Asymptotic equivalence of discretely observed diffusion processes and their Euler scheme: small variance case

This paper establishes the global asymptotic equivalence, in the sense of the Le Cam $\Delta$-distance, between scalar diffusion models with unknown drift function and small variance on the one side, and nonparametric autoregressive models on the other side. The time horizon $T$ is kept fixed and both the cases of discrete and continuous observation of the path are treated. We allow non constant diffusion coefficient, bounded but possibly tending to zero. The asymptotic equivalences are established by constructing explicit equivalence mappings.Comment: 21 page

The malignant phenotype in breast cancer is driven by eIF4A1-mediated changes in the translational landscape

Human mRNA DeXD/H-box helicases are ubiquitous molecular motors that are required for the majority of cellular processes that involve RNA metabolism. One of the most abundant is eIF4A, which is required during the initiation phase of protein synthesis to unwind regions of highly structured mRNA that would otherwise impede the scanning ribosome. Dysregulation of protein synthesis is associated with tumorigenesis, but little is known about the detailed relationships between RNA helicase function and the malignant phenotype in solid malignancies. Therefore, immunohistochemical analysis was performed on over 3000 breast tumors to investigate the relationship among expression of eIF4A1, the helicase-modulating proteins eIF4B, eIF4E and PDCD4, and clinical outcome. We found eIF4A1, eIF4B and eIF4E to be independent predictors of poor outcome in ER-negative disease, while in contrast, the eIF4A1 inhibitor PDCD4 was related to improved outcome in ER-positive breast cancer. Consistent with these data, modulation of eIF4A1, eIF4B and PCDC4 expression in cultured MCF7 cells all restricted breast cancer cell growth and cycling. The eIF4A1-dependent translatome of MCF7 cells was defined by polysome profiling, and was shown to be highly enriched for several classes of oncogenic genes, including G-protein constituents, cyclins and protein kinases, and for mRNAs with G/C-rich 5′UTRs with potential to form G-quadruplexes and with 3′UTRs containing microRNA target sites. Overall, our data show that dysregulation of mRNA unwinding contributes to the malignant phenotype in breast cancer via preferential translation of a class of genes involved in pro-oncogenic signaling at numerous levels. Furthermore, immunohistochemical tests are promising biomarkers for tumors sensitive to anti-helicase therapies

Breast Cancer

Breast cancer remains one of the leading causes of cancer morbidity and mortality. Despite significant advances in treatment of breast cancer a substantial proportion of women affected by this disease succumb to it. Survival of patients with advanced disease, chemoresistant tumors or a suboptimal response to endocrine therapy is significantly shortened. Hence, further understanding of disease pathogenesis is required to enhance the arsenal of approaches to cure this deadly ailment. Recent advances in biochemistry, molecular cell biology and cancer research highlighted the importance of dysregulation of protein synthesis, translation, in the development and progression of tumors. This dysregulation appears to take place at an early stage of translation, called translation initiation, that is a highly controlled and rate-limiting step of the protein synthesis. In this chapter we summarize decades of knowledge accumulated in regards to the role of translation and its regulation in the development and progression of breast cancer. We then extensively discuss applications of this knowledge in diagnosis and treatment of breast cancer.SCOPUS: ch.binfo:eu-repo/semantics/publishe