New identities involving q-Euler polynomials of higher order

In this paper we give new identities involving q-Euler polynomials of higher order.Comment: 11 page

A note on the values of the weighted q-Bernstein polynomials and modified q-Genocchi numbers with weight alpha and beta via the p-adic q-integral on Zp

The rapid development of q-calculus has led to the discovery of new generalizations of Bernstein polynomials and Genocchi polynomials involving q-integers. The present paper deals with weighted q-Bernstein polynomials and q-Genocchi numbers with weight alpha and beta. We apply the method of generating function and p-adic q-integral representation on Zp, which are exploited to derive further classes of Bernstein polynomials and q-Genocchi numbers and polynomials. To be more precise we summarize our results as follows, we obtain some combinatorial relations between q-Genocchi numbers and polynomials with weight alpha and beta. Furthermore, we derive an integral representation of weighted q-Bernstein polynomials of degree n on Zp. Also we deduce a fermionic p-adic q-integral representation of product weighted q-Bernstein polynomials of different degrees n1,n2,...on Zp and show that it can be written with q-Genocchi numbers with weight alpha and beta which yields a deeper insight into the effectiveness of this type of generalizations. Our new generating function possess a number of interesting properties which we state in this paper.Comment: 10 page

Comprehensive Screening of Eight Known Causative Genes in Congenital Hypothyroidism With Gland-in-Situ.

CONTEXT: Lower TSH screening cutoffs have doubled the ascertainment of congenital hypothyroidism (CH), particularly cases with a eutopically located gland-in-situ (GIS). Although mutations in known dyshormonogenesis genes or TSHR underlie some cases of CH with GIS, systematic screening of these eight genes has not previously been undertaken. OBJECTIVE: Our objective was to evaluate the contribution and molecular spectrum of mutations in eight known causative genes (TG, TPO, DUOX2, DUOXA2, SLC5A5, SLC26A4, IYD, and TSHR) in CH cases with GIS. Patients, Design, and Setting: We screened 49 CH cases with GIS from 34 ethnically diverse families, using next-generation sequencing. Pathogenicity of novel mutations was assessed in silico. PATIENTS, DESIGN, AND SETTING: We screened 49 CH cases with GIS from 34 ethnically diverse families, using next-generation sequencing. Pathogenicity of novel mutations was assessed in silico. RESULTS: Twenty-nine cases harbored likely disease-causing mutations. Monogenic defects (19 cases) most commonly involved TG (12), TPO (four), DUOX2 (two), and TSHR (one). Ten cases harbored triallelic (digenic) mutations: TG and TPO (one); SLC26A4 and TPO (three), and DUOX2 and TG (six cases). Novel variants overall included 15 TG, six TPO, and three DUOX2 mutations. Genetic basis was not ascertained in 20 patients, including 14 familial cases. CONCLUSIONS: The etiology of CH with GIS remains elusive, with only 59% attributable to mutations in TSHR or known dyshormonogenesis-associated genes in a cohort enriched for familial cases. Biallelic TG or TPO mutations most commonly underlie severe CH. Triallelic defects are frequent, mandating future segregation studies in larger kindreds to assess their contribution to variable phenotype. A high proportion (∼41%) of unsolved or ambiguous cases suggests novel genetic etiologies that remain to be elucidated.This study made use of data generated by the UK10K Project and we acknowledge the contribution of the UK10K Consortium. This work was supported by Wellcome Trust Grants 100585/Z/12/Z (to N.S.), and 095564/Z/11/Z (to V.K.C.) and the National Institute for Health Research Cambridge Biomedical Research Center (to V.K.C., N.S.). E.G.S and C.A.A. are supported by the Wellcome Trust (098051). Funding for the UK10K Project was provided by the Wellcome Trust under award WT091310

Identities involving values of Bernstein, q-Bernoulli and q-Euler polynomials

In this paper we give some relation involving values of q-Bernoulli, q-Euler and Bernstein polynomials. From these relations, we obtain some interesting identities on the q-Bernoulli, q-Euler and Bernstein polynomials.Comment: 12 page

Cellular differentiation determines the expression of the hypoxia-inducible protein NDRG1 in pancreatic cancer

N-myc downstream-regulated gene-1 (NDRG1) is a recently described hypoxia-inducible protein that is upregulated in various human cancers. Pancreatic ductal adenocarcinoma, called pancreatic cancer, is a highly aggressive cancer that is characterised by its avascular structure, which results in a severe hypoxic environment. In this study, we investigated whether NDRG1 is upregulated in these tumours, thus providing a novel marker for malignant cells in the pancreas. By immunohistochemistry, we observed that NDRG1 was highly expressed in well-differentiated cells of pancreatic cancer, whereas the poorly differentiated tumour cells were negative. In addition, hyperplastic islets and ducts of nonquiescent pancreatic tissue were positive. To further explore its selective expression in tumours, two well-established pancreatic cancer cell lines of unequal differentiation status were exposed to 2% oxygen. NDRG1 mRNA and protein were upregulated by hypoxia in the moderately differentiated Capan-1 cells; however, its levels remained unchanged in the poorly differentiated Panc-1 cell line. Taken together, our data suggest that NDRG1 will not serve as a reliable marker of tumour cells in the pancreas, but may serve as a marker of differentiation. Furthermore, we present the novel finding that cellular differentiation may be an important factor that determines the hypoxia-induced regulation of NDRG1

The N-Myc Down Regulated Gene1 (NDRG1) Is a Rab4a Effector Involved in Vesicular Recycling of E-Cadherin

Cell to cell adhesion is mediated by adhesion molecules present on the cell surface. Downregulation of molecules that form the adhesion complex is a characteristic of metastatic cancer cells. Downregulation of the N-myc down regulated gene1 (NDRG1) increases prostate and breast metastasis. The exact function of NDRG1 is not known. Here by using live cell confocal microscopy and in vitro reconstitution, we report that NDRG1 is involved in recycling the adhesion molecule E-cadherin thereby stabilizing it. Evidence is provided that NDRG1 recruits on recycling endosomes in the Trans Golgi network by binding to phosphotidylinositol 4-phosphate and interacts with membrane bound Rab4aGTPase. NDRG1 specifically interacts with constitutively active Rab4aQ67L mutant protein and not with GDP-bound Rab4aS22N mutant proving NDRG1 as a novel Rab4a effector. Transferrin recycling experiments reveals NDRG1 colocalizes with transferrin during the recycling phase. NDRG1 alters the kinetics of transferrin recycling in cells. NDRG1 knockdown cells show a delay in recycling transferrin, conversely NDRG1 overexpressing cells reveal an increase in rate of transferrin recycling. This novel finding of NDRG1 as a recycling protein involved with recycling of E-cadherin will aid in understanding NDRG1 role as a metastasis suppressor protein