On equicontinuity of homeomorphisms with finite distortion in the plane

It is stated equicontinuity and normality of families $\frak{F}^{\Phi}$ of the so--called homeomorphisms with finite distortion on conditions that $K_{f}(z)$ has finite mean oscillation, singularities of logarithmic type or integral constraints of the type $\int\Phi\left(K_{f}(z)\right)dx\,dy<\infty$ in a domain D\subset{\C}. It is shown that the found conditions on the function $\Phi$ are not only sufficient but also necessary for equicontinuity and normality of such families of mappings.Comment: 18 page

Use of Genomic DNA as an Indirect Reference for Identifying Gender-Associated Transcripts in Morphologically Identical, but Chromosomally Distinct, Schistosoma mansoni Cercariae

BACKGROUND: The use of DNA microarray technology to study global Schistosoma gene expression has led to the rapid identification of novel biological processes, pathways or associations. Implementation of standardized DNA microarray protocols across laboratories would assist maximal interpretation of generated datasets and extend productive application of this technology. METHODOLOGY/PRINCIPAL FINDINGS: Utilizing a new Schistosoma mansoni oligonucleotide DNA microarray composed of 37,632 elements, we show that schistosome genomic DNA (gDNA) hybridizes with less variation compared to complex mixed pools of S. mansoni cDNA material (R = 0.993 for gDNA compared to R = 0.956 for cDNA during ‘self versus self’ hybridizations). Furthermore, these effects are species-specific, with S. japonicum or Mus musculus gDNA failing to bind significantly to S. mansoni oligonucleotide DNA microarrays (e.g R = 0.350 when S. mansoni gDNA is co-hybridized with S. japonicum gDNA). Increased median fluorescent intensities (209.9) were also observed for DNA microarray elements hybridized with S. mansoni gDNA compared to complex mixed pools of S. mansoni cDNA (112.2). Exploiting these valuable characteristics, S. mansoni gDNA was used in two-channel DNA microarray hybridization experiments as a common reference for indirect identification of gender-associated transcripts in cercariae, a schistosome life-stage in which there is no overt sexual dimorphism. This led to the identification of 2,648 gender-associated transcripts. When compared to the 780 gender-associated transcripts identified by hybridization experiments utilizing a two-channel direct method (co-hybridization of male and female cercariae cDNA), indirect methods using gDNA were far superior in identifying greater quantities of differentially expressed transcripts. Interestingly, both methods identified a concordant subset of 188 male-associated and 156 female-associated cercarial transcripts, respectively. Gene ontology classification of these differentially expressed transcripts revealed a greater diversity of categories in male cercariae. Quantitative real-time PCR analysis confirmed the DNA microarray results and supported the reliability of this platform for identifying gender-associated transcripts. CONCLUSIONS/SIGNIFICANCE: Schistosome gDNA displays characteristics highly suitable for the comparison of two-channel DNA microarray results obtained from experiments conducted independently across laboratories. The schistosome transcripts identified here demonstrate, for the first time, that gender-associated patterns of expression are already well established in the morphologically identical, but chromosomally distinct, cercariae stage

Glycogen synthesis in the astrocyte: from glycogenin to proglycogen to glycogen

The astrocyte of the newborn rat brain has proven to be a versatile system in which to study glycogen biogenesis. We have taken advantage of the rapid stimulation of glycogen synthesis that occurs when glucose is fed to astrocytes, and the marked limitation on this synthesis that occurs in astrocytes previously exposed to ammonium ions. These observations have been related to our earlier reports of the initiation of glycogen synthesis on a protein primer, glycogenin, and the discovery of a low‐molecular‐weight form of glycogen, proglycogen. The following conclusions have been drawn: 1) In the ammonia‐treated astrocytes starved of glucose, free glycogenin is present. 2) When these astrocytes are fed with glucose, proglycogen is synthesized from the glycogenin primer by a glycogen‐synthase‐like UDPglucose transglucosylase activity (proglycogen synthase) distinct from the well‐recognized glycogen synthase, and synthesis stops at this point. 3) Proglycogen is the precursor of macromolecular glycogen, which is synthesized from proglycogen by glycogen synthase when glucose is fed to untreated astrocytes, accounting for the much greater accumulation of total glycogen. 4) The stimulus to proglycogen and macroglycogen synthesis that occurs on feeding glucose to untreated or ammonia‐treated astrocytes is the result of the activation of proglycogen synthase, not of glycogen synthase. 5) Therefore, in the synthesis of macromolecular glycogen from glycogenin via proglycogen, the step between glycogenin and proglycogen is rate‐limiting. 6) The discovery of additional potential control points in glycogen synthesis, now emerging, may assist the identification of so‐far‐unexplained aberrations of glycogen metabolism.—Lomako, J., Lomako, W. M., Whelan, W. J., Dombro, R. S., Neary, J. T., and Norenberg, M. D. Glycogen synthesis in the astrocyte: from glycogen to proglycogen to glycogen. FASEB J. 7: 1386‐1393; 1993

Lebesgue constants for polyhedral sets and polynomial interpolation on Lissajous\u2013Chebyshev nodes

To analyze the absolute condition number of multivariate polynomial interpolation on Lissajous\u2013Chebyshev node points, we derive upper and lower bounds for the respective Lebesgue constant. The proof is based on a relation between the Lebesgue constant for the polynomial interpolation problem and the Lebesgue constant linked to the polyhedral partial sums of Fourier series. The magnitude of the obtained bounds is determined by a product of logarithms of the side lengths of the considered polyhedral sets and shows the same behavior as the magnitude of the Lebesgue constant for polynomial interpolation on the tensor product Chebyshev grid

Quantitative assessment of human muscle glycogen granules size and number in subcellular locations during recovery from prolonged exercise

Although data relating to muscle glycogen are interpreted as showing it is homogenous when quantified biochemically, it is actually in granules in specific subcellular locations. We hypothesized that postexercise restoration of muscle glycogen would occur initially by an increase in granule number followed by an increase in size, and also that restoration would differ in various subcellular locations. Five men performed prolonged exercise and had muscle biopsies taken at 0, 4, 24 and 48 h of recovery. We quantified granule number and size as well as the total volume of glycogen in the subsarcolemmal and the intra- and intermyofibrillar regions, using transmission electron microscopy. Muscle glycogen was reduced to 36 ± 8.3 mmol glucosyl units (kg dry weight)−1 at exhaustion, and was preferentially depleted and subsequently repleted in the intramyofibrillar space. The repletion rate was greatest in the first 4 h; this was associated with a 186% increase in number (P ≤ 0.05) and no change in particle size (P ≥ 0.05). From 4 h to 48 h, there was an increase in particle size (P ≤ 0.05) but not number (P ≥ 0.05). Net rate of G volume synthesis per unit area was 50% greater (P ≤ 0.05) in the subsarcolemmal than the myofibrillar compartment. Conversely, the net rate of single-particle volume synthesis was greater (P ≤ 0.05) in the myofibrillar than the subsarcolemmal compartment. Glycogen granules varied in size and number depending on location, and in all compartments resynthesis of glycogen was characterized initially by an increase in granule number and later by an increase in size