Direct and inverse source problems for degenerate parabolic equations

Degenerate parabolic partial differential equations (PDEs) with vanishing or unbounded leading coefficient make the PDE non-uniformly parabolic, and new theories need to be developed in the context of practical applications of such rather unstudied mathematical models arising in porous media, population dynamics, financial mathematics, etc. With this new challenge in mind, this paper considers investigating newly formulated direct and inverse problems associated with non-uniform parabolic PDEs where the leading space- and time-dependent coefficient is allowed to vanish on a non-empty, but zero measure, kernel set. In the context of inverse analysis, we consider the linear but ill-posed identification of a space-dependent source from a time-integral observation of the weighted main dependent variable. For both, this inverse source problem as well as its corresponding direct formulation, we rigorously investigate the question of well-posedness. We also give examples of inverse problems for which sufficient conditions guaranteeing the unique solvability are fulfilled, and present the results of numerical simulations. It is hoped that the analysis initiated in this study will open up new avenues for research in the field of direct and inverse problems for degenerate parabolic equations with applications

Author Correction: Abnormal contractility in human heart myofibrils from patients with dilated cardiomyopathy due to mutations in TTN and contractile protein genes

Correction to: Scientific Reportshttps://doi.org/10.1038/s41598-017-13675-8, published online 01 November 201

Ischemia-Reperfusion Injury Leads to Distinct Temporal Cardiac Remodeling in Normal versus Diabetic Mice

Diabetes is associated with higher incidence of myocardial infarction (MI) and increased propensity for subsequent events post-MI. Here we conducted a temporal analysis of the influence of diabetes on cardiac dysfunction and remodeling after ischemia reperfusion (IR) injury in mice. Diabetes was induced using streptozotocin and IR performed by ligating the left anterior descending coronary artery for 30 min followed by reperfusion for up to 42 days. We first evaluated changes in cardiac function using echocardiography after 24 hours reperfusion and observed IR injury significantly decreased the systolic function, such as ejection fraction, fractional shortening and end systolic left ventricular volume (LVESV) in both control and diabetic mice. The longitudinal systolic and diastolic strain rate were altered after IR, but there were no significant differences between diabetic mice and controls. However, a reduced ability to metabolize glucose was observed in the diabetic animals as determined by PET-CT scanning using 2-deoxy-2-(18F)fluoro-D-glucose. Interestingly, after 24 hours reperfusion diabetic mice showed a reduced infarct size and less apoptosis indicated by TUNEL analysis in heart sections. This may be explained by increased levels of autophagy detected in diabetic mice hearts. Similar increases in IR-induced macrophage infiltration detected by CD68 staining indicated no change in inflammation between control and diabetic mice. Over time, control mice subjected to IR developed mild left ventricular dilation whereas diabetic mice exhibited a decrease in both end diastolic left ventricular volume and LVESV with a decreased intraventricular space and thicker left ventricular wall, indicating concentric hypertrophy. This was associated with marked increases in fibrosis, indicted by Masson trichrome staining, of heart sections in diabetic IR group. In summary, we demonstrate that diabetes principally influences distinct IR-induced chronic changes in cardiac function and remodeling, while a smaller infarct size and elevated levels of autophagy with similar cardiac function are observed in acute phase

Involvement of Autophagy in Cardiac Remodeling in Transgenic Mice with Cardiac Specific Over-Expression of Human Programmed Cell Death 5

Programmed cell death 5 (PDCD5) is a cytosolic protein suppressing growth of multiple types of cancer cells through activating p53. We hypothesized that PDCD5 plays an essential role in cardiac remodeling and function. PDCD5 was significantly up-regulated in the hearts from mice subjected to angiotensin II treatment or transverse aortic constriction. Thus, we generated transgenic mice over-expressing human PDCD5 under the control of alpha myosin heavy chain promoter to examine the role of PDCD5 in cardiac remodeling. Transgenic founder died spontaneously displayed enlarged heart. The high PDCD5 over-expressing line (10-fold) showed reduced survival rate, increase in heart weight normalized to body weight. Real-Time RT-PCR analysis revealed fetal gene program was up-regulated. Echocardiography and histopathological examination showed characteristics of dilated cardiomyopathy and heart failure in transgenic mice. Western blot and immunohistochemistry analysis showed autophagy was dramatically increased in transgenic mice as compared to WT littermates control mice, while apoptosis remained unchanged. The enhanced autophagy in high over-expressing line was associated with significant increase in p53 activity and its downstream target damage-regulated autophagy modulator expression. The low over-expressing line (3.5-fold) appeared normal, but was more susceptible to angiotensin II-induced cardiac hypertrophy. This study is the first providing evidence that PDCD5 plays an important role in cardiac remodeling

Cathepsin S Deficiency Results in Abnormal Accumulation of Autophagosomes in Macrophages and Enhances Ang II–Induced Cardiac Inflammation

BACKGROUND: Cathepsin S (Cat S) is overexpressed in human atherosclerotic and aneurysmal tissues and may contributes to degradation of extracellular matrix, especially elastin, in inflammatory diseases. We aimed to define the role of Cat S in cardiac inflammation and fibrosis induced by angiotensin II (Ang II) in mice. METHODS AND RESULTS: Cat S-knockout (Cat S(-/-)) and littermate wild-type (WT) C57BL/6J mice were infused continuously with Ang II (750 ng/kg/min) or saline for 7 days. Cat S(-/-) mice showed severe cardiac fibrosis, including elevated expression of collagen I and α-smooth muscle actin (α-SMA), as compared with WT mice. Moreover, macrophage infiltration and expression of inflammatory cytokines (tumor necrosis factor α, transforming growth factor β and interleukin 1β) were significantly greater in Cat S(-/-) than WT hearts. These Ang II-induced effects in Cat S(-/-) mouse hearts was associated with abnormal accumulation of autophagosomes and reduced clearance of damaged mitochondria, which led to increased levels of reactive oxygen species (ROS) and activation of nuclear factor-kappa B (NF-κB) in macrophages. CONCLUSION: Cat S in lysosomes is essential for mitophagy processing in macrophages, deficiency in Cat S can increase damaged mitochondria and elevate ROS levels and NF-κB activity in hypertensive mice, so it regulates cardiac inflammation and fibrosis

A new class of glycomimetic drugs to prevent free fatty acid-induced endothelial dysfunction

Background: Carbohydrates play a major role in cell signaling in many biological processes. We have developed a set of glycomimetic drugs that mimic the structure of carbohydrates and represent a novel source of therapeutics for endothelial dysfunction, a key initiating factor in cardiovascular complications. Purpose: Our objective was to determine the protective effects of small molecule glycomimetics against free fatty acid­induced endothelial dysfunction, focusing on nitric oxide (NO) and oxidative stress pathways. Methods: Four glycomimetics were synthesized by the stepwise transformation of 2,5­dihydroxybenzoic acid to a range of 2,5­substituted benzoic acid derivatives, incorporating the key sulfate groups to mimic the interactions of heparan sulfate. Endothelial function was assessed using acetylcholine­induced, endotheliumdependent relaxation in mouse thoracic aortic rings using wire myography. Human umbilical vein endothelial cell (HUVEC) behavior was evaluated in the presence or absence of the free fatty acid, palmitate, with or without glycomimetics (1µM). DAF­2 and H2DCF­DA assays were used to determine nitric oxide (NO) and reactive oxygen species (ROS) production, respectively. Lipid peroxidation colorimetric and antioxidant enzyme activity assays were also carried out. RT­PCR and western blotting were utilized to measure Akt, eNOS, Nrf­2, NQO­1 and HO­1 expression. Results: Ex vivo endothelium­dependent relaxation was significantly improved by the glycomimetics under palmitate­induced oxidative stress. In vitro studies showed that the glycomimetics protected HUVECs against the palmitate­induced oxidative stress and enhanced NO production. We demonstrate that the protective effects of pre­incubation with glycomimetics occurred via upregulation of Akt/eNOS signaling, activation of the Nrf2/ARE pathway, and suppression of ROS­induced lipid peroxidation. Conclusion: We have developed a novel set of small molecule glycomimetics that protect against free fatty acidinduced endothelial dysfunction and thus, represent a new category of therapeutic drugs to target endothelial damage, the first line of defense against cardiovascular disease