Semiclassical low energy scattering for one-dimensional Schr\"odinger operators with exponentially decaying potentials

We consider semiclassical Schr\"odinger operators on the real line of the form $$H(\hbar)=-\hbar^2 \frac{d^2}{dx^2}+V(\cdot;\hbar)$$ with $\hbar>0$ small. The potential $V$ is assumed to be smooth, positive and exponentially decaying towards infinity. We establish semiclassical global representations of Jost solutions $f_\pm(\cdot,E;\hbar)$ with error terms that are uniformly controlled for small $E$ and $\hbar$, and construct the scattering matrix as well as the semiclassical spectral measure associated to $H(\hbar)$. This is crucial in order to obtain decay bounds for the corresponding wave and Schr\"odinger flows. As an application we consider the wave equation on a Schwarzschild background for large angular momenta $\ell$ where the role of the small parameter $\hbar$ is played by $\ell^{-1}$. It follows from the results in this paper and \cite{DSS2}, that the decay bounds obtained in \cite{DSS1}, \cite{DS} for individual angular momenta $\ell$ can be summed to yield the sharp $t^{-3}$ decay for data without symmetry assumptions.Comment: 44 pages, minor modifications in order to match the published version, will appear in Annales Henri Poincar

The Radial Wave Operator in Similarity Coordinates

We present a rigorous functional analytic setting to study the radial wave equation in similarity coordinates. As an application we analyse linear stability of the fundamental self--similar solution of the wave equation with a focusing power nonlinearity.Comment: Minor corrections in order to match the published versio

Bifurcation and fine structure phenomena in critical collapse of a self-gravitating σ\sigma-field

Building on previous work on the critical behavior in gravitational collapse of the self-gravitating SU(2) $\sigma$-field and using high precision numerical methods we uncover a fine structure hidden in a narrow window of parameter space. We argue that this numerical finding has a natural explanation within a dynamical system framework of critical collapse

The Growth and Tumor Suppressors NORE1A and RASSF1A Are Targets for Calpain-Mediated Proteolysis

Background: NORE1A and RASSF1A are growth and tumour suppressors inactivated in a variety of cancers. Methylation of NORE1A and RASSF1A promoters is the predominant mechanism for downregulation of these proteins; however, other mechanisms are likely to exist. Methodology/Principal Findings: Here we describe a proteolysis of NORE1A and RASSF1A by calpains as alternative mechanism of their downregulation. Extracts of H358 cell line, a human bronchoalveolar carcinoma, and H460, a large cell carcinoma, were capable of proteolysis of NORE1A protein in the calpain-dependent manner. Likewise, RASSF1A tumor suppressor was proteolyzed by the H358 cell extract. Addition of calpain inhibitor to H358 and H460 cells growing in tissue culture resulted in re-expression of endogenous NORE1A. A survey of 10 human lung tumours revealed that three of them contain an activity capable of inducing NORE1A degradation. Conclusions/Significance: Thus, degradation by calpains is a novel mechanism for downregulation of NORE1A and RASSF1A proteins and might be the mechanism allowing cancer cells to escape growth suppression

Differential Analysis of Ovarian and Endometrial Cancers Identifies a Methylator Phenotype

Despite improved outcomes in the past 30 years, less than half of all women diagnosed with epithelial ovarian cancer live five years beyond their diagnosis. Although typically treated as a single disease, epithelial ovarian cancer includes several distinct histological subtypes, such as papillary serous and endometrioid carcinomas. To address whether the morphological differences seen in these carcinomas represent distinct characteristics at the molecular level we analyzed DNA methylation patterns in 11 papillary serous tumors, 9 endometrioid ovarian tumors, 4 normal fallopian tube samples and 6 normal endometrial tissues, plus 8 normal fallopian tube and 4 serous samples from TCGA. For comparison within the endometrioid subtype we added 6 primary uterine endometrioid tumors and 5 endometrioid metastases from uterus to ovary. Data was obtained from 27,578 CpG dinucleotides occurring in or near promoter regions of 14,495 genes. We identified 36 locations with significant increases or decreases in methylation in comparisons of serous tumors and normal fallopian tube samples. Moreover, unsupervised clustering techniques applied to all samples showed three major profiles comprising mostly normal samples, serous tumors, and endometrioid tumors including ovarian, uterine and metastatic origins. The clustering analysis identified 60 differentially methylated sites between the serous group and the normal group. An unrelated set of 25 serous tumors validated the reproducibility of the methylation patterns. In contrast, >1,000 genes were differentially methylated between endometrioid tumors and normal samples. This finding is consistent with a generalized regulatory disruption caused by a methylator phenotype. Through DNA methylation analyses we have identified genes with known roles in ovarian carcinoma etiology, whereas pathway analyses provided biological insight to the role of novel genes. Our finding of differences between serous and endometrioid ovarian tumors indicates that intervention strategies could be developed to specifically address subtypes of epithelial ovarian cancer

Identifying microRNA/mRNA dysregulations in ovarian cancer

Abstract Background MicroRNAs are a class of noncoding RNA molecules that co-regulate the expression of multiple genes via mRNA transcript degradation or translation inhibition. Since they often target entire pathways, they may be better drug targets than genes or proteins. MicroRNAs are known to be dysregulated in many tumours and associated with aggressive or poor prognosis phenotypes. Since they regulate mRNA in a tissue specific manner, their functional mRNA targets are poorly understood. In previous work, we developed a method to identify direct mRNA targets of microRNA using patient matched microRNA/mRNA expression data using an anti-correlation signature. This method, applied to clear cell Renal Cell Carcinoma (ccRCC), revealed many new regulatory pathways compromised in ccRCC. In the present paper, we apply this method to identify dysregulated microRNA/mRNA mechanisms in ovarian cancer using data from The Cancer Genome Atlas (TCGA). Methods TCGA Microarray data was normalized and samples whose class labels (tumour or normal) were ambiguous with respect to consensus ensemble K-Means clustering were removed. Significantly anti-correlated and correlated genes/microRNA differentially expressed between tumour and normal samples were identified. TargetScan was used to identify gene targets of microRNA. Results We identified novel microRNA/mRNA mechanisms in ovarian cancer. For example, the expression level of RAD51AP1 was found to be strongly anti-correlated with the expression of hsa-miR-140-3p, which was significantly down-regulated in the tumour samples. The anti-correlation signature was present separately in the tumour and normal samples, suggesting a direct causal dysregulation of RAD51AP1 by hsa-miR-140-3p in the ovary. Other pairs of potentially biological relevance include: hsa-miR-145/E2F3, hsa-miR-139-5p/TOP2A, and hsa-miR-133a/GCLC. We also identified sets of positively correlated microRNA/mRNA pairs that are most likely result from indirect regulatory mechanisms. Conclusions Our findings identify novel microRNA/mRNA relationships that can be verified experimentally. We identify both generic microRNA/mRNA regulation mechanisms in the ovary as well as specific microRNA/mRNA controls which are turned on or off in ovarian tumours. Our results suggest that the disease process uses specific mechanisms which may be significant for their utility as early detection biomarkers or in the development of microRNA therapies in treating ovarian cancers. The positively correlated microRNA/mRNA pairs suggest the existence of novel regulatory mechanisms that proceed via intermediate states (indirect regulation) in ovarian tumorigenesis.</p

Expression profiling identifies genes involved in neoplastic transformation of serous ovarian cancer

Background: The malignant potential of serous ovarian tumors, the most common ovarian tumor subtype, varies from benign to low malignant potential (LMP) tumors to frankly invasive cancers. Given the uncertainty about the relationship between these different forms, we compared their patterns of gene expression. Methods: Expression profiling was carried out on samples of 7 benign, 7 LMP and 28 invasive (moderate and poorly differentiated) serous tumors and four whole normal ovaries using oligonucleotide microarrays representing over 21,000 genes. Results: We identified 311 transcripts that distinguished invasive from benign tumors, and 20 transcripts that were significantly differentially expressed between invasive and LMP tumors at p < 0.01 (with multiple testing correction). Five genes that were differentially expressed between invasive and either benign or normal tissues were validated by real time PCR in an independent panel of 46 serous tumors (4 benign, 7 LMP, 35 invasive). Overexpression of SLPI and WNT7A and down-regulation of C6orf31, PDGFRA and GLTSCR2 were measured in invasive and LMP compared with benign and normal tissues. Over-expression of WNT7A in an ovarian cancer cell line led to increased migration and invasive capacity. Conclusion: These results highlight several genes that may play an important role across the spectrum of serous ovarian tumorigenesis

Molecular and phenotypic characterisation of paediatric glioma cell lines as models for preclinical drug development.

Although paediatric high grade gliomas resemble their adult counterparts in many ways, there appear to be distinct clinical and biological differences. One important factor hampering the development of new targeted therapies is the relative lack of cell lines derived from childhood glioma patients, as it is unclear whether the well-established adult lines commonly used are representative of the underlying molecular genetics of childhood tumours. We have carried out a detailed molecular and phenotypic characterisation of a series of paediatric high grade glioma cell lines in comparison to routinely used adult lines