On the probabilistic Cauchy theory for nonlinear dispersive PDEs

In this note, we review some of the recent developments in the well-posedness theory of nonlinear dispersive partial differential equations with random initial data.Comment: 26 pages. To appear in Landscapes of Time-Frequency Analysis, Appl. Numer. Harmon. Ana

Bmp and Nodal Independently Regulate lefty1 Expression to Maintain Unilateral Nodal Activity during Left-Right Axis Specification in Zebrafish

In vertebrates, left-right (LR) axis specification is determined by a ciliated structure in the posterior region of the embryo. Fluid flow in this ciliated structure is responsible for the induction of unilateral left-sided Nodal activity in the lateral plate mesoderm, which in turn regulates organ laterality. Bmp signalling activity has been implied in repressing Nodal expression on the right side, however its mechanism of action has been controversial. In a forward genetic screen for mutations that affect LR patterning, we identified the zebrafish linkspoot (lin) mutant, characterized by cardiac laterality and mild dorsoventral patterning defects. Mapping of the lin mutation revealed an inactivating missense mutation in the Bmp receptor 1aa (bmpr1aa) gene. Embryos with a mutation in lin/bmpr1aa and a novel mutation in its paralogue, bmpr1ab, displayed a variety of dorsoventral and LR patterning defects with increasing severity corresponding with a decrease in bmpr1a dosage. In Bmpr1a-deficient embryos we observed bilateral expression of the Nodal-related gene, spaw, coupled with reduced expression of the Nodal-antagonist lefty1 in the midline. Using genetic models to induce or repress Bmp activity in combination with Nodal inhibition or activation, we found that Bmp and Nodal regulate lefty1 expression in the midline independently of each other. Furthermore, we observed that the regulation of lefty1 by Bmp signalling is required for its observed downregulation of Nodal activity in the LPM providing a novel explanation for this phenomenon. From these results we propose a two-step model in which Bmp regulates LR patterning. Prior to the onset of nodal flow and Nodal activation, Bmp is required to induce lefty1 expression in the midline. When nodal flow has been established and Nodal activity is apparent, both Nodal and Bmp independently are required for lefty1 expression to assure unilateral Nodal activation and correct LR patterning

Zebrafish arl6ip1 Is Required for Neural Crest Development during Embryogenesis

BACKGROUND:Although the embryonic expression pattern of ADP ribosylation factor-like 6 interacting protein 1 (Arl6ip1) has been reported, its function in neural crest development is unclear. METHODS/PRINCIPAL FINDINGS:We found that knockdown of Arl6ip1 caused defective embryonic neural crest derivatives that were particularly severe in craniofacial cartilages. Expressions of the ectodermal patterning factors msxb, dlx3b, and pax3 were normal, but the expressions of the neural crest specifier genes foxd3, snai1b, and sox10 were greatly reduced. These findings suggest that arl6ip1 is essential for specification of neural crest derivatives, but not neural crest induction. Furthermore, we revealed that the streams of crestin- and sox10-expressing neural crest cells, which migrate ventrally from neural tube into trunk, were disrupted in arl6ip1 morphants. This migration defect was not only in the trunk neural crest, but also in the enteric tract where the vagal-derived neural crest cells failed to populate the enteric nervous system. We found that this migration defect was induced by dampened Shh signaling, which may have resulted from defective cilia. These data further suggested that arl6ip1 is required for neural crest migration. Finally, by double-staining of TUNEL and crestin, we confirmed that the loss of neural crest cells could not be attributed to apoptosis. CONCLUSIONS/SIGNIFICANCE:Therefore, we concluded that arl6ip1 is required for neural crest migration and sublineage specification

A genome-wide association scan in admixed Latin Americans identifies loci influencing facial and scalp hair features

We report a genome-wide association scan in over 6,000 Latin Americans for features of scalp hair (shape, colour, greying, balding) and facial hair (beard thickness, monobrow, eyebrow thickness). We found 18 signals of association reaching genome-wide significance (P values 5 × 10−8 to 3 × 10−119), including 10 novel associations. These include novel loci for scalp hair shape and balding, and the first reported loci for hair greying, monobrow, eyebrow and beard thickness. A newly identified locus influencing hair shape includes a Q30R substitution in the Protease Serine S1 family member 53 (PRSS53). We demonstrate that this enzyme is highly expressed in the hair follicle, especially the inner root sheath, and that the Q30R substitution affects enzyme processing and secretion. The genome regions associated with hair features are enriched for signals of selection, consistent with proposals regarding the evolution of human hair

An NF-κB and Slug Regulatory Loop Active in Early Vertebrate Mesoderm

BACKGROUND: In both Drosophila and the mouse, the zinc finger transcription factor Snail is required for mesoderm formation; its vertebrate paralog Slug (Snai2) appears to be required for neural crest formation in the chick and the clawed frog Xenopus laevis. Both Slug and Snail act to induce epithelial to mesenchymal transition (EMT) and to suppress apoptosis. METHODOLOGY & PRINCIPLE FINDINGS: Morpholino-based loss of function studies indicate that Slug is required for the normal expression of both mesodermal and neural crest markers in X. laevis. Both phenotypes are rescued by injection of RNA encoding the anti-apoptotic protein Bcl-xL; Bcl-xL's effects are dependent upon IκB kinase-mediated activation of the bipartite transcription factor NF-κB. NF-κB, in turn, directly up-regulates levels of Slug and Snail RNAs. Slug indirectly up-regulates levels of RNAs encoding the NF-κB subunit proteins RelA, Rel2, and Rel3, and directly down-regulates levels of the pro-apopotic Caspase-9 RNA. CONCLUSIONS/SIGNIFICANCE: These studies reveal a Slug/Snail–NF-κB regulatory circuit, analogous to that present in the early Drosophila embryo, active during mesodermal formation in Xenopus. This is a regulatory interaction of significance both in development and in the course of inflammatory and metastatic disease

Current perspectives of the signaling pathways directing neural crest induction

The neural crest is a migratory population of embryonic cells with a tremendous potential to differentiate and contribute to nearly every organ system in the adult body. Over the past two decades, an incredible amount of research has given us a reasonable understanding of how these cells are generated. Neural crest induction involves the combinatorial input of multiple signaling pathways and transcription factors, and is thought to occur in two phases from gastrulation to neurulation. In the first phase, FGF and Wnt signaling induce NC progenitors at the border of the neural plate, activating the expression of members of the Msx, Pax, and Zic families, among others. In the second phase, BMP, Wnt, and Notch signaling maintain these progenitors and bring about the expression of definitive NC markers including Snail2, FoxD3, and Sox9/10. In recent years, additional signaling molecules and modulators of these pathways have been uncovered, creating an increasingly complex regulatory network. In this work, we provide a comprehensive review of the major signaling pathways that participate in neural crest induction, with a focus on recent developments and current perspectives. We provide a simplified model of early neural crest development and stress similarities and differences between four major model organisms: Xenopus, chick, zebrafish, and mouse