significant perturbation to their architecture, including the presence of non-β cells or dead β cells. In clusters with nβ>∼100, coordinated β-cell bursting can be maintained at up to 70% of β-cell loss, which is consistent with laboratory and clinical findings of islets. Our results suggest that the bursting characteristics of a β-cell cluster depend quantitatively on its architecture in a non-linear fashion. These findings are important to understand the islet bursting phenomenon and the regulation of insulin secretion, under both physiological and pathological conditions

Obesity-Related Oxidative Stress: the Impact of Physical Activity and Diet Manipulation

Obesity-related oxidative stress, the imbalance between pro-oxidants and antioxidants (e.g., nitric oxide), has been linked to metabolic and cardiovascular disease, including endothelial dysfunction and atherosclerosis. Reactive oxygen species (ROS) are essential for physiological functions including gene expression, cellular growth, infection defense, and modulating endothelial function. However, elevated ROS and/or diminished antioxidant capacity leading to oxidative stress can lead to dysfunction. Physical activity also results in an acute state of oxidative stress. However, it is likely that chronic physical activity provides a stimulus for favorable oxidative adaptations and enhanced physiological performance and physical health, although distinct responses between aerobic and anaerobic activities warrant further investigation. Studies support the benefits of dietary modification as well as exercise interventions in alleviating oxidative stress susceptibility. Since obese individuals tend to demonstrate elevated markers of oxidative stress, the implications for this population are significant. Therefore, in this review our aim is to discuss (i) the role of oxidative stress and inflammation as associated with obesity-related diseases, (ii) the potential concerns and benefits of exercise-mediated oxidative stress, and (iii) the advantageous role of dietary modification, including acute or chronic caloric restriction and vitamin D supplementation

Protein kinase C and cardiac dysfunction: a review

Heart failure (HF) is a physiological state in which cardiac output is insufficient to meet the needs of the body. It is a clinical syndrome characterized by impaired ability of the left ventricle to either fill or eject blood efficiently. HF is a disease of multiple aetiologies leading to progressive cardiac dysfunction and it is the leading cause of deaths in both developed and developing countries. HF is responsible for about 73,000 deaths in the UK each year. In the USA, HF affects 5.8 million people and 550,000 new cases are diagnosed annually. Cardiac remodelling (CD), which plays an important role in pathogenesis of HF, is viewed as stress response to an index event such as myocardial ischaemia or imposition of mechanical load leading to a series of structural and functional changes in the viable myocardium. Protein kinase C (PKC) isozymes are a family of serine/threonine kinases. PKC is a central enzyme in the regulation of growth, hypertrophy, and mediators of signal transduction pathways. In response to circulating hormones, activation of PKC triggers a multitude of intracellular events influencing multiple physiological processes in the heart, including heart rate, contraction, and relaxation. Recent research implicates PKC activation in the pathophysiology of a number of cardiovascular disease states. Few reports are available that examine PKC in normal and diseased human hearts. This review describes the structure, functions, and distribution of PKCs in the healthy and diseased heart with emphasis on the human heart and, also importantly, their regulation in heart failure