The mixed problem for the Laplacian in Lipschitz domains

We consider the mixed boundary value problem or Zaremba's problem for the Laplacian in a bounded Lipschitz domain in R^n. We specify Dirichlet data on part of the boundary and Neumann data on the remainder of the boundary. We assume that the boundary between the sets where we specify Dirichlet and Neumann data is a Lipschitz surface. We require that the Neumann data is in L^p and the Dirichlet data is in the Sobolev space of functions having one derivative in L^p for some p near 1. Under these conditions, there is a unique solution to the mixed problem with the non-tangential maximal function of the gradient of the solution in L^p of the boundary. We also obtain results with data from Hardy spaces when p=1.Comment: Version 5 includes a correction to one step of the main proof. Since the paper appeared long ago, this submission includes the complete paper, followed by a short section that gives the correction to one step in the proo

Cellulose acetate phthalate, a common pharmaceutical excipient, inactivates HIV-1 and blocks the coreceptor binding site on the virus envelope glycoprotein gp120

BACKGROUND: Cellulose acetate phthalate (CAP), a pharmaceutical excipient used for enteric film coating of capsules and tablets, was shown to inhibit infection by the human immunodeficiency virus type 1 (HIV-1) and several herpesviruses. CAP formulations inactivated HIV-1, herpesvirus types 1 (HSV-1) and 2 (HSV-2) and the major nonviral sexually transmitted disease (STD) pathogens and were effective in animal models for vaginal infection by HSV-2 and simian immunodeficiency virus. METHODS: Enzyme-linked immunoassays and flow cytometry were used to demonstrate CAP binding to HIV-1 and to define the binding site on the virus envelope. RESULTS: 1) CAP binds to HIV-1 virus particles and to the envelope glycoprotein gp120; 2) this leads to blockade of the gp120 V3 loop and other gp120 sites resulting in diminished reactivity with HIV-1 coreceptors CXCR4 and CCR5; 3) CAP binding to HIV-1 virions impairs their infectivity; 4) these findings apply to both HIV-1 IIIB, an X4 virus, and HIV-1 BaL, an R5 virus. CONCLUSIONS: These results provide support for consideration of CAP as a topical microbicide of choice for prevention of STDs, including HIV-1 infection

Anti-HIV-1 activity of cellulose acetate phthalate: Synergy with soluble CD4 and induction of "dead-end" gp41 six-helix bundles

BACKGROUND: Cellulose acetate phthalate (CAP), a promising candidate microbicide for prevention of sexual transmission of the human immunodeficiency virus type 1 (HIV-1) and other sexually transmitted disease (STD) pathogens, was shown to inactivate HIV-1 and to block the coreceptor binding site on the virus envelope glycoprotein gp120. It did not interfere with virus binding to CD4. Since CD4 is the primary cellular receptor for HIV-1, it was of interest to study CAP binding to HIV-1 complexes with soluble CD4 (sCD4) and its consequences, including changes in the conformation of the envelope glycoprotein gp41 within virus particles. METHODS: Enzyme-linked immunosorbent assays (ELISA) were used to study CAP binding to HIV-1-sCD4 complexes and to detect gp41 six-helix bundles accessible on virus particles using antibodies specific for the α-helical core domain of gp41. RESULTS: 1) Pretreatment of HIV-1 with sCD4 augments subsequent binding of CAP; 2) there is synergism between CAP and sCD4 for inhibition of HIV-1 infection; 3) treatment of HIV-1 with CAP induced the formation of gp41 six-helix bundles. CONCLUSIONS: CAP and sCD4 bind to distinct sites on HIV-1 IIIB and BaL virions and their simultaneous binding has profound effects on virus structure and infectivity. The formation of gp41 six-helical bundles, induced by CAP, is known to render the virus incompetent for fusion with target cells thus preventing infection

Alterations in the gut microbiome implicate key taxa and metabolic pathways across inflammatory arthritis phenotypes

Musculoskeletal diseases affect up to 20% of adults worldwide. The gut microbiome has been implicated in inflammatory conditions, but large-scale metagenomic evaluations have not yet traced the routes by which immunity in the gut affects inflammatory arthritis. To characterize the community structure and associated functional processes driving gut microbial involvement in arthritis, the Inflammatory Arthritis Microbiome Consortium investigated 440 stool shotgun metagenomes comprising 221 adults diagnosed with rheumatoid arthritis, ankylosing spondylitis, or psoriatic arthritis and 219 healthy controls and individuals with joint pain without an underlying inflammatory cause. Diagnosis explained about 2% of gut taxonomic variability, which is comparable in magnitude to inflammatory bowel disease. We identified several candidate microbes with differential carriage patterns in patients with elevated blood markers for inflammation. Our results confirm and extend previous findings of increased carriage of typically oral and inflammatory taxa and decreased abundance and prevalence of typical gut clades, indicating that distal inflammatory conditions, as well as local conditions, correspond to alterations to the gut microbial composition. We identified several differentially encoded pathways in the gut microbiome of patients with inflammatory arthritis, including changes in vitamin B salvage and biosynthesis and enrichment of iron sequestration. Although several of these changes characteristic of inflammation could have causal roles, we hypothesize that they are mainly positive feedback responses to changes in host physiology and immune homeostasis. By connecting taxonomic alternations to functional alterations, this work expands our understanding of the shifts in the gut ecosystem that occur in response to systemic inflammation during arthritis

In vivo and in vitro studies of Th17 response to specific immunotherapy in house dust mite-induced allergic rhinitis patients

10.1371/journal.pone.0091950PLoS ONE93-POLN

Sobolev spaces on non-Lipschitz subsets of Rn with application to boundary integral equations on fractal screens

We study properties of the classical fractional Sobolev spaces on non-Lipschitz subsets of Rn. We investigate the extent to which the properties of these spaces, and the relations between them, that hold in the well-studied case of a Lipschitz open set, generalise to non-Lipschitz cases. Our motivation is to develop the functional analytic framework in which to formulate and analyse integral equations on non-Lipschitz sets. In particular we consider an application to boundary integral equations for wave scattering by planar screens that are non-Lipschitz, including cases where the screen is fractal or has fractal boundary

A Pivotal Role of Vitamin B9 in the Maintenance of Regulatory T Cells In Vitro and In Vivo

Dietary factors regulate immunological function, but the underlying mechanisms remain elusive. Here we show that vitamin B9 is a survival factor for regulatory T (Treg) cells expressing high levels of vitamin B9 receptor (folate receptor 4). In vitamin B9-reduced condition in vitro, Treg cells could be differentiated from naïve T cells but failed to survive. The impaired survival of Treg cells was associated with decreased expression of anti-apoptotic Bcl2 and independent of IL-2. In vivo depletion of dietary vitamin B9 resulted in the reduction of Treg cells in the small intestine, a site for the absorption of dietary vitamin B9. These findings provide a new link between diet and the immune system, which could maintain the immunological homeostasis in the intestine

Myd88 Is Required for an Antibody Response to Retroviral Infection

Although retroviruses have been extensively studied for many years, basic questions about how retroviral infections are detected by the immune system and which innate pathways are required for the generation of immune responses remain unanswered. Defining these pathways and how they contribute to the anti-retroviral immune responses would assist in the development of more effective vaccines for retroviral pathogens such as HIV. We have investigated the roles played by CD11c+ dendritic cells (DCs) and by Toll-like receptor (TLR) signaling pathways in the generation of an anti-retroviral immune response against a mouse retroviral pathogen, Friend murine leukemia virus (F-MLV). Specific deletion of DCs during F-MLV infection caused a significant increase in viral titers at 14 days post-infection, indicating the importance of DCs in immune control of the infection. Similarly, Myd88 knockout mice failed to control F-MLV, and sustained high viral titers (107 foci/spleen) for several months after infection. Strikingly, both DC-depleted mice and Myd88 knockout mice exhibited only a partial reduction of CD8+ T cell responses, while the IgG antibody response to F-MLV was completely lost. Furthermore, passive transfer of immune serum from wild-type mice to Myd88 knockout mice rescued control of F-MLV. These results identify TLR signaling and CD11c+ DCs as playing critical roles in the humoral response to retroviruses

Bioinformatics for the human microbiome project

Microbes inhabit virtually all sites of the human body, yet we know very little about the role they play in our health. In recent years, there has been increasing interest in studying human-associated microbial communities, particularly since microbial dysbioses have now been implicated in a number of human diseases [1]–[3]. Dysbiosis, the disruption of the normal microbial community structure, however, is impossible to define without first establishing what “normal microbial community structure” means within the healthy human microbiome. Recent advances in sequencing technologies have made it feasible to perform large-scale studies of microbial communities, providing the tools necessary to begin to address this question [4], [5]. This led to the implementation of the Human Microbiome Project (HMP) in 2007, an initiative funded by the National Institutes of Health Roadmap for Biomedical Research and constructed as a large, genome-scale community research project [6]. Any such project must plan for data analysis, computational methods development, and the public availability of tools and data; here, we provide an overview of the corresponding bioinformatics organization, history, and results from the HMP (Figure 1).National Institutes of Health (U.S.) (NIH U54HG004969)National Institutes of Health (U.S.) (grant R01HG004885)National Institutes of Health (U.S.) (grant R01HG005975)National Institutes of Health (U.S.) (grant R01HG005969