In this paper we present the construction of a group Hopf algebra on the class of rational tangles. A locally finite partial order on this class is introduced and a topology is generated. An interval coalgebra structure associated with the locally finite partial order is specified. Irrational and real tangles are introduced and their relation with rational tangles are studied. The existence of the maximal real tangle is described in detail.

Zebrafish provide a highly versatile model in which to study vertebrate development. Many recent studies have elucidated early events in the organogenesis of the zebrafish pancreas; however, several aspects of early endocrine pancreas formation in the zebrafish are not homologous to the mammalian system. To better identify mechanisms of islet formation in the zebrafish, with true homology to those observed in mammals, we have temporally and spatially characterized zebrafish secondary islet formation. As is the case in the mouse, we show that Notch inhibition leads to precocious differentiation of endocrine tissues. Furthermore, we have used transgenic fish expressing fluorescent markers under the control of a Notch-responsive element to observe the precursors of these induced endocrine cells. These pancreatic Notch-responsive cells represent a novel population of putative progenitors that are associated with larval pancreatic ductal epithelium, suggesting functional homology between secondary islet formation in zebrafish and the secondary transition in mammals. We also show that Notch-responsive cells persist in the adult pancreas and possess the classical characteristics of centroacinar cells, a cell type believed to be a multipotent progenitor cell in adult mammalian pancreas.

Multicellular aggregates of circulating tumor cells (CTC clusters) are potent initiators of distant organ metastasis. However, it is currently assumed that CTC clusters are too large to pass through narrow vessels to reach these organs. Here, we present evidence that challenges this assumption through the use of microfluidic devices designed to mimic human capillary constrictions and CTC clusters obtained from patient and cancer cell origins. Over 90% of clusters containing up to 20 cells successfully traversed 5-to 10-μm constrictions even in whole blood. Clusters rapidly and reversibly reorganized into single-file chain-like geometries that substantially reduced their hydrodynamic resistances. Xenotransplantation of human CTC clusters into zebrafish showed similar reorganization and transit through capillary-sized vessels in vivo. Preliminary experiments demonstrated that clusters could be disrupted during transit using drugs that affected cellular interaction energies. These findings suggest that CTC clusters may contribute a greater role to tumor dissemination than previously believed and may point to strategies for combating CTC cluster-initiated metastasis.microfluidics | cancer metastasis | CTC clusters | circulating tumor cell cluster microemboli | capillary microhemodynamics

The limited generation of neurons during adulthood is controlled by a balance between quiescence and recruitment of neural stem cells (NSCs). We use here the germinal zone of the zebrafish adult telencephalon to examine how the frequency of NSC divisions is regulated. We show, using several in vivo techniques, that progenitors transit back and forth between the quiescent and dividing state, according to varying levels of Notch activity: Notch induction drives progenitors into quiescence, whereas blocking Notch massively reinitiates NSC division and subsequent commitment toward becoming neurons. Notch activation appears predominantly triggered by newly recruited progenitors onto their neighbors, suggesting an involvement of Notch in a self-limiting mechanism, once neurogenesis is started. These results identify for the first time a lateral inhibition-like mechanism in the context of adult neurogenesis and suggest that the equilibrium between quiescence and neurogenesis in the adult brain is controlled by fluctuations of Notch activity, thereby regulating the amount of adult-born neurons.

Haematopoietic stem cells (HSCs) are a self-renewing population that continuously replenish all blood and immune cells during the lifetime of an individual1, 2. HSCs are used clinically to treat a wide array of diseases, including acute leukaemias and congenital blood disorders, but obtaining suitable numbers of cells and finding immune compatible donors remain serious problems. These concerns have led to an interest in the conversion of embryonic stem cells or induced pluripotent stem cells into HSCs, which is not possible using current methodologies. To accomplish this goal, it is critical to understand the native mechanisms involved in specification of HSCs during embryonic development. Here we demonstrate that Wnt16 controls a novel genetic regulatory network required for HSC specification. Non-canonical signaling by Wnt16 is required for somitic expression of the Notch ligands deltaC (dlc) and deltaD (dld), and these ligands are in turn required for establishment of definitive haematopoiesis. Notch signalling downstream of Dlc/Dld is earlier than, and distinct from known cell-autonomous requirements for Notch, strongly suggesting that novel Notch-dependent relay signal(s) induce the first HSCs in parallel to other established pathways. Our results demonstrate that somite-specific gene expression is required for the production of haemogenic endothelium.

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Highlights d prkdc À/À , il2rga À/À zebrafish reared at 37 C engraft a wide array of human cancers d Growth and therapy responses can be dynamically visualized at single-cell resolution d Combination olaparib and temozolomide kill xenografted human rhabdomyosarcoma d Engrafting patient-derived cancers opens new avenues for personalized therapy Authors

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