Self-Similar Tilings of Fractal Blow-Ups

New tilings of certain subsets of $\mathbb{R}^{M}$ are studied, tilings associated with fractal blow-ups of certain similitude iterated function systems (IFS). For each such IFS with attractor satisfying the open set condition, our construction produces a usually infinite family of tilings that satisfy the following properties: (1) the prototile set is finite; (2) the tilings are repetitive (quasiperiodic); (3) each family contains self-similartilings, usually infinitely many; and (4) when the IFS is rigid in an appropriate sense, the tiling has no non-trivial symmetry; in particular the tiling is non-periodic

Hypertrophic scar regression is linked to the occurrence of endothelial dysfunction

<div><p>Most microvessels have been shown to become stenosed or completely occluded during hypertrophic scar progression. Here, we examined the morphology of capillary endothelial cells (ECs) and fibroblasts using immunofluorescence staining for CD31 and alpha-smooth muscle actin (α-SMA) and electron microscopy. In addition, ECs and fibroblasts were isolated from scar tissues, and the levels of transforming growth factor beta 1 (TGF-β1), platelet-derived growth factor (PDGF), endothelin 1 (ET-1), vascular endothelial growth factor (VEGF) and basic fibroblast growth factor (bFGF) were assayed using ELISAs. Furthermore, we assessed cell viability, total collagen production, and cell apoptosis in hypertrophic scar-derived fibroblasts cultured with EC-conditioned medium. Then, anti-TGF-β1, anti-PDGF, anti-ET-1, anti-VEGF, and anti-bFGF neutralising antibodies were individually added to the EC medium to identify which growth factor plays a more important role in inhibiting fibroblasts biology. Our results showed microvessel lumen occlusion and EC atrophy during scar development, particularly in regressive scars (RSs). Additionally, EC growth factor secretion decreased and reached the lowest levels in RSs. Furthermore, based on the culture results, RS EC medium inhibited fibroblast viability and collagen production and induced apoptosis. Moreover, TGF-β1, PDGF, and bFGF played more important roles in these processes than VEGF and ET-1. The endothelial dysfunction occurring in hypertrophic scars contributes to fibroblast inhibition and scar regression, and reduced TGF-β1, PDGF, and bFGF levels play key roles during this process.</p></div

NEDD4-1 binds and ubiquitinates pThoc1.

<p>A) 293 cell extracts were immunoprecipitated with a pThoc1 specific antibody or non-specific IgG, and the immunoprecipitates analyzed for the presence of NEDD4-1 by western blotting. Input levels of pThoc1 and NEDD4-1 were assayed by western blotting. β-actin serves as a loading control. B) Immunopurified pThoc1 was mixed with the indicated amount of purified recombinant NEDD4-1 in an in vitro reconstituted ubiquitination reaction. pThoc1 poly-ubiquitination was analyzed by western blotting (top panel). Input levels of pThoc1 or NEDD4-1 (bottom panel) were determined by western blotting.</p

pThoc1 poly-ubiquitination correlates with NEDD4-1 levels in cells.

<p>A) HeLa cells were transfected with the <i>THOC1</i> and His-Ub expression vectors (all lanes). In addition, cells were transfected with a wild type <i>NEDD4-1</i> expression vector (NEDD4-1), a catalytic dead <i>NEDD4-1</i> mutant (NEDD4-1 mut), or were treated with MG132 as indicated. Total cell protein extracts were purified by metal chelate chromatography and purified protein analyzed for the presence of pThoc1 by western blotting (top panel). The middle panel shows relative input levels of pThoc1. The bottom panel shows relative input levels of NEDD4-1. B) HeLa cells engineered to express tetracycline inducible <i>NEDD4-1</i> targeted shRNA were transfected with <i>Thoc1</i> and His-UB expression vectors (both lanes), treated with MG132 (both lanes), or treated with tetracycline. Total cell protein extracts were purified and analyzed as in A). C) Wild type or Nedd4-1 knockout murine embryonic fibroblasts were transfected with the <i>Thoc1</i> and His-Ub expression vectors, and treated with MG132 as indicated. His-Ub containing proteins were purified and analyzed for the presence of pThoc1 as above. Input levels of pThoc1 and NEDD4-1 were determined by western blotting while β-actin serves as a loading control. The NEDD4-1 immunoreactive band detected in NEDD4-1 null cells is a non-specific background protein that becomes detectable upon MG132 treatment.</p