On the asymptotic formula for Goldbach numbers in short intervals

Let $R(k)=\sum\limits_{l+m=k}\Lambda(l)\Lambda(m)$, \Sing(k) = 2 \prod\limits_{p>2}\left(1-\frac{1}{(p-1)^2}\right) \prod\limits_{\substack{ p\mid k\\ p>2 }} \left(\frac{p-1}{p-2}\right) if $k$ is even and \Sing(k) =0 if $k$ is odd. It is known that R(k) \sim k\Sing(k) as $N\to \infty$ for almost all $k\in [N,2N]$ and that \sum_{k\in [n,n+H)}R(k) \sim \sum_{k\in [n,n+H)} k\Sing(k) \quad\hbox{for} \quad n\to \infty \eqno{(1)} uniformly for $H\geq n^{1/6+\epsilon}$. Here we prove, assuming $N^\epsilon\leq H\leq N^{1/6+\epsilon}$ and $N\to\infty$, that (1) holds for almost all $n\in [N,2N]$

Lung surfactant in subacute pulmonary disease

Pulmonary surfactant is a surface active material composed of both lipids and proteins that is produced by alveolar type II pneumocytes. Abnormalities of surfactant in the immature lung or in the acutely inflamed mature lung are well described. However, in a variety of subacute diseases of the mature lung, abnormalities of lung surfactant may also be of importance. These diseases include chronic obstructive pulmonary disease, asthma, cystic fibrosis, interstitial lung disease, pneumonia, and alveolar proteinosis. Understanding of the mechanisms that disturb the lung surfactant system may lead to novel rational therapies for these diseases

Water-Soluble Fullerene (C60) Derivatives as Nonviral Gene-Delivery Vectors

A new class of water-soluble C60 transfecting agents has been prepared using Hirsch-Bingel chemistry and assessed for their ability to act as gene-delivery vectors in vitro. In an effort to elucidate the relationship between the hydrophobicity of the fullerene core, the hydrophilicity of the water-solubilizing groups, and the overall charge state of the C60 vectors in gene delivery and expression, several different C60 derivatives were synthesized to yield either positively charged, negatively charged, or neutral chemical functionalities under physiological conditions. These fullerene derivatives were then tested for their ability to transfect cells grown in culture with DNA carrying the green fluorescent protein (GFP) reporter gene. Statistically significant expression of GFP was observed for all forms of the C60 derivatives when used as DNA vectors and compared to the ability of naked DNA alone to transfect cells. However, efficient in vitro transfection was only achieved with the two positively charged C60 derivatives, namely, an octa-amino derivatized C60 and a dodeca-amino derivatized C60 vector. All C60 vectors showed an increase in toxicity in a dose-dependent manner. Increased levels of cellular toxicity were observed for positively charged C60 vectors relative to the negatively charged and neutral vectors. Structural analyses using dynamic light scattering and optical microscopy offered further insights into possible correlations between the various derivatized C60 compounds, the C60 vector/DNA complexes, their physical attributes (aggregation, charge) and their transfection efficiencies. Recently, similar Gd@C60-based compounds have demonstrated potential as advanced contrast agents for magnetic resonance imaging (MRI). Thus, the successful demonstration of intracellular DNA uptake, intracellular transport, and gene expression from DNA using C60 vectors suggests the possibility of developing analogous Gd@C60-based vectors to serve simultaneously as both therapeutic and diagnostic agents

Mab21l2 Is Essential for Embryonic Heart and Liver Development

During mouse embryogenesis, proper formation of the heart and liver is especially important and is crucial for embryonic viability. In this study, we showed that Mab21l2 was expressed in the trabecular and compact myocardium, and that deletion of Mab21l2 resulted in a reduction of the trabecular myocardium and thinning of the compact myocardium. Mab21l2-deficient embryonic hearts had decreased expression of genes that regulate cell proliferation and apoptosis of cardiomyocytes. These results show that Mab21l2 functions during heart development by regulating the expression of such genes. Mab21l2 was also expressed in the septum transversum mesenchyme (STM). Epicardial progenitor cells are localized to the anterior surface of the STM (proepicardium), and proepicardial cells migrate onto the surface of the heart and form the epicardium, which plays an important role in heart development. The rest of the STM is essential for the growth and survival of hepatoblasts, which are bipotential progenitors for hepatocytes and cholangiocytes. Proepicardial cells in Mab21l2-deficient embryos had defects in cell proliferation, which led to a small proepicardium, in which α4 integrin expression, which is essential for the migration of proepicardial cells, was down-regulated, suggesting that defects occurred in its migration. In Mab21l2-deficient embryos, epicardial formation was defective, suggesting that Mab21l2 plays important roles in epicardial formation through the regulation of the cell proliferation of proepicardial cells and the migratory process of proepicardial cells. Mab21l2-deficient embryos also exhibited hypoplasia of the STM surrounding hepatoblasts and decreased hepatoblast proliferation with a resultant loss of defective morphogenesis of the liver. These findings demonstrate that Mab21l2 plays a crucial role in both heart and liver development through STM formation

The insecure airway: a comparison of knots and commercial devices for securing endotracheal tubes

BACKGROUND: Endotracheal Tubes (ETTs) are commonly secured using adhesive tape, cloth tape, or commercial devices. The objectives of the study were (1) To compare degrees of movement of ETTs secured with 6 different commercial devices and (2) To compare movement of ETTs secured with cloth tape tied with 3 different knots (hitches). METHODS: A 17 cm diameter PVC tube with 14 mm "mouth" hole in the side served as a mannequin. ETTs were subjected to repeated jerks, using a cable and pulley system. Measurements: (1) Total movement of ETTs relative to "mouth" (measure used for devices) (2) Slippage of ETT through securing knot (measure used for knots). RESULTS: Among commercial devices, the Dale(® )showed less movement than other devices, although some differences between devices did not reach significance. Among knots, Magnus and Clove Hitches produced less slippage than the Cow Hitch, but these differences did not reach statistical significance. CONCLUSION: Among devices tested, the Dale(® )was most secure. Within the scope offered by the small sample sizes, there were no statistically significant differences between the knots in this study

A global view of porcine transcriptome in three tissues from a full-sib pair with extreme phenotypes in growth and fat deposition by paired-end RNA sequencing

<p>Abstract</p> <p>Background</p> <p>Elucidation of the pig transcriptome is essential for interpreting functional elements of the genome and understanding the genetic architecture of complex traits such as fat deposition, metabolism and growth.</p> <p>Results</p> <p>Here we used massive parallel high-throughput RNA sequencing to generate a high-resolution map of the porcine mRNA and miRNA transcriptome in liver, longissimus dorsi and abdominal fat from two full-sib F₂hybrid pigs with segregated phenotypes on growth, blood physiological and biochemical parameters, and fat deposition. We obtained 8,508,418-10,219,332 uniquely mapped reads that covered 78.0% of the current annotated transcripts and identified 48,045-122,931 novel transcript fragments, which constituted 17,085-29,499 novel transcriptional active regions in six tested samples. We found that about 18.8% of the annotated genes showed alternative splicing patterns, and alternative 3' splicing is the most common type of alternative splicing events in pigs. Cross-tissue comparison revealed that many transcriptional events are tissue-differential and related to important biological functions in their corresponding tissues. We also detected a total of 164 potential novel miRNAs, most of which were tissue-specifically identified. Integrated analysis of genome-wide association study and differential gene expression revealed interesting candidate genes for complex traits, such as <it>IGF2, CYP1A1, CKM </it>and <it>CES1 </it>for heart weight, hemoglobin, pork pH value and serum cholesterol, respectively.</p> <p>Conclusions</p> <p>This study provides a global view of the complexity of the pig transcriptome, and gives an extensive new knowledge about alternative splicing, gene boundaries and miRNAs in pigs. Integrated analysis of genome wide association study and differential gene expression allows us to find important candidate genes for porcine complex traits.</p

Generation of human vascular smooth muscle subtypes provides insight into embryological origin-dependent disease susceptibility.

Heterogeneity of embryological origins is a hallmark of vascular smooth muscle cells (SMCs) and may influence the development of vascular disease. Differentiation of human pluripotent stem cells (hPSCs) into developmental origin-specific SMC subtypes remains elusive. Here we describe a chemically defined protocol in which hPSCs were initially induced to form neuroectoderm, lateral plate mesoderm or paraxial mesoderm. These intermediate populations were further differentiated toward SMCs (>80% MYH11(+) and ACTA2(+)), which displayed contractile ability in response to vasoconstrictors and invested perivascular regions in vivo. Derived SMC subtypes recapitulated the unique proliferative and secretory responses to cytokines previously documented in studies using aortic SMCs of distinct origins. Notably, this system predicted increased extracellular matrix degradation by SMCs derived from lateral plate mesoderm, which was confirmed using rat aortic SMCs from corresponding origins. This differentiation approach will have broad applications in modeling origin-dependent disease susceptibility and in developing bioengineered vascular grafts for regenerative medicine