Variational approach in weighted Sobolev spaces to scattering by unbounded rough surfaces

We consider the problem of scattering of time harmonic acoustic waves by an unbounded sound soft surface which is assumed to lie within a finite distance of some plane. The paper is concerned with the study of an equivalent variational formulation of this problem set in a scale of weighted Sobolev spaces. We prove well-posedness of this variational formulation in an energy space with weights which extends previous results in the unweighted setting [S. Chandler-Wilde and P. Monk, SIAM J. Math. Anal., 37 (2005), pp. 598–618] to more general inhomogeneous terms in the Helmholtz equation. In particular, in the two-dimensional case, our approach covers the problem of plane wave incidence, whereas in the three-dimensional case, incident spherical and cylindrical waves can be treated. As a further application of our results, we analyze a finite section type approximation, whereby the variational problem posed on an infinite layer is approximated by a variational problem on a bounded region.

The SV2A ligand levetiracetam inhibits presynaptic Ca2+ channels via an intracellular pathway

Levetiracetam (LEV) is a prominent antiepileptic drug (AED) which binds to neuronal synaptic vesicle glycoprotein 2A (SV2A) protein and has reported effects on ion channels, but retains a poorly-defined mechanism of action. Here, we investigate inhibition of voltage-dependent Ca2+ (CaV) channels as a potential mechanism by which LEV imparts effects on neuronal activity. We used electrophysiological methods to investigate the effects of LEV on cholinergic synaptic transmission and CaV channel activity in superior cervical ganglion neurons (SCGNs). In parallel, we investigated effects of the LEV ‘inactive’ R-enantiomer, UCB L060. Thus, LEV, but not UCB L060 (each 100 μM), inhibited synaptic transmission between SCGNs in long-term culture in a time-dependent manner, significantly reducing excitatory postsynaptic potentials (EPSP) following ≥30 min application. In isolated SCGNs, LEV pretreatment (≥1 h), but not acute (5 min) application, significantly inhibited whole-cell IBa amplitude. In current clamp recordings, LEV reduced the amplitude of the afterhyperpolarizing potential (AHP) in a Ca2+-dependent manner, but also increased action potential (AP) latency in a Ca2+-independent manner, suggesting further mechanisms associated with reduced excitability. Intracellular LEV application (4-5 min) caused a rapid inhibition of IBa amplitude to an extent comparable to that seen following extracellular LEV pretreatment ( ≥ 1 h). Neither pretreatment nor intracellular application of UCB L060 produced any inhibitory effects on IBa amplitude. These results identify a stereospecific intracellular pathway by which LEV inhibits presynaptic CaV channels; resultant reductions in neuronal excitability are proposed to contribute to the anticonvulsant effects of LEV.

Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the $p$-version

Plane wave discontinuous Galerkin (PWDG) methods are a class of Trefftz-type methods for the spatial discretization of boundary value problems for the Helmholtz operator $-\Delta-\omega^2$, $\omega>0$. They include the so-called ultra weak variational formulation from [O. Cessenat and B. Després, SIAM J. Numer. Anal., 35 (1998), pp. 255–299]. This paper is concerned with the a priori convergence analysis of PWDG in the case of $p$-refinement, that is, the study of the asymptotic behavior of relevant error norms as the number of plane wave directions in the local trial spaces is increased. For convex domains in two space dimensions, we derive convergence rates, employing mesh skeleton-based norms, duality techniques from [P. Monk and D. Wang, Comput. Methods Appl. Mech. Engrg., 175 (1999), pp. 121–136], and plane wave approximation theory.

Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations

In this paper, we extend to the time-harmonic Maxwell equations the p-version analysis technique developed in [R. Hiptmair, A. Moiola and I. Perugia, Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the p-version, SIAM J. Numer. Anal., 49 (2011), 264-284] for Trefftz-discontinuous Galerkin approximations of the Helmholtz problem. While error estimates in a mesh-skeleton norm are derived parallel to the Helmholtz case, the derivation of estimates in a mesh-independent norm requires new twists in the duality argument. The particular case where the local Trefftz approximation spaces are built of vector-valued plane wave functions is considered, and convergence rates are derived.

Intermittent Escherichia coli O157:H7 colonisation at the terminal rectum mucosa of conventionally-reared lambs

In cattle, the lymphoid rich regions of the rectal-anal mucosa at the terminal rectum are the preferred site for Escherichia coli O157:H7 colonisation. All cattle infected by rectal swab administration demonstrate long-term E. coli O157:H7 colonisation, whereas orally challenged cattle do not demonstrate long-term E. coli O157:H7 colonisation in all animals. Oral, but not rectal challenge of sheep with E. coli O157:H7 has been reported, but an exact site for colonisation in sheep is unknown. To determine if E. coli O157:H7 can effectively colonise the ovine terminal rectum, in vitro organ culture (IVOC) was initiated. Albeit sparsely, large, densely packed E. coli O157:H7 micro-colonies were observed on the mucosa of ovine and control bovine terminal rectum explants. After necropsy of orally inoculated lambs, bacterial enumeration of the proximal and distal gastrointestinal tract did suggest a preference for E. coli O157:H7 colonisation at the ovine terminal rectum, albeit for both lymphoid rich and non-lymphoid sites. As reported for cattle, rectal inoculation studies were then conducted to determine if all lambs would demonstrate persistent colonisation at the terminal rectum. After necropsy of E. coli O157:H7 rectally inoculated lambs, most animals were not colonised at gastrointestinal sites proximal to the rectum, however, large densely packed micro-colonies of E. coli O157:H7 were observed on the ovine terminal rectum mucosa. Nevertheless, at the end point of the study (day 14), only one lamb had E. coli O157:H7 micro-colonies associated with the terminal rectum mucosa. A comparison of E. coli O157:H7 shedding yielded a similar pattern of persistence between rectally and orally inoculated lambs. The inability of E. coli O157:H7 to effectively colonise the terminal rectum mucosa of all rectally inoculated sheep in the long term, suggests that E. coli O157:H7 may colonise this site, but less effectively than reported previously for cattle.

Colonization of 8-week-old conventionally reared goats by Escherichia coli O157:H7 after oral inoculation

Enterohaemorrhagic Escherichia coli O157 : H7 infections of man have been associated with consumption of unpasteurized goat's milk and direct contact with kid goats on petting farms, yet little is known about colonization of goats with this organism. To assess the contribution of flagella and intimin of E coli O157 : H7 in colonization of the goat, 8-week-old conventionally reared goats were inoculated orally in separate experiments with 1 X 10(10) c.f.u. of a non-verotoxigenic strain of E coli O157: H7 (strain NCTC 12900 Nal(r)), an aflagellate derivative (DMB1) and an intimin-deficient derivative (DMB2). At 24 In after inoculation, the three E coli O157 : H7 strains were shed at approximately 5 X 1 04 c.f.u. (g faeces)(-1) from all animals. Significantly fewer intimin-deficient bacteria were shed only on days 2 (P = 0(.)003) and 4 (P = 0(.)014), whereas from day 7 to 29 there were no differences. Tissues from three animals inoculated with wild-type E coli O157 : H7 strain NCTC 12900 Nalr were sampled at 24,48 and 96 In after inoculation and the organism was cultured from the large intestine of all three animals and from the duodenum and ileum of the animal examined at 96 h. Tissues were examined histologically but attaching-effacing (AE) lesions were not observed at any intestinal site of the animals examined at 24 or 48 In. However, the animal examined at 96 h, which had uniquely shed approximately 1 x 10(7) E coli O157: H7 (g faeces)(-1) for the preceding 3 days, showed a heavy, diffuse infection with cryptosporidia. and abundant, multifocal AE lesions in the distal colon, rectum and at the recto-anal junction. These AE lesions were confirmed by immunohistochemistry to be associated with E coli O157: H7.

Influence of colostrum deprivation and concurrent Cryptosporidium parvum infection on the colonization and persistence of Escherichia coli O157:H7 in young lambs

Escherichia coli O157: H7 and Cryptosporidium parvum infections of man have been associated with direct contact with small ruminants. Colostrum protects neonates against gastrointestinal pathogens, and orphan lambs, which are common on petting farms, may be deprived of this protection. In a recent study, it was demonstrated that high shedding of E coli O157 : H7 by an 8-week-old goat kid was associated with coincidental C. parvum infection. Furthermore, both pathogens were co-located in the distal gastrointestinal tract. It was hypothesized that colostrum deprivation and pre-infection with C. parvum predisposed young ruminants to colonization and increased shedding of E coli O157: H7. To test this, 21 lambs 5 weeks of age were divided into four groups as follows: (A) colostrum-deprived and inoculated with E coli O157: H7, (B) colostrum-deprived and inoculated with C. parvum and then E coli O157: H7, (C) conventionally reared and inoculated with E coli O157: H7, (D) conventionally reared and inoculated with C. parvum and then E coli O15 7: H7. C. parvum was detected between 8 and 12 days post-inoculation in most of the infected lambs. At 24 h post-inoculation with E coli O157: H7, all lambs were shedding between 5 x 10(4) and 5 x 10(7) c.f.u. E coli O157: H7 per gram of faeces. E coli O157: H7 was shed in higher numbers in the groups pre-inoculated with C. parvum, whether conventionally reared or colostrum-deprived. Interestingly, for the colostrum-deprived lambs on day 3, a significant difference in shedding of E coli O157: H7 was observed (P= 0-038), with the lambs inoculated with E coli alone yielding higher counts than those pre-inoculated with C. parvum. From day 15 onwards, shedding of E coli O157: H7 was highest from the colostrum-deprived C. parvum-infected lambs, then (in descending order of shedding) the colostrum-deprived lambs, the conventionally reared lambs infected with C. parvum, and the conventionally reared animals. In total, four animals were euthanized, two at 24 h and two at 96 h post inoculation with E coli 0 157: H7 (two conventionally reared and two colostrum-deprived). All animals euthanized were from groups pre-inoculated with C. parvum prior to challenge with E coli O157 : H7. On examination of tissues, in three of the four animals examined, multifocal attaching and effacing lesions were observed in the caecum, colon, rectum and at the recto-anal junction, and were confirmed by immunolhistochemistry to be associated with E coli O157: H7.

(Non-)ergodicity of a degenerate diffusion modeling the fiber lay down process

We analyze the large time behavior of a stochastic model for the lay down of fibers on a moving conveyor belt in the production process of nonwovens. It is shown that under weak conditions this degenerate diffusion process has a unique invariant distribution and is even geometrically ergodic. This generalizes results from previous works [M. Grothaus and A. Klar, SIAM J. Math. Anal., 40 (2008), pp. 968–983; J. Dolbeault et al., arXiv:1201.2156] concerning the case of a stationary conveyor belt, in which the situation of a moving conveyor belt has been left open.

Direct observation of membrane insertion by enveloped virus matrix proteins by phosphate displacement

Enveloped virus release is driven by poorly understood proteins that are functional analogs of the coat protein assemblies that mediate intracellular vesicle trafficking. We used differential electron density mapping to detect membrane integration by membrane-bending proteins from five virus families. This demonstrates that virus matrix proteins replace an unexpectedly large portion of the lipid content of the inner membrane face, a generalized feature likely to play a role in reshaping cellular membranes.

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].

Inhibition of LRRK2 kinase activity stimulates macroautophagy

Leucine Rich Repeat Kinase 2 (LRRK2) is one of the most important genetic contributors to Parkinson's disease. LRRK2 has been implicated in a number of cellular processes, including macroautophagy. To test whether LRRK2 has a role in regulating autophagy, a specific inhibitor of the kinase activity of LRRK2 was applied to human neuroglioma cells and downstream readouts of autophagy examined. The resulting data demonstrate that inhibition of LRRK2 kinase activity stimulates macroautophagy in the absence of any alteration in the translational targets of mTORC1, suggesting that LRRK2 regulates autophagic vesicle formation independent of canonical mTORC1 signaling. This study represents the first pharmacological dissection of the role LRRK2 plays in the autophagy/lysosomal pathway, emphasizing the importance of this pathway as a marker for LRRK2 physiological function. Moreover it highlights the need to dissect autophagy and lysosomal activities in the context of LRRK2 related pathologies with the final aim of understanding their aetiology and identifying specific target for disease modifying therapies in patients.

Arenavirus budding resulting from viral-protein-associated cell membrane curvature

Viral replication occurs within cells, with release (and onward infection) primarily achieved through two alternative mechanisms: lysis, in which virions emerge as the infected cell dies and bursts open; or budding, in which virions emerge gradually from a still living cell by appropriating a small part of the cell membrane. Virus budding is a poorly understood process that challenges current models of vesicle formation. Here, a plausible mechanism for arenavirus budding is presented, building on recent evidence that viral proteins embed in the inner lipid layer of the cell membrane. Experimental results confirm that viral protein is associated with increased membrane curvature, whereas a mathematical model is used to show that localized increases in curvature alone are sufficient to generate viral buds. The magnitude of the protein-induced curvature is calculated from the size of the amphipathic region hypothetically removed from the inner membrane as a result of translation, with a change in membrane stiffness estimated from observed differences in virion deformation as a result of protein depletion. Numerical results are based on experimental data and estimates for three arenaviruses, but the mechanisms described are more broadly applicable. The hypothesized mechanism is shown to be sufficient to generate spontaneous budding that matches well both qualitatively and quantitatively with experimental observations.

Interaction between a cationic surfactant-like peptide and lipid vesicles and its relationship to antimicrobial activity

We investigate the properties of an antimicrobial surfactant-like peptide (Ala)6(Arg), A6R, containing a cationic headgroup. The interaction of this peptide with zwitterionic (DPPC) lipid vesicles is investigated using a range of microscopic, X-ray scattering, spectroscopic, and calorimetric methods. The β-sheet structure adopted by A6R is disrupted in the presence of DPPC. A strong effect on the small-angle X-ray scattering profile is observed: the Bragg peaks from the DPPC bilayers in the vesicle walls are eliminated in the presence of A6R and only bilayer form factor peaks are observed. All of these observations point to the interaction of A6R with DPPC bilayers. These studies provide insight into interactions between a model cationic peptide and vesicles, relevant to understanding the action of antimicrobial peptides on lipid membranes. Notably, peptide A6R exhibits antimicrobial activity without membrane lysis.

Alanine-rich amphiphilic peptide containing the RGD cell adhesion motif: a coating material for human fibroblast attachment and culture

We studied the self-assembly of peptide A6RGD (A: alanine, R: arginine, G: glycine, D: aspartic acid) in water, and the use of A6RGD substrates as coatings to promote the attachment of human cornea stromal fibroblasts (hCSFs). The self-assembled motif of A6RGD was shown to depend on the peptide concentration in water, where both vesicle and fibril formation were observed. Oligomers were detected for 0.7 wt% A6RGD, which evolved into short peptide fibres at 1.0 wt% A6RGD, while a co-existence of vesicles and long peptide fibres was revealed for 2–15 wt% A6RGD. A6RGD vesicle walls were shown to have a multilayer structure built out of highly interdigitated A6 units, while A6RGD fibres were based on β-sheet assemblies. Changes in the self-assembly motif with concentration were reflected in the cell culture assay results. Films dried from 0.1–1.0 wt% A6RGD solutions allowed hCSFs to attach and significantly enhanced cell proliferation relative to the control. In contrast, films dried from 2.5 wt% A6RGD solutions were toxic to hCSFs.

Culture bag systems for clinical applications of adult human neural crest-derived stem cells

Introduction Facing the challenging treatment of neurodegenerative diseases as well as complex craniofacial injuries such as those common after cancer therapy, the field of regenerative medicine increasingly relies on stem cell transplantation strategies. Here, neural crest-derived stem cells (NCSCs) offer many promising applications, although scale up of clinical-grade processes prior to potential transplantations is currently limiting. In this study, we aimed to establish a clinical-grade, cost-reducing cultivation system for NCSCs isolated from the adult human nose using cGMP-grade Afc-FEP bags. Methods We cultivated human neural crest-derived stem cells from inferior turbinate (ITSCs) in a cell culture bag system using Afc-FEP bags in human blood plasma-supplemented medium. Investigations of viability, proliferation and expression profile of bag-cultured ITSCs were followed by DNA-content and telomerase activity determination. Cultivated ITSCs were introduced to directed in vitro differentiation assays to assess their potential for mesodermal and ectodermal differentiation. Mesodermal differentiation was determined using an enzyme activity assay (alkaline phosphatase, ALP), respective stainings (Alizarin Red S, Von Kossa and Oil Red O), and RT-PCR, while immunocytochemistry and synaptic vesicle recycling were applied to assay neuroectodermal differentiation of ITSCs. Results When cultivated within Afc-FEP bags, ITSCs grew three-dimensionally in a human blood plasma-derived matrix, thereby showing unchanged morphology, proliferation capability, viability and expression profile in comparison to three dimensionally-cultured ITSCs growing in standard cell culture plastics. Genetic stability of bag-cultured ITSCs was further accompanied by unchanged telomerase activity. Importantly, ITSCs retained their potential to differentiate into mesodermal cell types, particularly including ALP-active, Alizarin Red S-, and Von Kossa-positive osteogenic cell types, as well as adipocytes positive in Oil Red O assays. Bag culture further did not affect the potential of ITSCs to undergo differentiation into neuroectodermal cell types coexpressing β-III-tubulin and MAP2 and exhibiting the capability for synaptic vesicle recycling. Conclusions Here, we report for the first time the successful cultivation of human NCSCs within cGMP-grade Afc-FEP bags using a human blood plasma-supplemented medium. Our findings particularly demonstrate the unchanged differentiation capability and genetic stability of the cultivated NCSCs, suggesting the great potential of this culture system for future medical applications in the field of regenerative medicine.