Combinatorial Trigonometry with Chebyshev Polynomials

We provide a combinatorial proof of the trigonometric identity cos(nθ) = Tncos(θ),where Tn is the Chebyshev polynomial of the first kind. We also provide combinatorial proofs of other trigonometric identities, including those involving Chebyshev polynomials of the second kind

Differences in Candidate Gene Association between European Ancestry and African American Asthmatic Children

Candidate gene case-control studies have identified several single nucleotide polymorphisms (SNPs) that are associated with asthma susceptibility. Most of these studies have been restricted to evaluations of specific SNPs within a single gene and within populations from European ancestry. Recently, there is increasing interest in understanding racial differences in genetic risk associated with childhood asthma. Our aim was to compare association patterns of asthma candidate genes between children of European and African ancestry.Using a custom-designed Illumina SNP array, we genotyped 1,485 children within the Greater Cincinnati Pediatric Clinic Repository and Cincinnati Genomic Control Cohort for 259 SNPs in 28 genes and evaluated their associations with asthma. We identified 14 SNPs located in 6 genes that were significantly associated (p-values <0.05) with childhood asthma in African Americans. Among Caucasians, 13 SNPs in 5 genes were associated with childhood asthma. Two SNPs in IL4 were associated with asthma in both races (p-values <0.05). Gene-gene interaction studies identified race specific sets of genes that best discriminate between asthmatic children and non-allergic controls.We identified IL4 as having a role in asthma susceptibility in both African American and Caucasian children. However, while IL4 SNPs were associated with asthma in asthmatic children with European and African ancestry, the relative contributions of the most replicated asthma-associated SNPs varied by ancestry. These data provides valuable insights into the pathways that may predispose to asthma in individuals with European vs. African ancestry

Functional Variant in the Autophagy-Related 5 Gene Promotor is Associated with Childhood Asthma

Rationale and Objective: Autophagy is a cellular process directed at eliminating or recycling cellular proteins. Recently, the autophagy pathway has been implicated in immune dysfunction, the pathogenesis of inflammatory disorders, and response to viral infection. Associations between two genes in the autophagy pathway, ATG5 and ATG7, with childhood asthma were investigated. Methods: Using genetic and experimental approaches, we examined the association of 13 HapMap-derived tagging SNPs in ATG5 and ATG7 with childhood asthma in 312 asthmatic and 246 non-allergic control children. We confirmed our findings by using independent cohorts and imputation analysis. Finally, we evaluated the functional relevance of a disease associated SNP. Measurements and Main Results: We demonstrated that ATG5 single nucleotide polymorphisms rs12201458 and rs510432 were associated with asthma (p = 0.00085 and 0.0025, respectively). In three independent cohorts, additional variants in ATG5 in the same LD block were associated with asthma (p,0.05). We found that rs510432 was functionally relevant and conferred significantly increased promotor activity. Furthermore, Atg5 expression was increased in nasal epithelium of acute asthmatics compared to stable asthmatics and non-asthmatic controls. Conclusion: Genetic variants in ATG5, including a functional promotor variant, are associated with childhood asthma. Thes

Identification of KIF3A as a Novel Candidate Gene for Childhood Asthma Using RNA Expression and Population Allelic Frequencies Differences

Asthma is a chronic inflammatory disease with a strong genetic predisposition. A major challenge for candidate gene association studies in asthma is the selection of biologically relevant genes.Using epithelial RNA expression arrays, HapMap allele frequency variation, and the literature, we identified six possible candidate susceptibility genes for childhood asthma including ADCY2, DNAH5, KIF3A, PDE4B, PLAU, SPRR2B. To evaluate these genes, we compared the genotypes of 194 predominantly tagging SNPs in 790 asthmatic, allergic and non-allergic children. We found that SNPs in all six genes were nominally associated with asthma (p<0.05) in our discovery cohort and in three independent cohorts at either the SNP or gene level (p<0.05). Further, we determined that our selection approach was superior to random selection of genes either differentially expressed in asthmatics compared to controls (p = 0.0049) or selected based on the literature alone (p = 0.0049), substantiating the validity of our gene selection approach. Importantly, we observed that 7 of 9 SNPs in the KIF3A gene more than doubled the odds of asthma (OR = 2.3, p<0.0001) and increased the odds of allergic disease (OR = 1.8, p<0.008). Our data indicate that KIF3A rs7737031 (T-allele) has an asthma population attributable risk of 18.5%. The association between KIF3A rs7737031 and asthma was validated in 3 independent populations, further substantiating the validity of our gene selection approach.Our study demonstrates that KIF3A, a member of the kinesin superfamily of microtubule associated motors that are important in the transport of protein complexes within cilia, is a novel candidate gene for childhood asthma. Polymorphisms in KIF3A may in part be responsible for poor mucus and/or allergen clearance from the airways. Furthermore, our study provides a promising framework for the identification and evaluation of novel candidate susceptibility genes

Designing clinical trials for assessing the effects of cognitive training and physical activity interventions on cognitive outcomes: The Seniors Health and Activity Research Program Pilot (SHARP-P) Study, a randomized controlled trial

<p>Abstract</p> <p>Background</p> <p>The efficacy of non-pharmacological intervention approaches such as physical activity, strength, and cognitive training for improving brain health has not been established. Before definitive trials are mounted, important design questions on participation/adherence, training and interventions effects must be answered to more fully inform a full-scale trial.</p> <p>Methods</p> <p>SHARP-P was a single-blinded randomized controlled pilot trial of a 4-month physical activity training intervention (PA) and/or cognitive training intervention (CT) in a 2 × 2 factorial design with a health education control condition in 73 community-dwelling persons, aged 70-85 years, who were at risk for cognitive decline but did not have mild cognitive impairment.</p> <p>Results</p> <p>Intervention attendance rates were higher in the CT and PACT groups: CT: 96%, PA: 76%, PACT: 90% (p=0.004), the interventions produced marked changes in cognitive and physical performance measures (p≤0.05), and retention rates exceeded 90%. There were no statistically significant differences in 4-month changes in composite scores of cognitive, executive, and episodic memory function among arms. Four-month improvements in the composite measure increased with age among participants assigned to physical activity training but decreased with age for other participants (intervention*age interaction p = 0.01). Depending on the choice of outcome, two-armed full-scale trials may require fewer than 1,000 participants (continuous outcome) or 2,000 participants (categorical outcome).</p> <p>Conclusions</p> <p>Good levels of participation, adherence, and retention appear to be achievable for participants through age 85 years. Care should be taken to ensure that an attention control condition does not attenuate intervention effects. Depending on the choice of outcome measures, the necessary sample sizes to conduct four-year trials appear to be feasible.</p> <p>Trial Registration</p> <p>Clinicaltrials.gov Identifier: <a href="http://www.clinicaltrials.gov/ct2/show/NCT00688155">NCT00688155</a></p

Vanin-1 expression and methylation discriminate pediatric asthma corticosteroid treatment response

BackgroundThere is considerable heterogeneity in asthma treatment response.ObjectiveWe sought to identify biomarkers of corticosteroid treatment response in children with asthma and evaluate the utility and mechanistic basis of these biomarkers.MethodsChildren (5-18 years) presenting to the emergency department with an acute asthma exacerbation were recruited and followed during hospitalization. Nasal epithelial cells were collected on presentation to the emergency department (T0) and 18 to 24 hours later (T1), and T1/T0 gene expression ratios were analyzed to identify genes associated with good and poor corticosteroid treatment response phenotypes. The utility of these genes in discriminating between systemic corticosteroid treatment response groups was then tested prospectively in a new cohort of patients. A gene candidate (vanin-1 [VNN1]) that consistently distinguished good versus poor response phenotypes was further studied in an experimental asthma model, and VNN1 promoter methylation was measured by means of bisulfite pyrosequencing in patients.ResultsVNN1 mRNA expression changes were associated with systemic corticosteroid treatment response in children with acute asthma, and VNN1 was required for optimal response to corticosteroid treatment in an experimental asthma model. A CpG site within the VNN1 promoter was differentially methylated between good versus poor treatment response groups, and methylation at this site correlated with VNN1 mRNA expression.ConclusionsWe have identified a biological basis for poor corticosteroid treatment response that can be used to distinguish a subgroup of asthmatic children who respond poorly to systemic corticosteroid treatment. VNN1 contributes to corticosteroid responsiveness, and changes in VNN1 nasal epithelial mRNA expression and VNN1 promoter methylation might be clinically useful biomarkers of treatment response in asthmatic children