Total edge irregularity strength of join of path and complement of a complete graph

An edge irregular total k-labeling of a graph G is a labeling of the vertices and edges of G with labels from the set {1, 2, ..., k} in such a way that any two different edges have distinct weights. The weight of an edge uv is the sum of the label of uv and the labels of vertices u and v. The minimum k for which the graph G has an edge irregular total k-labeling is called the total edge irregularity strength of G. In this paper, we determine the exact value of the total edge irregularity strength of Pn + Km.Publisher's Versio

Protective Effects of Positive Lysosomal Modulation in Alzheimer's Disease Transgenic Mouse Models

Alzheimer's disease (AD) is an age-related neurodegenerative pathology in which defects in proteolytic clearance of amyloid β peptide (Aβ) likely contribute to the progressive nature of the disorder. Lysosomal proteases of the cathepsin family exhibit up-regulation in response to accumulating proteins including Aβ1–42. Here, the lysosomal modulator Z-Phe-Ala-diazomethylketone (PADK) was used to test whether proteolytic activity can be enhanced to reduce the accumulation events in AD mouse models expressing different levels of Aβ pathology. Systemic PADK injections in APPSwInd and APPswe/PS1ΔE9 mice caused 3- to 8-fold increases in cathepsin B protein levels and 3- to 10-fold increases in the enzyme's activity in lysosomal fractions, while neprilysin and insulin-degrading enzyme remained unchanged. Biochemical analyses indicated the modulation predominantly targeted the active mature forms of cathepsin B and markedly changed Rab proteins but not LAMP1, suggesting the involvement of enhanced trafficking. The modulated lysosomal system led to reductions in both Aβ immunostaining as well as Aβx-42 sandwich ELISA measures in APPSwInd mice of 10–11 months. More extensive Aβ deposition in 20-22-month APPswe/PS1ΔE9 mice was also reduced by PADK. Selective ELISAs found that a corresponding production of the less pathogenic Aβ1–38 occurs as Aβ1–42 levels decrease in the mouse models, indicating that PADK treatment leads to Aβ truncation. Associated with Aβ clearance was the elimination of behavioral and synaptic protein deficits evident in the two transgenic models. These findings indicate that pharmacologically-controlled lysosomal modulation reduces Aβ1–42 accumulation, possibly through intracellular truncation that also influences extracellular deposition, and in turn offsets the defects in synaptic composition and cognitive functions. The selective modulation promotes clearance at different levels of Aβ pathology and provides proof-of-principle for small molecule therapeutic development for AD and possibly other protein accumulation disorders

Reduced intracellular Aβ_1–42 staining corresponds with enhanced cathepsin B.

<p>Fixed brain sections from vehicle-treated wildtype mice (wt) and from the APP-PS1 mice treated with vehicle (veh) or PADK were double-stained for Aβ_1–42 (green) and cathepsin B (red). Immunofluorescence images of CA1 pyramidal neurons (arrows) are shown, with view-field widths of 56 µm.</p

Lysosomal modulation is associated with preservation of synaptic markers in APP_SwInd and APP-PS1 mice.

<p>Transgenic and wildtype (wt) mice were injected daily with PADK (+) or vehicle (–) for 9–11 days. Equal protein aliquots of hippocampal homogenates were analyzed by immunoblot for synaptic markers and actin, showing PADK-improved levels of GluA1 and synapsin II (syn II) in transgenic mice (A). The mean GluA1 immunoreactivities±SEM are shown for vehicle-treated wildtypes and for the vehicle- and PADK-treated transgenics (B). Post hoc tests compared to vehicle-treated transgenics: **<i>P</i><0.001.</p

PADK-mediated reductions of intraneuronal accumulation in the APP_SwInd mice.

<p>Non-transgenic control (wt) and APP_SwInd mice were treated with 9 daily injections of PADK or vehicle. Brain sections were stained with the 6E10 antibody, and photomicrographs indicate PADK-mediated reductions of the intracellular labeling in hippocampal subfields and piriform cortex (A). Image analysis for densitometric quantification was conducted across view-fields of four different neuronal layers (B), and mean integrated optical densities were plotted (±SEM). Individual ANOVAs: <i>P</i><0.0001; Tukey's post hoc tests compared to APP_SwInd+vehicle: **<i>P</i><0.001. Size bar: 40 µm, CA1 and DG; 65 µm, piriform cortex. DG, dentate gyrus; sg, stratum granulosum; sp, stratum pyramidale.</p

PADK selectively enhances cathepsin B levels in two transgenic mouse models.

<p>APP_SwInd and APP-PS1 mice were injected i.p. daily with PADK (20 mg/kg; n = 11−13) or vehicle (n = 10) for 9–11 days. Hippocampal homogenates were analyzed by immunoblot and mean immunoreactivities are shown for active cathepsin B (CB), neprilysin (nep), insulin-degrading enzyme (IDE), α-secretase (α-sec), and LAMP1.</p><p>***<i>P</i><0.0001, unpaired t-test.</p