Spectral Properties and Linear Stability of Self-Similar Wave Maps

We study co--rotational wave maps from $(3+1)$--Minkowski space to the three--sphere $S^3$. It is known that there exists a countable family $\{f_n\}$ of self--similar solutions. We investigate their stability under linear perturbations by operator theoretic methods. To this end we study the spectra of the perturbation operators, prove well--posedness of the corresponding linear Cauchy problem and deduce a growth estimate for solutions. Finally, we study perturbations of the limiting solution which is obtained from $f_n$ by letting $n \to \infty$.Comment: Some extensions added 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

RASSF1A and the rs2073498 Cancer Associated SNP

RASSF1A is one of the most frequently inactivated tumor suppressors yet identified in human cancer. It is pro-apoptotic and appears to function as a scaffolding protein that interacts with a variety of other tumor suppressors to modulate their function. It can also complex with the Ras oncoprotein and may serve to integrate pro-growth and pro-death signaling pathways. A SNP has been identified that is present in approximately 29% of European populations [rs2073498, A(133)S]. Several studies have now presented evidence that this SNP is associated with an enhanced risk of developing breast cancer. We have used a proteomics based approach to identify multiple differences in the pattern of protein/protein interactions mediated by the wild type compared to the SNP variant protein. We have also identified a significant difference in biological activity between wild type and SNP variant protein. However, we have found only a very modest association of the SNP with breast cancer predisposition

Upregulation of the cell-cycle regulator RGC-32 in Epstein-Barr virus-immortalized cells

Epstein-Barr virus (EBV) is implicated in the pathogenesis of multiple human tumours of lymphoid and epithelial origin. The virus infects and immortalizes B cells establishing a persistent latent infection characterized by varying patterns of EBV latent gene expression (latency 0, I, II and III). The CDK1 activator, Response Gene to Complement-32 (RGC-32, C13ORF15), is overexpressed in colon, breast and ovarian cancer tissues and we have detected selective high-level RGC-32 protein expression in EBV-immortalized latency III cells. Significantly, we show that overexpression of RGC-32 in B cells is sufficient to disrupt G2 cell-cycle arrest consistent with activation of CDK1, implicating RGC-32 in the EBV transformation process. Surprisingly, RGC-32 mRNA is expressed at high levels in latency I Burkitt's lymphoma (BL) cells and in some EBV-negative BL cell-lines, although RGC-32 protein expression is not detectable. We show that RGC-32 mRNA expression is elevated in latency I cells due to transcriptional activation by high levels of the differentially expressed RUNX1c transcription factor. We found that proteosomal degradation or blocked cytoplasmic export of the RGC-32 message were not responsible for the lack of RGC-32 protein expression in latency I cells. Significantly, analysis of the ribosomal association of the RGC-32 mRNA in latency I and latency III cells revealed that RGC-32 transcripts were associated with multiple ribosomes in both cell-types implicating post-initiation translational repression mechanisms in the block to RGC-32 protein production in latency I cells. In summary, our results are the first to demonstrate RGC-32 protein upregulation in cells transformed by a human tumour virus and to identify post-initiation translational mechanisms as an expression control point for this key cell-cycle regulator

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

Pumilio directs deadenylation-associated translational repression of the cyclin-dependent kinase 1 activator RGC-32

Response gene to complement-32 (RGC-32) activates cyclin-dependent kinase 1, regulates the cell cycle and is deregulated in many human tumours. We previously showed that RGC-32 expression is upregulated by the cancer-associated Epstein-Barr virus (EBV) in latently infected B cells through the relief of translational repression. We now show that EBV infection of naïve primary B cells also induces RGC-32 protein translation. In EBV-immortalised cell lines, we found that RGC-32 depletion resulted in cell death, indicating a key role in B cell survival. Studying RGC-32 translational control in EBV-infected cells, we found that the RGC-32 3′untranslated region (3′UTR) mediates translational repression. Repression was dependent on a single Pumilio binding element (PBE) adjacent to the polyadenylation signal. Mutation of this PBE did not affect mRNA cleavage, but resulted in increased polyA tail length. Consistent with Pumilio-dependent recruitment of deadenylases, we found that depletion of Pumilio in EBV-infected cells increased RGC-32 protein expression and polyA tail length. The extent of Pumilio binding to the endogenous RGC-32 mRNA in EBV-infected cell lines also correlated with RGC-32 protein expression. Our data demonstrate the importance of RGC-32 for the survival of EBV-immortalised B cells and identify Pumilio as a key regulator of RGC-32 translation