Selection Lemmas for various geometric objects

Selection lemmas are classical results in discrete geometry that have been well studied and have applications in many geometric problems like weak epsilon nets and slimming Delaunay triangulations. Selection lemma type results typically show that there exists a point that is contained in many objects that are induced (spanned) by an underlying point set. In the first selection lemma, we consider the set of all the objects induced (spanned) by a point set $P$. This question has been widely explored for simplices in $\mathbb{R}^d$, with tight bounds in $\mathbb{R}^2$. In our paper, we prove first selection lemma for other classes of geometric objects. We also consider the strong variant of this problem where we add the constraint that the piercing point comes from $P$. We prove an exact result on the strong and the weak variant of the first selection lemma for axis-parallel rectangles, special subclasses of axis-parallel rectangles like quadrants and slabs, disks (for centrally symmetric point sets). We also show non-trivial bounds on the first selection lemma for axis-parallel boxes and hyperspheres in $\mathbb{R}^d$. In the second selection lemma, we consider an arbitrary $m$ sized subset of the set of all objects induced by $P$. We study this problem for axis-parallel rectangles and show that there exists an point in the plane that is contained in $\frac{m^3}{24n^4}$ rectangles. This is an improvement over the previous bound by Smorodinsky and Sharir when $m$ is almost quadratic

A Mild Form of SLC29A3 Disorder: A Frameshift Deletion Leads to the Paradoxical Translation of an Otherwise Noncoding mRNA Splice Variant

We investigated two siblings with granulomatous histiocytosis prominent in the nasal area, mimicking rhinoscleroma and Rosai-Dorfman syndrome. Genome-wide linkage analysis and whole-exome sequencing identified a homozygous frameshift deletion in SLC29A3, which encodes human equilibrative nucleoside transporter-3 (hENT3). Germline mutations in SLC29A3 have been reported in rare patients with a wide range of overlapping clinical features and inherited disorders including H syndrome, pigmented hypertrichosis with insulin-dependent diabetes, and Faisalabad histiocytosis. With the exception of insulin-dependent diabetes and mild finger and toe contractures in one sibling, the two patients with nasal granulomatous histiocytosis studied here displayed none of the many SLC29A3-associated phenotypes. This mild clinical phenotype probably results from a remarkable genetic mechanism. The SLC29A3 frameshift deletion prevents the expression of the normally coding transcripts. It instead leads to the translation, expression, and function of an otherwise noncoding, out-of-frame mRNA splice variant lacking exon 3 that is eliminated by nonsense-mediated mRNA decay (NMD) in healthy individuals. The mutated isoform differs from the wild-type hENT3 by the modification of 20 residues in exon 2 and the removal of another 28 amino acids in exon 3, which include the second transmembrane domain. As a result, this new isoform displays some functional activity. This mechanism probably accounts for the narrow and mild clinical phenotype of the patients. This study highlights the ‘rescue’ role played by a normally noncoding mRNA splice variant of SLC29A3, uncovering a new mechanism by which frameshift mutations can be hypomorphic

Assembly of Connexin43 into Gap Junctions Is Regulated Differentially by E-Cadherin and N-Cadherin in Rat Liver Epithelial Cells

E-cadherin and N-cadherin affect the assembly of connexin43 into gap junctions differentially. N-cadherin disrupts assembly by triggering endocytosis of connexin43, whereas E-cadherin facilitates the assembly

Alternatively Spliced Landscape of PPARγ mRNA in Podocytes Is Distinct from Adipose Tissue

Podocytes are highly differentiated epithelial cells, and their structural and functional integrity is compromised in a majority of glomerular and renal diseases, leading to proteinuria, chronic kidney disease, and kidney failure. Traditional agonists (e.g., pioglitazone) and selective modulators (e.g., GQ-16) of peroxisome-proliferator-activated-receptor-γ (PPARγ) reduce proteinuria in animal models of glomerular disease and protect podocytes from injury via PPARγ activation. This indicates a pivotal role for PPARγ in maintaining glomerular function through preservation of podocytes distinct from its well-understood role in driving insulin sensitivity and adipogenesis. While its transcriptional role in activating adipokines and adipogenic genes is well-established in adipose tissue, liver and muscle, understanding of podocyte PPARγ signaling remains limited. We performed a comprehensive analysis of PPARγ mRNA variants due to alternative splicing, in human podocytes and compared with adipose tissue. We found that podocytes express the ubiquitous PPARγ Var 1 (encoding γ1) and not Var2 (encoding γ2), which is mostly restricted to adipose tissue and liver. Additionally, we detected expression at very low level of Var4, and barely detectable levels of other variants, Var3, Var11, VartORF4 and Var9, in podocytes. Furthermore, a distinct podocyte vs. adipocyte PPAR-promoter-response-element containing gene expression, enrichment and pathway signature was observed, suggesting differential regulation by podocyte specific PPARγ1 variant, distinct from the adipocyte-specific γ2 variant. In summary, podocytes and glomeruli express several PPARγ variants, including Var1 (γ1) and excluding adipocyte-specific Var2 (γ2), which may have implications in podocyte specific signaling and pathophysiology. This suggests that that new selective PPARγ modulators can be potentially developed that will be able to distinguish between the two forms, γ1 and γ2, thus forming a basis of novel targeted therapeutic avenues

Facilitated mitochondrial import of antiviral and anticancer nucleoside drugs by human equilibrative nucleoside transporter-3

human equilibrative nucleoside transporter-3 (hENT3) was recently reported as a pH-dependent, intracellular (lysosomal) transporter capable of transporting anti-human immunodeficiency virus (HIV) dideoxynucleosides (ddNs). Because most anti-HIV ddNs (e.g., zidovudine, AZT) exhibit clinical mitochondrial toxicity, we investigated whether hENT3 facilitates transport of anti-HIV ddNs into the mitochondria. Cellular fractionation and immunofluorescence microscopy studies in several human cell lines identified a substantial presence of hENT3 in the mitochondria, with additional presence at the cell surface of two placental cell lines (JAR, JEG3). Mitochondrial or cell surface hENT3 expression was confirmed in human hepatocytes and placental tissues, respectively. Unlike endogenous hENT3, yellow fluorescent protein (YFP)-tagged hENT3 was partially directed to the lysosomes. Xenopus oocytes expressing NH2-terminal-deleted hENT3 (expressed at the cell surface) showed pH-dependent interaction with several classes of nucleosides (anti-HIV ddNs, gemcitabine, fialuridine, ribavirin) that produce mitochondrial toxicity. Transport studies in hENT3 gene-silenced JAR cells showed significant reduction in mitochondrial transport of nucleosides and nucleoside drugs. Our data suggest that cellular localization of hENT3 is cell type dependent and the native transporter is substantially expressed in mitochondria and/or cell surface. hENT3-mediated mitochondrial transport may play an important role in mediating clinically observed mitochondrial toxicity of nucleoside drugs. In addition, our finding that hENT3 is a mitochondrial transporter is consistent with the recent finding that mutations in the hENT3 gene cause an autosomal recessive disorder in humans called the H syndrome