On The Monotonicity Properties of Additive Representation Functions

If A is a set of positive integers, let R-1(n) be the number of solutions of a + a' = n, a, a' G A, and let R-2(n) and R-3(n) denote the number of solutions with the additional restrictions a < a', and a < a' respectively. The monotonicity properties of the three functions R-1(n), R-2(n), and R-3(n) are studied and compared

Mechanisms and Modulation of Oxidative/Nitrative Stress in Type 4 Cardio-Renal Syndrome and Renal Sarcopenia

Chronic kidney disease (CKD) is a public health problem and a recognized risk factor for cardiovascular diseases (CVD). CKD could amplify the progression of chronic heart failure leading to the development of type 4 cardio-renal syndrome (T4CRS). The severity and persistence of heart failure are strongly associated with mortality risk in T4CRS. CKD is also a catabolic state leading to renal sarcopenia which is characterized by the loss of skeletal muscle strength and physical function. Renal sarcopenia also promotes the development of CVD and increases the mortality in CKD patients. In turn, heart failure developed in T4CRS could result in chronic muscle hypoperfusion and metabolic disturbances leading to or aggravating the renal sarcopenia. The interplay of multiple factors (e.g., comorbidities, over-activated renin-angiotensin-aldosterone system [RAAS], sympathetic nervous system [SNS], oxidative/nitrative stress, inflammation, etc.) may result in the progression of T4CRS and renal sarcopenia. Among these factors, oxidative/nitrative stress plays a crucial role in the complex pathomechanism and interrelationship between T4CRS and renal sarcopenia. In the heart and skeletal muscle, mitochondria, nicotinamide adenine dinucleotide phosphate (NADPH) oxidases, uncoupled nitric oxide synthase (NOS) and xanthine oxidase are major ROS sources producing superoxide anion (O2·−) and/or hydrogen peroxide (H2O2). O2·− reacts with nitric oxide (NO) forming peroxynitrite (ONOO−) which is a highly reactive nitrogen species (RNS). High levels of ROS/RNS cause lipid peroxidation, DNA damage, interacts with both DNA repair enzymes and transcription factors, leads to the oxidation/nitration of key proteins involved in contractility, calcium handling, metabolism, antioxidant defense mechanisms, etc. It also activates the inflammatory response, stress signals inducing cardiac hypertrophy, fibrosis, or cell death via different mechanisms (e.g., apoptosis, necrosis) and dysregulates autophagy. Therefore, the thorough understanding of the mechanisms which lead to perturbations in oxidative/nitrative metabolism and its relationship with pro-inflammatory, hypertrophic, fibrotic, cell death and other pathways would help to develop strategies to counteract systemic and tissue oxidative/nitrative stress in T4CRS and renal sarcopenia. In this review, we also focus on the effects of some well-known and novel pharmaceuticals, nutraceuticals, and physical exercise on cardiac and skeletal muscle oxidative/nitrative stress in T4CRS and renal sarcopenia

Isolated hypercholesterolemia leads to steatosis in the liver without affecting the pancreas

Abstract Background Lipid accumulation in the liver and pancreas is primarily caused by combined hyperlipidemia. However, the effect of isolated hypercholesterolemia without hypertriglyceridemia is not fully described. Therefore, our aim was to investigate whether hypercholesterolemia alone leads to alterations both in hepatic and pancreatic lipid panel and histology in rats. Methods Male Wistar rats were fed with 2% cholesterol +0.25% cholate-supplemented diet or standard chow for 12 weeks. Blood was collected at weeks 0, 4, 8 and 12 to measure serum cholesterol and triglyceride levels. At week 12, both the pancreas and the liver were isolated for further histological and biochemical analysis. Hepatic and plasma fatty acid composition was assessed by gas chromatography. Expression of mRNA of major enzymes involved in saturated/unsaturated fatty acid synthesis was analyzed by qPCR. In separate experiments serum enzyme activities and insulin levels were measured at week 9. Results At week 12, rats fed with 2% cholesterol +0.25% cholate-supplemented diet were characterized by elevated serum cholesterol (4.09 ± 0.20 vs. 2.89 ± 0.22 mmol/L, *p < 0.05) while triglyceride (2.27 ± 0.05 vs. 2.03 ± 0.03 mmol/L) and glucose levels (5.32 ± 0.14 vs. 5.23 ± 0.10 mmol/L) remained unchanged. Isolated hypercholesterolemia increased hepatic lipid accumulation, hepatic cholesterol (5.86 ± 0.22 vs. 1.60 ± 0.15 ng/g tissue, *p < 0.05) and triglyceride contents (19.28 ± 1.42 vs. 6.78 ± 0.71 ng/g tissue, *p < 0.05), and hepatic nitrotyrosine level (4.07 ± 0.52 vs. 2.59 ± 0.31 ng/mg protein, *p < 0.05). The histology and tissue lipid content of the pancreas was not affected. Serum total protein level, alanine aminotransferase (ALT) and aspartate aminotransferase (AST) activities remained unchanged in response to isolated hypercholesterolemia while serum alkaline phosphatase activity (ALP) significantly increased. Plasma insulin levels did not change in response to isolated hypercholesterolemia suggesting an intact endocrine function of the pancreas. Isolated hypercholesterolemia caused a significantly increased hepatic and serum fatty acid level associated with a marked alteration of fatty acid composition. Hepatic expression of Δ9-desaturase (SCD1) was increased 4.92×, while expression of Δ5-desaturase and Δ6-desaturase were decreased (0.447× and 0.577×, respectively) due to isolated hypercholesterolemia. Conclusions Isolated hypercholesterolemia leads to hepatic steatosis and marked alterations in the hepatic lipid profile without affecting the pancreas. Altered fatty acid profile might mediate harmful effects of cholesterol in the liver

Small ball probability, Inverse theorems, and applications

Let $\xi$ be a real random variable with mean zero and variance one and $A={a_1,...,a_n}$ be a multi-set in $\R^d$. The random sum $$S_A := a_1 \xi_1 + ... + a_n \xi_n$$ where $\xi_i$ are iid copies of $\xi$ is of fundamental importance in probability and its applications. We discuss the small ball problem, the aim of which is to estimate the maximum probability that $S_A$ belongs to a ball with given small radius, following the discovery made by Littlewood-Offord and Erdos almost 70 years ago. We will mainly focus on recent developments that characterize the structure of those sets $A$ where the small ball probability is relatively large. Applications of these results include full solutions or significant progresses of many open problems in different areas.Comment: 47 page

The history of degenerate (bipartite) extremal graph problems

This paper is a survey on Extremal Graph Theory, primarily focusing on the case when one of the excluded graphs is bipartite. On one hand we give an introduction to this field and also describe many important results, methods, problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version of our survey presented in Erdos 100. In this version 2 only a citation was complete

Transcriptomic alterations in the heart of non-obese type 2 diabetic Goto-Kakizaki rats

BACKGROUND: There is a spectacular rise in the global prevalence of type 2 diabetes mellitus (T2DM) due to the worldwide obesity epidemic. However, a significant proportion of T2DM patients are non-obese and they also have an increased risk of cardiovascular diseases. As the Goto-Kakizaki (GK) rat is a well-known model of non-obese T2DM, the goal of this study was to investigate the effect of non-obese T2DM on cardiac alterations of the transcriptome in GK rats. METHODS: Fasting blood glucose, serum insulin and cholesterol levels were measured at 7, 11, and 15 weeks of age in male GK and control rats. Oral glucose tolerance test and pancreatic insulin level measurements were performed at 11 weeks of age. At week 15, total RNA was isolated from the myocardium and assayed by rat oligonucleotide microarray for 41,012 genes, and then expression of selected genes was confirmed by qRT-PCR. Gene ontology and protein-protein network analyses were performed to demonstrate potentially characteristic gene alterations and key genes in non-obese T2DM. RESULTS: Fasting blood glucose, serum insulin and cholesterol levels were significantly increased, glucose tolerance and insulin sensitivity were significantly impaired in GK rats as compared to controls. In hearts of GK rats, 204 genes showed significant up-regulation and 303 genes showed down-regulation as compared to controls according to microarray analysis. Genes with significantly altered expression in the heart due to non-obese T2DM includes functional clusters of metabolism (e.g. Cyp2e1, Akr1b10), signal transduction (e.g. Dpp4, Stat3), receptors and ion channels (e.g. Sln, Chrng), membrane and structural proteins (e.g. Tnni1, Mylk2, Col8a1, Adam33), cell growth and differentiation (e.g. Gpc3, Jund), immune response (e.g. C3, C4a), and others (e.g. Lrp8, Msln, Klkc1, Epn3). Gene ontology analysis revealed several significantly enriched functional inter-relationships between genes influenced by non-obese T2DM. Protein-protein interaction analysis demonstrated that Stat is a potential key gene influenced by non-obese T2DM. CONCLUSIONS: Non-obese T2DM alters cardiac gene expression profile. The altered genes may be involved in the development of cardiac pathologies and could be potential therapeutic targets in non-obese T2DM

The effect of a preparation of minerals, vitamins and trace elements on the cardiac gene expression pattern in male diabetic rats

BACKGROUND: Diabetic patients have an increased risk of developing cardiovascular diseases, which are the leading cause of death in developed countries. Although multivitamin products are widely used as dietary supplements, the effects of these products have not been investigated in the diabetic heart yet. Therefore, here we investigated if a preparation of different minerals, vitamins, and trace elements (MVT) affects the cardiac gene expression pattern in experimental diabetes. METHODS: Two-day old male Wistar rats were injected with streptozotocin (i.p. 100 mg/kg) or citrate buffer to induce diabetes. From weeks 4 to 12, rats were fed with a vehicle or a MVT preparation. Fasting blood glucose measurement and oral glucose tolerance test were performed at week 12, and then total RNA was isolated from the myocardium and assayed by rat oligonucleotide microarray for 41012 oligonucleotides. RESULTS: Significantly elevated fasting blood glucose concentration and impaired glucose tolerance were markedly improved by MVT-treatment in diabetic rats at week 12. Genes with significantly altered expression due to diabetes include functional clusters related to cardiac hypertrophy (e.g. caspase recruitment domain family, member 9; cytochrome P450, family 26, subfamily B, polypeptide; FXYD domain containing ion transport regulator 3), stress response (e.g. metallothionein 1a; metallothionein 2a; interleukin-6 receptor; heme oxygenase (decycling) 1; and glutathione S-transferase, theta 3), and hormones associated with insulin resistance (e.g. resistin; FK506 binding protein 5; galanin/GMAP prepropeptide). Moreover the expression of some other genes with no definite cardiac function was also changed such as e.g. similar to apolipoprotein L2; brain expressed X-linked 1; prostaglandin b2 synthase (brain). MVT-treatment in diabetic rats showed opposite gene expression changes in the cases of 19 genes associated with diabetic cardiomyopathy. In healthy hearts, MVT-treatment resulted in cardiac gene expression changes mostly related to immune response (e.g. complement factor B; complement component 4a; interferon regulatory factor 7; hepcidin). CONCLUSIONS: MVT-treatment improved diagnostic markers of diabetes. This is the first demonstration that MVT-treatment significantly alters cardiac gene expression profile in both control and diabetic rats. Our results and further studies exploring the mechanistic role of individual genes may contribute to the prevention or diagnosis of cardiac complications in diabetes

Anti-diabetic effect of a preparation of vitamins, minerals and trace elements in diabetic rats: a gender difference

BACKGROUND: Although multivitamin products are widely used as dietary supplements to maintain health or as special medical food in certain diseases, the effects of these products were not investigated in diabetes mellitus, a major cardiovascular risk factor. Therefore, here we investigated if a preparation of different minerals, vitamins, and trace elements (MVT) for human use affects the severity of experimental diabetes. METHODS: Two days old neonatal Wistar rats from both genders were injected with 100 mg/kg of streptozotocin or its vehicle to induce diabetes. At week 4, rats were fed with an MVT preparation or vehicle for 8 weeks. Well established diagnostic parameters of diabetes, i.e. fasting blood glucose and oral glucose tolerance test were performed at week 4, 8 and 12. Moreover, serum insulin and blood HbA1c were measured at week 12. RESULTS: An impaired glucose tolerance has been found in streptozotocin-treated rats in both genders at week 4. In males, fasting blood glucose and HbA1c were significantly increased and glucose tolerance and serum insulin was decreased at week 12 in the vehicle-treated diabetic group as compared to the vehicle-treated non-diabetic group. All of the diagnostic parameters of diabetes were significantly improved by MVT treatment in male rats. In females, streptozotocin treatment resulted in a less severe prediabetic-like phenotype as only glucose tolerance and HbA1c were altered by the end of the study in the vehicle-treated diabetic group as compared to the vehicle-treated non-diabetic group. MVT treatment failed to improve the diagnostic parameters of diabetes in female streptozotocin-treated rats. CONCLUSION: This is the first demonstration that MVT significantly attenuates the progression of diabetes in male rats with chronic experimental diabetes. Moreover, we have confirmed that females are less sensitive to STZ-induced diabetes and MVT preparation did not show protection against prediabetic state. This may suggest a gender difference in the pathogenesis of diabetes

In vivo MRI and ex vivo histological assessment of the cardioprotection induced by ischemic preconditioning, postconditioning and remote conditioning in a closed-chest porcine model of reperfused acute myocardial infarction: importance of microvasculature

BACKGROUND: Cardioprotective value of ischemic post- (IPostC), remote (RIC) conditioning in acute myocardial infarction (AMI) is unclear in clinical trials. To evaluate cardioprotection, most translational animal studies and clinical trials utilize necrotic tissue referred to the area at risk (AAR) by magnetic resonance imaging (MRI). However, determination of AAR by MRI' may not be accurate, since MRI-indices of microvascular damage, i.e., myocardial edema and microvascular obstruction (MVO), may be affected by cardioprotection independently from myocardial necrosis. Therefore, we assessed the effect of IPostC, RIC conditioning and ischemic preconditioning (IPreC; positive control) on myocardial necrosis, edema and MVO in a clinically relevant, closed-chest pig model of AMI. METHODS AND RESULTS: Acute myocardial infarction was induced by a 90-min balloon occlusion of the left anterior descending coronary artery (LAD) in domestic juvenile female pigs. IPostC (6 x 30 s ischemia/reperfusion after 90-min occlusion) and RIC (4 x 5 min hind limb ischemia/reperfusion during 90-min LAD occlusion) did not reduce myocardial necrosis as assessed by late gadolinium enhancement 3 days after reperfusion and by ex vivo triphenyltetrazolium chloride staining 3 h after reperfusion, however, the positive control, IPreC (3 x 5 min ischemia/reperfusion before 90-min LAD occlusion) did. IPostC and RIC attenuated myocardial edema as measured by cardiac T2-weighted MRI 3 days after reperfusion, however, AAR measured by Evans blue staining was not different among groups, which confirms that myocardial edema is not a measure of AAR, IPostC and IPreC but not RIC decreased MVO. CONCLUSION: We conclude that IPostC and RIC interventions may protect the coronary microvasculature even without reducing myocardial necrosis