This book provides a clear exposition of the flourishing field of fixed point theory. Starting from the basics of Banach's contraction theorem, most of the main results and techniques are developed: fixed point results are established for several classes of maps and the three main approaches to establishing continuation principles are presented. The theory is applied to many areas of interest in analysis. Topological considerations play a crucial role, including a final chapter on the relationship with degree theory. Researchers and graduate students in applicable analysis will find this to be a useful survey of the fundamental principles of the subject. The very extensive bibliography and close to 100 exercises mean that it can be used both as a text and as a comprehensive reference work, currently the only one of its type.

Transforming growth factor-β (TGF-β) signaling regulates many diverse cellular activities through both canonical (SMAD-dependent) and non-canonical branches, which includes the mitogen-activated protein kinase (MAPK), Rho-like guanosine triphosphatase and phosphatidylinositol-3-kinase/AKT pathways. Here, we demonstrate that miR-335 directly targets and downregulates genes in the TGF-β non-canonical pathways, including the Rho-associated coiled-coil containing protein (ROCK1) and MAPK1, resulting in reduced phosphorylation of downstream pathway members. Specifically, inhibition of ROCK1 and MAPK1 reduces phosphorylation levels of the motor protein myosin light chain (MLC) leading to a significant inhibition of the invasive and migratory potential of neuroblastoma cells. Additionally, miR-335 targets the leucine-rich alpha-2-glycoprotein 1 (LRG1) messenger RNA, which similarly results in a significant reduction in the phosphorylation status of MLC and a decrease in neuroblastoma cell migration and invasion. Thus, we link LRG1 to the migratory machinery of the cell, altering its activity presumably by exerting its effect within the non-canonical TGF-β pathway. Moreover, we demonstrate that the MYCN transcription factor, whose coding sequence is highly amplified in a particularly clinically aggressive neuroblastoma tumor subtype, directly binds to a region immediately upstream of the miR-335 transcriptional start site, resulting in transcriptional repression. We conclude that MYCN contributes to neuroblastoma cell migration and invasion, by directly downregulating miR-335, resulting in the upregulation of the TGF-β signaling pathway members ROCK1, MAPK1 and putative member LRG1, which positively promote this process. Our results provide novel insight into the direct regulation of TGF-β non-canonical signaling by miR-335, which in turn is downregulated by MYCN.

Background:Neuroblastoma remains a major cause of cancer-linked mortality in children. miR-204 has been used in microRNA expression signatures predictive of neuroblastoma patient survival. The aim of this study was to explore the independent association of miR-204 with survival in a neuroblastoma cohort, and to investigate the phenotypic effects mediated by miR-204 expression in neuroblastoma.Methods:Neuroblastoma cell lines were transiently transfected with miR-204 mimics and assessed for cell viability using MTS assays. Apoptosis levels in cell lines were evaluated by FACS analysis of Annexin V-/propidium iodide-stained cells transfected with miR-204 mimics and treated with chemotherapy drug or vehicle control. Potential targets of miR-204 were validated using luciferase reporter assays.Results:miR-204 expression in primary neuroblastoma tumours was predictive of patient event-free and overall survival, independent of established known risk factors. Ectopic miR-204 expression significantly increased sensitivity to cisplatin and etoposide in vitro. miR-204 direct targeting of the 3′ UTR of BCL2 and NTRK2 (TrkB) was confirmed.Conclusion:miR-204 is a novel predictor of outcome in neuroblastoma, functioning, at least in part, through increasing sensitivity to cisplatin by direct targeting and downregulation of anti-apoptotic BCL2. miR-204 also targets full-length NTRK2, a potent oncogene involved with chemotherapy drug resistance in neuroblastoma.