On the numerical approximation of p-biharmonic and ∞-biharmonic functions

In [KP16] (arXiv:1605.07880) the authors introduced a second-order variational problem in L∞. The associated equation, coined the ∞-Bilaplacian, is a \emph{third order} fully nonlinear PDE given by Δ2∞u:=(Δu)3|D(Δu)|2=0. In this work we build a numerical method aimed at quantifying the nature of solutions to this problem which we call ∞-Biharmonic functions. For fixed p we design a mixed finite element scheme for the pre-limiting equation, the p-Bilaplacian Δ2pu:=Δ(|Δu|p−2Δu)=0. We prove convergence of the numerical solution to the weak solution of Δ2pu=0 and show that we are able to pass to the limit p→∞. We perform various tests aimed at understanding the nature of solutions of Δ2∞u and in 1-d we prove convergence of our discretisation to an appropriate weak solution concept of this problem, that of -solutions

Brain microtubule-associated proteins modulate microtubule dynamic instability in vitro : real-time-observations using video microscopy

We used video assays to study the dynamic instability behavior of individual microtubules assembled in vitro with purified tau, purified MAP2 or a preparation of unfractionated heat-stable MAPs. Axoneme-nucleated microtubules were assembled from pure tubulin at concentrations between 4 and 9 microM in the presence of MAPs, and observed by video-differential interference contrast microscopy. Microtubules co-assembled with each MAP preparation exhibited the elongation and rapid shortening phases and the abrupt transitions (catastrophe and rescue) characteristic of dynamic instability. Each MAP preparation increased the microtubule elongation rate above that for purified tubulin alone by decreasing the tubulin subunit dissociation rate during elongation. The brain MAPs used in this study reduced the rate of microtubule rapid shortening, but allowed significant loss of polymer during the shortening phase. Purified tau and MAP2 decreased the frequency of catastrophe and increased the frequency of rescue, while the heat-stable MAPs suppressed catastrophe at all but the lowest tubulin concentrations. Thus, each of these MAPs modulates, but does not abolish, dynamic instability behavior of microtubules. We propose a model to explain how MAP2 and tau bind to the microtubule lattice at sites along protofilaments so that the MAPs promote polymerization, but do not significantly block the mechanism of rapid shortening inherent in the tubulin lattice. Rapid shortening, when it occurs, proceeds primarily by the dissociation of short fragments of protofilaments, which contain the bound MAPs

Refining trace metal temperature proxies in cold-water scleractinian and stylasterid corals

The Li/Mg, Sr/Ca and oxygen isotopic (O) compositions of many marine biogenic carbonates are sensitive to seawater temperature. Corals, as cosmopolitan marine taxa with carbonate skeletons that can be precisely dated, represent ideal hosts for these geochemical proxies. However, efforts to calibrate and refine temperature proxies in cold-water corals (<20 °C) remain limited. Here we present skeletal Li/Mg, Sr/Ca, O and carbon isotope (C) data from live-collected specimens of aragonitic scleractinian corals (Balanophyllia, Caryophyllia, Desmophyllum, Enallopsammia, Flabellum, Lophelia, and Vaughanella), both aragonitic and high-Mg calcitic stylasterid genera (Stylaster and Errina), and shallow-water high-Mg calcite crustose coralline algae (Lithophyllum, Hydrolithon, and Neogoniolithon). We interpret these data in conjunction with results from previously explored taxa including aragonitic zooxanthellate scleractinia and foraminifera, and high-Mg calcite octocorals. We show that Li/Mg ratios covary most strongly with seawater temperature, both for aragonitic and high-Mg calcitic taxa, making for reliable and universal seawater temperature proxies. Combining all of our biogenic aragonitic Li/Mg data with previous calibration efforts we report a refined relationship to temperature: Li/MgAll Aragonite = (). This calibration now permits paleo-temperature reconstruction to better than ±3.4 °C (95% prediction intervals) across biogenic aragonites, regardless of taxon, from 0 to 30 °C. For taxa in this study, aragonitic stylasterid Li/Mg offers the most robust temperature proxy (Li/MgStylasterid (Arag) = ()) with a reproducibility of ±2.3 °C. For the first time, we show that high-Mg calcites have a similar exponential relationship with temperature, but with a lower intercept value (Li/Mg = ()). This calibration opens the possibility of temperature reconstruction using high-Mg calcite corals and coralline algae. The commonality in the relationship between Li/Mg and temperature transcends phylogeny and suggests abiogenic trace metal incorporation mechanism

Association between urinary biomarkers of total sugars intake and measures of obesity in a cross-sectional study

Obesity is an important modifiable risk factor for chronic diseases. While there is increasing focus on the role of dietary sugars, there remains a paucity of data establishing the association between sugar intake and obesity in the general public. The objective of this study was to investigate associations of estimated sugar intake with odds for obesity in a representative sample of English adults. We used data from 434 participants of the 2005 Health Survey of England. Biomarkers for total sugar intake were measured in 24 h urine samples and used to estimate intake. Linear and logistic regression analyses were used to investigate associations between biomarker-based estimated intake and measures of obesity (body mass intake (BMI), waist circumference and waist-to-hip ratio) and obesity risk, respectively. Estimated sugar intake was significantly associated with BMI, waist circumference and waist-to-hip ratio; these associations remained significant after adjustment for estimated protein intake as a marker of non-sugar energy intake. Estimated sugar intake was also associated with increased odds for obesity based on BMI (OR 1.02; 95%CI 1.00-1.04 per 10g), waist-circumference (1.03; 1.01-1.05) and waist-to-hip ratio (1.04; 1.02-1.06); all OR estimates remained significant after adjusting for estimated protein intake. Our results strongly support positive associations between total sugar intake, measures of obesity and likelihood of being obese. It is the first time that such an association has been shown in a nationally-representative sample of the general population using a validated biomarker. This biomarker could be used to monitor the efficacy of public health interventions to reduce sugar intake

Phylogeny of Galactolipid Synthase Homologs Together with their Enzymatic Analyses Revealed a Possible Origin and Divergence Time for Photosynthetic Membrane Biogenesis

The photosynthetic membranes of cyanobacteria and chloroplasts of higher plants have remarkably similar lipid compositions. In particular, thylakoid membranes of both cyanobacteria and chloroplasts are composed of galactolipids, of which monogalactosyldiacylglycerol (MGDG) is the most abundant, although MGDG biosynthetic pathways are different in these organisms. Comprehensive phylogenetic analysis revealed that MGDG synthase (MGD) homologs of filamentous anoxygenic phototrophs Chloroflexi have a close relationship with MGDs of Viridiplantae (green algae and land plants). Furthermore, analyses for the sugar specificity and anomeric configuration of the sugar head groups revealed that one of the MGD homologs exhibited a true MGDG synthetic activity. We therefore presumed that higher plant MGDs are derived from this ancestral type of MGD genes, and genes involved in membrane biogenesis and photosystems have been already functionally associated at least at the time of Chloroflexi divergence. As MGD gene duplication is an important event during plastid evolution, we also estimated the divergence time of type A and B MGDs. Our analysis indicated that these genes diverged ∼323 million years ago, when Spermatophyta (seed plants) were appearing. Galactolipid synthesis is required to produce photosynthetic membranes; based on MGD gene sequences and activities, we have proposed a novel evolutionary model that has increased our understanding of photosynthesis evolution

Factors influencing feeding practices of extreme poor infants and young children in families of working mothers in Dhaka slums: A qualitative study

BackgroundNutritional status differs between infants and young children living in slum and non-slum conditions—infants and young children living in City Corporation slums are likely to have worse nutritional status compared to those from non-slums. Furthermore, families in slums tend to engage female labor in cash-earning activities as a survival strategy; hence, a higher percentage of mothers stay at work. However, little is known about feeding practices for infants and young children in families with working mothers in slums. This study aims to understand the factors that determine feeding practices for infants and young children living in families with working mothers in Dhaka slums.MethodsThis study adopted a qualitative approach. Sixteen In-depth Interviews, five Key Informant Interviews, and Focused Group Discussions were conducted with family members, community leaders, and program staff. Method triangulation and thematic analyses were conducted.ResultsFeeding practices for infants and young children in families with working mothers are broadly determined by mothers’ occupation, basis civic facilities, and limited family buying capacity. Although mothers have good nutritional knowledge, they negotiate between work and feeding their infants and young children. Household composition, access to cooking facilities, and poverty level were also found to be significant determining factors.ConclusionThe results suggest a trade-off between mothers’ work and childcare. The absence of alternative care support in homes and/or work places along with societal factors outweighs full benefits of project interventions. Improving alternative childcare support could reduce the burden of feeding practice experienced by working mothers and may improve nutritional outcomes

The TIP30 Protein Complex, Arachidonic Acid and Coenzyme A Are Required for Vesicle Membrane Fusion

Efficient membrane fusion has been successfully mimicked in vitro using artificial membranes and a number of cellular proteins that are currently known to participate in membrane fusion. However, these proteins are not sufficient to promote efficient fusion between biological membranes, indicating that critical fusogenic factors remain unidentified. We have recently identified a TIP30 protein complex containing TIP30, acyl-CoA synthetase long-chain family member 4 (ACSL4) and Endophilin B1 (Endo B1) that promotes the fusion of endocytic vesicles with Rab5a vesicles, which transport endosomal acidification enzymes vacuolar (H+)-ATPases (V-ATPases) to the early endosomes in vivo. Here, we demonstrate that the TIP30 protein complex facilitates the fusion of endocytic vesicles with Rab5a vesicles in vitro. Fusion of the two vesicles also depends on arachidonic acid, coenzyme A and the synthesis of arachidonyl-CoA by ACSL4. Moreover, the TIP30 complex is able to transfer arachidonyl groups onto phosphatidic acid (PA), producing a new lipid species that is capable of inducing close contact between membranes. Together, our data suggest that the TIP30 complex facilitates biological membrane fusion through modification of PA on membranes

A posteriori error estimates for the virtual element method

An a posteriori error analysis for the virtual element method (VEM) applied to general elliptic problems is presented. The resulting error estimator is of residual-type and applies on very general polygonal/polyhedral meshes. The estimator is fully computable as it relies only on quantities available from the VEM solution, namely its degrees of freedom and element-wise polynomial projection. Upper and lower bounds of the error estimator with respect to the VEM approximation error are proven. The error estimator is used to drive adaptive mesh refinement in a number of test problems. Mesh adaptation is particularly simple to implement since elements with consecutive co-planar edges/faces are allowed and, therefore, locally adapted meshes do not require any local mesh post-processing

Phosphorylation by Dyrk1A of Clathrin Coated Vesicle-Associated Proteins: Identification of the Substrate Proteins and the Effects of Phosphorylation

Dyrk1A phosphorylated multiple proteins in the clathrin-coated vesicle (CCV) preparations obtained from rat brains. Mass spectrometric analysis identified MAP1A, MAP2, AP180, and α- and β-adaptins as the phosphorylated proteins in the CCVs. Each protein was subsequently confirmed by [32P]-labeling and immunological methods. The Dyrk1A-mediated phosphorylation released the majority of MAP1A and MAP2 and enhanced the release of AP180 and adaptin subunits from the CCVs. Furthermore, Dyrk1A displaced adaptor proteins physically from CCVs in a kinase-concentration dependent manner. The clathrin heavy chain release rate, in contrast, was not affected by Dyrk1A. Surprisingly, the Dyrk1A-mediated phosphorylation of α- and β-adaptins led to dissociation of the AP2 complex, and released only β-adaptin from the CCVs. AP180 was phosphorylated by Dyrk1A also in the membrane-free fractions, but α- and β-adaptins were not. Dyrk1A was detected in the isolated CCVs and was co-localized with clathrin in neurons from mouse brain sections and from primary cultured rat hippocampus. Previously, we proposed that Dyrk1A inhibits the onset of clathrin-mediated endocytosis in neurons by phosphorylating dynamin 1, amphiphysin 1, and synaptojanin 1. Current results suggest that besides the inhibition, Dyrk1A promotes the uncoating process of endocytosed CCVs