Central factorials under the Kontorovich-Lebedev transform of polynomials

We show that slight modifications of the Kontorovich-Lebedev transform lead to an automorphism of the vector space of polynomials. This circumstance along with the Mellin transformation property of the modified Bessel functions perform the passage of monomials to central factorial polynomials. A special attention is driven to the polynomial sequences whose KL-transform is the canonical sequence, which will be fully characterized. Finally, new identities between the central factorials and the Euler polynomials are found.Comment: also available at http://cmup.fc.up.pt/cmup/ since the 2nd August 201

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

Abnormal lung function in adults with congenital heart disease: prevalence, relation to cardiac anatomy, and association with survival

BACKGROUND: Restrictive lung defects are associated with higher mortality in patients with acquired chronic heart failure. We investigated the prevalence of abnormal lung function, its relation to severity of underlying cardiac defect, its surgical history, and its impact on outcome across the spectrum of adult congenital heart disease. METHODS AND RESULTS: A total of 1188 patients with adult congenital heart disease (age, 33.1+/-13.1 years) undergoing lung function testing between 2000 and 2009 were included. Patients were classified according to the severity of lung dysfunction based on predicted values of forced vital capacity. Lung function was normal in 53% of patients with adult congenital heart disease, mildly impaired in 17%, and moderately to severely impaired in the remainder (30%). Moderate to severe impairment of lung function related to complexity of underlying cardiac defect, enlarged cardiothoracic ratio, previous thoracotomy/ies, body mass index, scoliosis, and diaphragm palsy. Over a median follow-up period of 6.7 years, 106 patients died. Moderate to severe impairment of lung function was an independent predictor of survival in this cohort. Patients with reduced force vital capacity of at least moderate severity had a 1.6-fold increased risk of death compared with patients with normal lung function (P=0.04). CONCLUSIONS: A reduced forced vital capacity is prevalent in patients with adult congenital heart disease; its severity relates to the complexity of the underlying heart defect, surgical history, and scoliosis. Moderate to severe impairment of lung function is an independent predictor of mortality in contemporary patients with adult congenital heart disease

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

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

PADK has no inhibitory effect on β-secretase activity.

<p>Recombinant human β-secretase (10 ng/ml) was incubated with different concentrations of PADK (open triangles), CA074me (circles), and β-secretase inhibitor IV (closed triangles), and the enzyme activity was determined with the SensiZyme assay kit that uses the procaspase-3 variant containing the β-secretase cleavage sequence Gly-Ser-Ser-Glu-Ile-Ser-Tyr-Glu-Val-Glu-Phe-Arg-Glu-Phe (A). Activity was expressed in absorbance units (mean±SEM), and only β-secretase inhibitor IV elicited inhibition with an IC₅₀ of 19.8±2.4 nM. The three compounds were also tested against cathepsin B activity using the fluorogenic substrate Z-Arg-Arg AMC (mean fluorescence units±SEM plotted). β-secretase inhibitor IV had no effect on the cathepsin B activity, and PADK and CA074me resulted in IC₅₀ values of 9,200±1,030 and 120±13 nM, respectively (B).</p

PADK-mediated enhancement across brain regions of transgenic mouse models.

<p>APP_SwInd (10–11 months of age) and APPswe/PS1ΔE9 mice (APP-PS1; 20–22 months) were injected i.p. daily with PADK (20 mg/kg; n = 11−13) or vehicle (n = 10) for 9–11 days. Active cathepsin B in tissue homogenates was measured by immunoblot, and the mean levels were compared to the respective mean immunoreactivity in vehicle-injected transgenic samples to determine the fold increase across brain regions (±SEM).</p

PADK reduces behavioral deficits in APP_SwInd and APP-PS1 mice.

<p>In the first model, vehicle-treated wildtype mice (n = 11) were tested with groups of vehicle- (n = 10) and PADK-treated APP_SwInd mice (n = 13) across trials on the suspended rod test (A), and time maintained on the rod during the third trial was plotted (means±SEM). The animal groups were also tested across consecutive days in the same novel field, and the percent change±SEM in exploratory distance on the second day compared to the first was determined (B). In the second model, age-matched vehicle-treated wildtypes were tested with groups of vehicle- (n = 10) and PADK-treated APP-PS1 mice (n = 11) for spontaneous alternation behavior in a T-maze (C); data are plotted as percent of maximum alternations possible (mean±SEM). Open field mobility assessment confirmed no change in mean grid crossings±SEM across the three groups of mice (D). Post hoc tests compared to vehicle-treated transgenics: *<i>P</i>≤0.01, **<i>P</i><0.001.</p

PADK decreases 6E10 immunostaining in APP-PS1 mouse brain.

<p>APP-PS1 mice were injected i.p. daily with PADK (20 mg/kg; n = 11) or vehicle (n = 10) for 11 days. Fixed tissue was sectioned and stained with the 6E10 antibody. Image analysis for densitometric quantification of the immunostaining (mean integrated optical density±SEM) was conducted across view-fields of the hippocampal CA1 stratum pyramidale (sp). Area of deposit labeling above background was also measured for view-fields of the hippocampal stratum radiatum (sr) and piriform cortex (mean percent of total measured area±SEM). ANOVAs: <i>P</i><0.0001; Tukey's post hoc tests compared to APP−PS1+vehicle.</p><p>**<i>P</i><0.001.</p