Construction and implementation of asymptotic expansions for Jacobi-type orthogonal polynomials

We are interested in the asymptotic behavior of orthogonal polynomials of the generalized Jacobi type as their degree n goes to ∞. These are defined on the interval [−1, 1] with weight function: w(x)=(1−x)α(1+x)βh(x),α,β>−1 and h(x) a real, analytic and strictly positive function on [−1, 1]. This information is available in the work of Kuijlaars et al. (Adv. Math. 188, 337–398 2004), where the authors use the Riemann–Hilbert formulation and the Deift–Zhou non-linear steepest descent method. We show that computing higher-order terms can be simplified, leading to their efficient construction. The resulting asymptotic expansions in every region of the complex plane are implemented both symbolically and numerically, and the code is made publicly available. The main advantage of these expansions is that they lead to increasing accuracy for increasing degree of the polynomials, at a computational cost that is actually independent of the degree. In contrast, the typical use of the recurrence relation for orthogonal polynomials in computations leads to a cost that is at least linear in the degree. Furthermore, the expansions may be used to compute Gaussian quadrature rules in O(n) operations, rather than O(n2) based on the recurrence relation

Salt Stress Induced Variation in DNA Methylation Pattern and Its Influence on Gene Expression in Contrasting Rice Genotypes

BACKGROUND: Salinity is a major environmental factor limiting productivity of crop plants including rice in which wide range of natural variability exists. Although recent evidences implicate epigenetic mechanisms for modulating the gene expression in plants under environmental stresses, epigenetic changes and their functional consequences under salinity stress in rice are underexplored. DNA methylation is one of the epigenetic mechanisms regulating gene expression in plant's responses to environmental stresses. Better understanding of epigenetic regulation of plant growth and response to environmental stresses may create novel heritable variation for crop improvement. METHODOLOGY/PRINCIPAL FINDINGS: Methylation sensitive amplification polymorphism (MSAP) technique was used to assess the effect of salt stress on extent and patterns of DNA methylation in four genotypes of rice differing in the degree of salinity tolerance. Overall, the amount of DNA methylation was more in shoot compared to root and the contribution of fully methylated loci was always more than hemi-methylated loci. Sequencing of ten randomly selected MSAP fragments indicated gene-body specific DNA methylation of retrotransposons, stress responsive genes, and chromatin modification genes, distributed on different rice chromosomes. Bisulphite sequencing and quantitative RT-PCR analysis of selected MSAP loci showed that cytosine methylation changes under salinity as well as gene expression varied with genotypes and tissue types irrespective of the level of salinity tolerance of rice genotypes. CONCLUSIONS/SIGNIFICANCE: The gene body methylation may have an important role in regulating gene expression in organ and genotype specific manner under salinity stress. Association between salt tolerance and methylation changes observed in some cases suggested that many methylation changes are not "directed". The natural genetic variation for salt tolerance observed in rice germplasm may be independent of the extent and pattern of DNA methylation which may have been induced by abiotic stress followed by accumulation through the natural selection process

Methodological issues in epidemiological studies of periodontitis - how can it be improved?

Background: This position paper was commissioned by the European Association of Dental Public Health, which has established six working groups to investigate the current status of six topics related to oral public health. One of these areas is epidemiology of periodontal diseases. Methods: Two theses "A systematic review of definitions of periodontitis and the methods that have been used to identify periodontitis" [1] and "Factors affecting community oral health care needs and provision" [2] formed the starting point for this position paper. Additional relevant and more recent publications were retrieved through a MEDLINE search. Results: The literature reveals a distinct lack of consensus and uniformity in the definition of periodontitis within epidemiological studies. There are also numerous differences in the methods used. The consequence is that data from studies using differing case definitions and differing survey methods are not easily interpretable or comparable. The limitations of the widely used Community Periodontal Index of Treatment Need (CPITN) and its more recent derivatives are widely recognized. Against this background, this position paper reviews the current evidence base, outlines existing problems and suggests how epidemiology of periodontal diseases may be improved. Conclusions: The remit of this working group was to review and discuss the existing evidence base of epidemiology of periodontal diseases and to identify future areas of work to further enhance it

A Protective Role for ELR+ Chemokines during Acute Viral Encephalomyelitis

The functional role of ELR-positive CXC chemokines in host defense during acute viral-induced encephalomyelitis was determined. Inoculation of the neurotropic JHM strain of mouse hepatitis virus (JHMV) into the central nervous system (CNS) of mice resulted in the rapid mobilization of PMNs expressing the chemokine receptor CXCR2 into the blood. Migration of PMNs to the CNS coincided with increased expression of transcripts specific for the CXCR2 ELR-positive chemokine ligands CXCL1, CXCL2, and CXCL5 within the brain. Treatment of JHMV-infected mice with anti-CXCR2 blocking antibody reduced PMN trafficking into the CNS by >95%, dampened MMP-9 activity, and abrogated blood-brain-barrier (BBB) breakdown. Correspondingly, CXCR2 neutralization resulted in diminished infiltration of virus-specific T cells, an inability to control viral replication within the brain, and 100% mortality. Blocking CXCR2 signaling did not impair the generation of virus-specific T cells, indicating that CXCR2 is not required to tailor anti-JHMV T cell responses. Evaluation of mice in which CXCR2 is genetically silenced (CXCR2−/− mice) confirmed that PMNs neither expressed CXCR2 nor migrated in response to ligands CXCL1, CXCL2, or CXCL5 in an in vitro chemotaxis assay. Moreover, JHMV infection of CXCR2−/− mice resulted in an approximate 60% reduction of PMN migration into the CNS, yet these mice survived infection and controlled viral replication within the brain. Treatment of JHMV-infected CXCR2−/− mice with anti-CXCR2 antibody did not modulate PMN migration nor alter viral clearance or mortality, indicating the existence of compensatory mechanisms that facilitate sufficient migration of PMNs into the CNS in the absence of CXCR2. Collectively, these findings highlight a previously unappreciated role for ELR-positive chemokines in enhancing host defense during acute viral infections of the CNS

NUDT2 Disruption Elevates Diadenosine Tetraphosphate (Ap4A) and Down-Regulates Immune Response and Cancer Promotion Genes.

Regulation of gene expression is one of several roles proposed for the stress-induced nucleotide diadenosine tetraphosphate (Ap4A). We have examined this directly by a comparative RNA-Seq analysis of KBM-7 chronic myelogenous leukemia cells and KBM-7 cells in which the NUDT2 Ap4A hydrolase gene had been disrupted (NuKO cells), causing a 175-fold increase in intracellular Ap4A. 6,288 differentially expressed genes were identified with P < 0.05. Of these, 980 were up-regulated and 705 down-regulated in NuKO cells with a fold-change ≥ 2. Ingenuity® Pathway Analysis (IPA®) was used to assign these genes to known canonical pathways and functional networks. Pathways associated with interferon responses, pattern recognition receptors and inflammation scored highly in the down-regulated set of genes while functions associated with MHC class II antigens were prominent among the up-regulated genes, which otherwise showed little organization into major functional gene sets. Tryptophan catabolism was also strongly down-regulated as were numerous genes known to be involved in tumor promotion in other systems, with roles in the epithelial-mesenchymal transition, proliferation, invasion and metastasis. Conversely, some pro-apoptotic genes were up-regulated. Major upstream factors predicted by IPA® for gene down-regulation included NFκB, STAT1/2, IRF3/4 and SP1 but no major factors controlling gene up-regulation were identified. Potential mechanisms for gene regulation mediated by Ap4A and/or NUDT2 disruption include binding of Ap4A to the HINT1 co-repressor, autocrine activation of purinoceptors by Ap4A, chromatin remodeling, effects of NUDT2 loss on transcript stability, and inhibition of ATP-dependent regulatory factors such as protein kinases by Ap4A. Existing evidence favors the last of these as the most probable mechanism. Regardless, our results suggest that the NUDT2 protein could be a novel cancer chemotherapeutic target, with its inhibition potentially exerting strong anti-tumor effects via multiple pathways involving metastasis, invasion, immunosuppression and apoptosis