An analysis of the practical DPG method

In this work we give a complete error analysis of the Discontinuous Petrov Galerkin (DPG) method, accounting for all the approximations made in its practical implementation. Specifically, we consider the DPG method that uses a trial space consisting of polynomials of degree $p$ on each mesh element. Earlier works showed that there is a "trial-to-test" operator $T$, which when applied to the trial space, defines a test space that guarantees stability. In DPG formulations, this operator $T$ is local: it can be applied element-by-element. However, an infinite dimensional problem on each mesh element needed to be solved to apply $T$. In practical computations, $T$ is approximated using polynomials of some degree $r > p$ on each mesh element. We show that this approximation maintains optimal convergence rates, provided that $r\ge p+N$, where $N$ is the space dimension (two or more), for the Laplace equation. We also prove a similar result for the DPG method for linear elasticity. Remarks on the conditioning of the stiffness matrix in DPG methods are also included.Comment: Mathematics of Computation, 201

Partial expansion of a Lipschitz domain and some applications

We show that a Lipschitz domain can be expanded solely near a part of its boundary, assuming that the part is enclosed by a piecewise C1 curve. The expanded domain as well as the extended part are both Lipschitz. We apply this result to prove a regular decomposition of standard vector Sobolev spaces with vanishing traces only on part of the boundary. Another application in the construction of low-regularity projectors into finite element spaces with partial boundary conditions is also indicated

An Analysis of the Practical DPG Method

We give a complete error analysis of the Discontinuous Petrov Galerkin (DPG) method, accounting for all the approximations made in its practical implementation. Specifically, we consider the DPG method that uses a trial space consisting of polynomials of degree p on each mesh element. Earlier works showed that there is a trial-to-test operator T, which when applied to the trial space, defines a test space that guarantees stability. In DPG formulations, this operator T is local: it can be applied element-by-element. However, an infinite dimensional problem on each mesh element needed to be solved to apply T. In practical computations, T is approximated using polynomials of some degree r \u3e p on each mesh element. We show that this approximation maintains optimal convergence rates, provided that r p + N, where N is the space dimension (two or more), for the Laplace equation. We also prove a similar result for the DPG method for linear elasticity. Remarks on the conditioning of the stiffness matrix in DPG methods are also included

A Locking-Free hp DPG Method for Linear Elasticity with Symmetric Stresses

We present two new methods for linear elasticity that simultaneously yield stress and displacement approximations of optimal accuracy in both the mesh size h and polynomial degree p. This is achieved within the recently developed discontinuous Petrov- Galerkin (DPG) framework. In this framework, both the stress and the displacement ap- proximations are discontinuous across element interfaces. We study locking-free convergence properties and the interrelationships between the two DPG methods

CD4+ T cell–independent vaccination against Pneumocystis carinii in mice

Host defenses are profoundly compromised in HIV-infected hosts due to progressive depletion of CD4(+) T lymphocytes. Moreover, deficient CD4(+) T lymphocytes impair vaccination approaches to prevent opportunistic infection. Therefore, we investigated a CD4(+) T cell–independent vaccine approach to a prototypic AIDS-defining infection, Pneumocystis carinii (PC) pneumonia. Here, we demonstrate that bone marrow–derived dendritic cells (DCs) expressing the murine CD40 ligand, when pulsed ex vivo by PC antigen, elicited significant titers of anti-PC IgG in CD4-deficient mice. Vaccinated animals demonstrated significant protection from PC infection, and this protection was the result of an effective humoral response, since adoptive transfer of CD4-depleted splenocytes or serum conferred this protection to CD4-deficient mice. Western blot analysis of PC antigen revealed that DC-vaccinated, CD4-deficient mice predominantly reacted to a 55-kDa PC antigen. These studies show promise for advances in CD4-independent vaccination against HIV-related pathogens

The chemistry of branched condensed phosphates.

Condensed phosphates may exist as linear, cyclic or branched structures. Due to their important role in nature, linear polyphosphates have been well studied. In contrast, branched phosphates (ultraphosphates) remain largely uncharacterised, because they were already described in 1950 as exceedingly unstable in the presence of water, epitomized in the antibranching-rule. This rule lacks experimental backup, since, to the best of our knowledge, no rational synthesis of defined ultraphosphates is known. Consequently, detailed studies of their chemical properties, reactivity and potential biological relevance remain elusive. Here, we introduce a general synthesis of monodisperse ultraphosphates. Hydrolysis half-lives up to days call the antibranching-rule into question. We provide evidence for the interaction of an enzyme with ultraphosphates and discover a rearrangement linearizing the branched structure. Moreover, ultraphosphate can phosphorylate nucleophiles such as amino acids and nucleosides with implications for prebiotic chemistry. Our results provide an entry point into the uncharted territory of branched condensed phosphates

Individual motile CD4+ T cells can participate in efficient multikilling through conjugation to multiple tumor cells

T cells genetically modified to express a CD19-specific chimeric antigen receptor (CAR) for the investigational treatment of B-cell malignancies comprise a heterogeneous population, and their ability to persist and participate in serial killing of tumor cells is a predictor of therapeutic success. We implemented Timelapse Imaging Microscopy in Nanowell Grids (TIMING) to provide direct evidence that CD4+CAR+ T cells (CAR4 cells) can engage in multikilling via simultaneous conjugation to multiple tumor cells. Comparisons of the CAR4 cells and CD8+CAR+ T cells (CAR8 cells) demonstrate that, although CAR4 cells can participate in killing and multikilling, they do so at slower rates, likely due to the lower granzyme B content. Significantly, in both sets of T cells, a minor subpopulation of individual T cells identified by their high motility demonstrated efficient killing of single tumor cells. A comparison of the multikiller and single-killer CAR+ T cells revealed that the propensity and kinetics of T-cell apoptosis were modulated by the number of functional conjugations. T cells underwent rapid apoptosis, and at higher frequencies, when conjugated to single tumor cells in isolation, and this effect was more pronounced on CAR8 cells. Our results suggest that the ability of CAR+ T cells to participate in multikilling should be evaluated in the context of their ability to resist activation-induced cell death. We anticipate that TIMING may be used to rapidly determine the potency of T-cell populations and may facilitate the design and manufacture of next-generation CAR+ T cells with improved efficacy. Cancer Immunol Res; 3(5); 473–82. ©2015 AACR

Synthetic community improves crop performance and alters rhizosphere microbial communities

Introduction: Harnessing synthetic communities (SynCom) of plant growth‐promoting (PGP) microorganisms is considered a promising approach to improve crop fitness and productivity. However, biotic mechanisms that underpin improved plant performance and the effects of delivery mode of synthetic community are poorly understood. These are critical knowledge gaps that constrain field efficacy of SynCom and hence large‐ scale adoption by the farming community. Material & Methods: In this study, a SynCom of four PGP microbial species was constructed and applied to either as seed dressing (treatment T1, applied at the time of sowing) or to soil (treatment T2, applied in soil at true leaf stage) across five different cotton (Gossypium hirsutum) cultivars. The impact of SynCom on plant growth, rhizosphere microbiome and soil nutrient availability, and how this was modified by plant variety and mode of applications, was assessed. Results: Results showed that the seed application of SynCom had the strongest positive impact on overall plant fitness, resulting in higher germination (14.3%), increased plant height (7.4%) and shoot biomass (5.4%). A significant increase in the number of flowers (10.4%) and yield (8.5%) was also observed in T1. The soil nitrate availability was enhanced by 28% and 55% under T1 and T2, respectively. Results further suggested that SynCom applications triggered enrichment of members from bacterial phyla Actinobacteria, Firmicutes and Cyanobacteria in the rhizosphere. A shift in fungal communities was also observed, with a significant increase in the relative abundance of fungi from phyla Chytridiomycota and Basidiomycota in SynCom treatments. A structural equation model suggested that SynCom directly increased crop productivity but also indirectly via impacting the alpha diversity of bacteria. Conclusion: Overall, this study provides mechanistic evidence that SynCom applications can shift rhizosphere microbial communities and improve soil fertility, plant growth, and crop productivity, suggesting that their use could contribute toward sustainable increase in farm productivity

Arginine starvation impairs mitochondrial respiratory function in ASS1-deficient breast cancer cells.

Autophagy is the principal catabolic response to nutrient starvation and is necessary to clear dysfunctional or damaged organelles, but excessive autophagy can be cytotoxic or cytostatic and contributes to cell death. Depending on the abundance of enzymes involved in molecule biosynthesis, cells can be dependent on uptake of exogenous nutrients to provide these molecules. Argininosuccinate synthetase 1 (ASS1) is a key enzyme in arginine biosynthesis, and its abundance is reduced in many solid tumors, making them sensitive to external arginine depletion. We demonstrated that prolonged arginine starvation by exposure to ADI-PEG20 (pegylated arginine deiminase) induced autophagy-dependent death of ASS1-deficient breast cancer cells, because these cells are arginine auxotrophs (dependent on uptake of extracellular arginine). Indeed, these breast cancer cells died in culture when exposed to ADI-PEG20 or cultured in the absence of arginine. Arginine starvation induced mitochondrial oxidative stress, which impaired mitochondrial bioenergetics and integrity. Furthermore, arginine starvation killed breast cancer cells in vivo and in vitro only if they were autophagy-competent. Thus, a key mechanism underlying the lethality induced by prolonged arginine starvation was the cytotoxic autophagy that occurred in response to mitochondrial damage. Last, ASS1 was either low in abundance or absent in more than 60% of 149 random breast cancer biosamples, suggesting that patients with such tumors could be candidates for arginine starvation therapy

Rosiglitazone Induces Mitochondrial Biogenesis in Differentiated Murine 3T3-L1 and C3H/10T1/2 Adipocytes

Growing evidence indicates that PPARγ agonists, including rosiglitazone (RSG), induce adipose mitochondrial biogenesis. By systematically analyzing mitochondrial gene expression in two common murine adipocyte models, the current study aimed to further establish the direct role of RSG and capture temporal changes in gene transcription. Microarray profiling revealed that in fully differentiated 3T3-L1 and C3H/10T1/2 adipocytes treated with RSG or DMSO vehicle for 1, 2, 4, 7, 24, and 48 hrs, RSG overwhelmingly increased mitochondrial gene transcripts time dependently. The timing of the increases was consistent with the cascade of organelle biogenesis, that is, initiated by induction of transcription factor(s), followed by increases in the biosynthesis machinery, and then by increases in functional components. The transcriptional increases were further validated by increased mitochondrial staining, citrate synthase activity, and O2 consumption, and were found to be associated with increased adiponectin secretion. The work provided further insight on the mechanism of PPARγ-induced mitochondrial biogenesis in differentiated adipocytes