Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

The postfusion structure of baculovirus gp64 supports a unified view of viral fusion machines

Viral fusion proteins mediate the merger of host and viral membranes during cell entry for all enveloped viruses. Baculovirus glycoprotein gp64 (gp64) is unusual in promoting entry into both insect and mammalian cells and is distinct from established class I and class II fusion proteins. We report the crystal structure of its postfusion form, which explains a number of gp64's biological properties including its cellular promiscuity, identifies the fusion peptides and shows it to be the third representative of a new class (III) of fusion proteins with unexpected structural homology with vesicular stomatitis virus G and herpes simplex virus type 1 gB proteins. We show that domains of class III proteins have counterparts in both class I and II proteins, suggesting that all these viral fusion machines are structurally more related than previously thought.

Dual-specificity phosphatases in the hypo-osmotic stress response of keratin-defective epithelial cell lines

Although mutations in intermediate filament proteins cause many human disorders, the detailed pathogenic mechanisms and the way these mutations affect cell metabolism are unclear. In this study, selected keratin mutations were analysed for their effect on the epidermal stress response. Expression profiles of two keratin-mutant cell lines from epidermolysis bullosa simplex patients (one severe and one mild) were compared to a control keratinocyte line before and after challenge with hypo-osmotic shock, a common physiological stress that transiently distorts cell shape. Fewer changes in gene expression were found in cells with the severely disruptive mutation (55 genes altered) than with the mild mutation (174 genes) or the wild type cells (261 genes) possibly due to stress response pre-activation in these cells. We identified 16 immediate-early genes contributing to a general cell response to hypo-osmotic shock, and 20 genes with an altered expression pattern in the mutant keratin lines only. A number of dual-specificity phosphatases (MKP-1, MKP-2, MKP-3, MKP-5 and hVH3) are differentially regulated in these cells, and their downstream targets p-ERK and p-p38 are significantly up-regulated in the mutant keratin lines. Our findings strengthen the case for the expression of mutant keratin proteins inducing physiological stress, and this intrinsic stress may affect the cell responses to secondary stresses in patients' skin.

Cardiac Na+/H+ exchanger during post-natal development in the rat: Changes in mRNA expression and sarcolemmal activity

We examined Na+–H+exchanger isoform 1 (NHE-1) mRNA expression in ventricular myocardium and its correlation with sarcolemmal NHE activity in isolated ventricular myocytes, during postnatal development in the rat. The expression of glyceraldehyde-3-phosphate dehydrogenase (GAPDH) mRNA did not change in ventricular myocardium between 2 and 42 days after birth. Therefore, at seven time points within that age range, GAPDH expression was used to normalize NHE-1 mRNA levels, as determined by reverse transcription polymerase chain reaction analysis. There was a progressive five-fold reduction in NHE-1 mRNA expression in ventricular myocardium from 2 days to 42 days of age. As an index of NHE activity, acid efflux rates (JH) were determined in single neonatal (2–4-day-old) and adult (42-day-old) ventricular myocytes (n=16/group) loaded with the pH fluoroprobe carboxy-seminaphthorhodafluor-1. In HEPES-buffered medium, basal intracellular pH (pHi) was similar at 7.28±0.02 in neonatal and 7.31±0.02 in adult myocytes, but intrinsic buffering power was lower in the former age group. The rate at which pHirecovered from a similar acid load was significantly greater in neonatal than in adult myocytes (0.36±0.07v0.16±0.02 pH units/min at pHi=6.8). This was reflected by a significantly greaterJH(22±4v9±1 pmol/cm2/s at pHi=6.8), indicating greater sarcolemmal NHE activity in neonatal myocytes. The concomitant reductions in tissue NHE-1 mRNA expression and sarcolemmal NHE activity suggest that myocardial NHE-1 is subject to regulation at the mRNA level during postnatal development.

Representing geometrical knowledge

This paper introduces perspex algebra which is being developed as a common representation of geometrical knowledge. A perspex can currently be interpreted in one of four ways. First, the algebraic perspex is a generalization of matrices, it provides the most general representation for all of the interpretations of a perspex. The algebraic perspex can be used to describe arbitrary sets of coordinates. The remaining three interpretations of the perspex are all related to square matrices and operate in a Euclidean model of projective space-time, called perspex space. Perspex space differs from the usual Euclidean model of projective space in that it contains the point at nullity. It is argued that the point at nullity is necessary for a consistent account of perspective in top-down vision. Second, the geometric perspex is a simplex in perspex space. It can be used as a primitive building block for shapes, or as a way of recording landmarks on shapes. Third, the transformational perspex describes linear transformations in perspex space that provide the affine and perspective transformations in space-time. It can be used to match a prototype shape to an image, even in so called 'accidental' views where the depth of an object disappears from view, or an object stays in the same place across time. Fourth, the parametric perspex describes the geometric and transformational perspexes in terms of parameters that are related to everyday English descriptions. The parametric perspex can be used to obtain both continuous and categorical perception of objects. The paper ends with a discussion of issues related to using a perspex to describe logic.

Rank histograms of stratified Monte-Carlo ensembles

The application of forecast ensembles to probabilistic weather prediction has spurred considerable interest in their evaluation. Such ensembles are commonly interpreted as Monte Carlo ensembles meaning that the ensemble members are perceived as random draws from a distribution. Under this interpretation, a reasonable property to ask for is statistical consistency, which demands that the ensemble members and the verification behave like draws from the same distribution. A widely used technique to assess statistical consistency of a historical dataset is the rank histogram, which uses as a criterion the number of times that the verification falls between pairs of members of the ordered ensemble. Ensemble evaluation is rendered more specific by stratification, which means that ensembles that satisfy a certain condition (e.g., a certain meteorological regime) are evaluated separately. Fundamental relationships between Monte Carlo ensembles, their rank histograms, and random sampling from the probability simplex according to the Dirichlet distribution are pointed out. Furthermore, the possible benefits and complications of ensemble stratification are discussed. The main conclusion is that a stratified Monte Carlo ensemble might appear inconsistent with the verification even though the original (unstratified) ensemble is consistent. The apparent inconsistency is merely a result of stratification. Stratified rank histograms are thus not necessarily flat. This result is demonstrated by perfect ensemble simulations and supplemented by mathematical arguments. Possible methods to avoid or remove artifacts that stratification induces in the rank histogram are suggested.

Heterogeneous surface expression of EspA translocon filaments by Escherichia coli O157:H7 is controlled at the posttranscriptional level

Type III secretion systems of enteric bacteria enable translocation of effector proteins into host cells. Secreted proteins of verotoxigenic Escherichia coli O157 strains include components of a translocation apparatus, EspA, -B, and -D, as well as "effectors" such as the translocated intimin receptor (Tir) and the mitochondrion-associated protein (Map). This research has investigated the regulation of LEE4 translocon proteins, in particular EspA. EspA filaments could not be detected on the bacterial cell surface when E. coli O157:H7 was cultured in M9 minimal medium but were expressed from only a proportion of the bacterial population when cultured in minimal essential medium modified with 25 mM HEPES. The highest proportions of EspA-filamented bacteria were detected in late exponential phase, after which filaments were lost rapidly from the bacterial cell surface. Our previous research had shown that human and bovine E. coli O157:H7 strains exhibit marked differences in EspD secretion levels. Here it is demonstrated that the proportion of the bacterial population expressing EspA filaments was associated with the level of EspD secretion. The ability of individual bacteria to express EspA filaments was not controlled at the level of LEE1-4 operon transcription, as demonstrated by using both beta-galactosidase and green fluorescent protein (GFP) promoter fusions. All bacteria, whether expressing EspA filaments or not, showed equivalent levels of GFP expression when LEEI-4 translational fusions were used. Despite this, the LEE4-espADB mRNA was more abundant from populations with a high proportion of nonsecreting bacteria (low secretors) than from populations with a high proportion of secreting and therefore filamented bacteria (high secretors). This research demonstrates that while specific environmental conditions are required to induce LEEI-4 expression, a further checkpoint exists before EspA filaments are produced on the bacterial surface and secretion of effector proteins occurs. This checkpoint in E. coli O157:H7 translocon expression is controlled by a posttranscriptional mechanism acting on LEE4-espADB mRNA. The heterogeneity in EspA filamentation could arise from phase-variable expression of regulators that control this posttranscriptional mechanism.

Agonist-induced endocytosis of rat somatostatin receptor 1

Somatostatin-receptor 1 (sst1) is an autoreceptor in the central nervous system that regulates the release of somatostatin. Sst1 is present intracellularly and at the cell surface. To investigate sst1 trafficking, rat sst1 tagged with epitope was expressed in rat insulinoma cells 1046-38 (RIN-1046-38) and tracked by antibody labeling. Confocal microscopic analysis revealed colocalization of intracellularly localized rat sst1-human simplex virus (HSV) with Rab5a-green fluorescent protein and Rab11a-green fluorescent protein, indicating the distribution of the receptor in endocytotic and recycling organelles. Somatostatin-14 induced internalization of cell surface receptors and reduction of binding sites on the cell surface. It also stimulated recruitment of intracellular sst1-HSV to the plasma membrane. Confocal analysis of sst1-HSV revealed that the receptor was initially transported within superficial vesicles. Prolonged stimulation of the cells with the peptide agonist induced intracellular accumulation of somatostatin-14. Because the number of cell surface binding sites did not change during prolonged stimulation, somatostatin-14 was internalized through a dynamic process of continuous endocytosis, recycling, and recruitment of intracellularly present sst1-HSV. Accumulated somatostatin-14 bypassed degradation via the endosomal-lysosomal route and was instead rapidly released as intact and biologically active somatostatin-14. Our results show for the first time that sst1 mediates a dynamic process of endocytosis, recycling, and re-endocytosis of its cognate ligand.

Pediastrum species as potential indicators of lake-level change in tropical South America

We explored the potential for using Pediastrum (Meyen), a genus of green alga commonly found in palaeoecological studies, as a proxy for lake-level change in tropical South America. The study site, Laguna La Gaiba (LLG) (17°45′S, 57°40′W), is a broad, shallow lake located along the course of the Paraguay River in the Pantanal, a 135,000-km2 tropical wetland located mostly in western Brazil, but extending into eastern Bolivia. Fourteen surface sediment samples were taken from LLG across a range of lake depths (2-5.2 m) and analyzed for Pediastrum. We found seven species, of which P. musteri (Tell et Mataloni), P. argentiniense (Bourr. et Tell), and P. cf. angulosum (Ehrenb.) ex Menegh. were identified as potential indicators of lake level. Results of the modern dataset were applied to 31 fossil Pediastrum assemblages spanning the early Holocene (12.0 kyr BP) to present to infer past lake level changes qualitatively. Early Holocene (12.0-9.8 kyr BP) assemblages do not show a clear signal, though abundance of P. simplex (Meyen) suggests relatively high lake levels. Absence of P. musteri, characteristic of deep, open water, and abundance of macrophyte-associated taxa indicate lake levels were lowest from 9.8 to 3.0 kyr BP. A shift to wetter conditions began at 4.4 kyr BP, indicated by the appearance of P. musteri, though inferred lake levels did not reach modern values until 1.4 kyr BP. The Pediastrum-inferred mid-Holocene lowstand is consistent with lower precipitation, previously inferred using pollen from this site, and is also in agreement with evidence for widespread drought in the South American tropics during the middle Holocene. An inference for steadily increasing lake level from 4.4 kyr BP to present is consistent with diatom-inferred water level rise at Lake Titicaca, and demonstrates coherence with the broad pattern of increasing monsoon strength from the late Holocene until present in tropical South America.