Two ideals connected with strong right upper porosity at a point

Let $SP$ be the set of upper strongly porous at $0$ subsets of $\mathbb R^{+}$ and let $\hat I(SP)$ be the intersection of maximal ideals $I \subseteq SP$. Some characteristic properties of sets $E\in\hat I(SP)$ are obtained. It is shown that the ideal generated by the so-called completely strongly porous at $0$ subsets of $\mathbb R^{+}$ is a proper subideal of $\hat I(SP).$Comment: 18 page

Arithmetic progressions in sets of fractional dimension

Let E\subset\rr be a closed set of Hausdorff dimension $\alpha$. We prove that if $\alpha$ is sufficiently close to 1, and if $E$ supports a probabilistic measure obeying appropriate dimensionality and Fourier decay conditions, then $E$ contains non-trivial 3-term arithmetic progressions.Comment: 42 page

NOD2-C2 - a novel NOD2 isoform activating NF-κB in a muramyl dipeptide-independent manner

<p>Abstract</p> <p>Background</p> <p>The innate immune system employs several receptor families that form the basis of sensing pathogen-associated molecular patterns. NOD (nucleotide-binding and oligomerization domain) like receptors (NLRs) comprise a group of cytosolic proteins that trigger protective responses upon recognition of intracellular danger signals. NOD2 displays a tandem caspase recruitment domain (CARD) architecture, which is unique within the NLR family.</p> <p>Findings</p> <p>Here, we report a novel alternative transcript of the <it>NOD2 </it>gene, which codes for a truncated tandem CARD only protein, called NOD2-C2. The transcript isoform is highest expressed in leucocytes, a natural barrier against pathogen invasion, and is strictly linked to promoter usage as well as predominantly to one allele of the single nucleotide polymorphism rs2067085. Contrary to a previously identified truncated single CARD NOD2 isoform, NOD2-S, NOD2-C2 is able to activate NF-κB in a dose dependent manner independently of muramyl dipeptide (MDP). On the other hand NOD2-C2 competes with MDPs ability to activate the NOD2-driven NF-κB signaling cascade.</p> <p>Conclusion</p> <p>NOD2 transcripts having included an alternative exon downstream of exon 3 (exon 3a) are the endogenous equivalents of a previously described <it>in vitro </it>construct with the putative protein composed of only the two N-terminal CARDs. This protein form (NOD2-C2) activates NF-κB independent of an MDP stimulus and is a potential regulator of NOD2 signaling.</p

Molecular basis of caspase-1 polymerization and its inhibition by a new capping mechanism

Inflammasomes are cytosolic caspase-1-activation complexes that sense intrinsic and extrinsic danger signals, and trigger inflammatory responses and pyroptotic cell death. Homotypic interactions among Pyrin domains and caspase recruitment domains (CARDs) in inflammasome-complex components mediate oligomerization into filamentous assemblies. Several cytosolic proteins consisting of only interaction domains exert inhibitory effects on inflammasome assembly. In this study, we determined the structure of the human caspase-1 CARD domain (caspase-1[superscript CARD]) filament by cryo-electron microscopy and investigated the biophysical properties of two caspase-1-like CARD-only proteins: human inhibitor of CARD (INCA or CARD17) and ICEBERG (CARD18). Our results reveal that INCA caps caspase-1 filaments, thereby exerting potent inhibition with low-nanomolar K[subscript i] on caspase-1[superscript CARD] polymerization in vitro and inflammasome activation in cells. Whereas caspase-1[superscript CARD] uses six complementary surfaces of three types for filament assembly, INCA is defective in two of the six interfaces and thus terminates the caspase-1 filament