Partial regularity and t-analytic sets for Banach function algebras

In this note we introduce the notion of t-analytic sets. Using this concept, we construct a class of closed prime ideals in Banach function algebras and discuss some problems related to Alling’s conjecture in H infinity. A description of all closed t-analytic sets for the disk-algebra is given. Moreover, we show that some of the assertions in [8] concerning the O-analyticity and S-regularity of certain Banach function algebras are not correct. We also determine the largest set on which a Douglas algebra is pointwise regular

A simple device for multiplex ELISA made from melt-extruded plastic microcapillary film

We present a simple device for multiplex quantitative enzyme-linked immunosorbant assays (ELISA) made from a novel melt-extruded microcapillary film (MCF) containing a parallel array of 200µm capillaries along its length. To make ELISA devices different protein antigens or antibodies were immobilised inside individual microcapillaries within long reels of MCF extruded from fluorinated ethylene propylene (FEP). Short pieces of coated film were cut and interfaced with a pipette, allowing sequential uptake of samples and detection solutions into all capillaries from a reagent well. As well as being simple to produce, these FEP MCF devices have excellent light transmittance allowing direct optical interrogation of the capillaries for simple signal quantification. Proof of concept experiments demonstrate both quantitative and multiplex assays in FEP MCF devices using a standard direct ELISA procedure and read using a flatbed scanner. This new multiplex immunoassay platform should find applications ranging from lab detection to point-of-care and field diagnostics

Clark measures and a theorem of Ritt

We determine when a finite Blaschke product B can be written, in a non-trivial way, as a composition of two finite Blaschke products (Ritt\u27s problem) in terms of the Clark measure for B. Our tools involve the numerical range of compressed shift operators and the geometry of certain polygons circumscribing the numerical range of the relevant operator. As a consequence of our results, we can determine, in terms of Clark measures, when two finite Blaschke products commute

Boundary interpolation and approximation by infinite Blaschke products

This paper considers the problem of boundary interpolation (in the sense of non-tangential limits) by Blaschke products and interpolating Blaschke products. Simple and constructive proofs, which also work in the more general situation of $H^\infty(\Omega)$ where $\Omega$ is a more general domain, are given of a number of results showing the existence of Blaschke products solving certain interpolation problems at a countable set of points on the circle. A variant of Frostman's theorem is also presented

Integrating Diverse Datasets Improves Developmental Enhancer Prediction

Gene-regulatory enhancers have been identified using various approaches, including evolutionary conservation, regulatory protein binding, chromatin modifications, and DNA sequence motifs. To integrate these different approaches, we developed EnhancerFinder, a two-step method for distinguishing developmental enhancers from the genomic background and then predicting their tissue specificity. EnhancerFinder uses a multiple kernel learning approach to integrate DNA sequence motifs, evolutionary patterns, and diverse functional genomics datasets from a variety of cell types. In contrast with prediction approaches that define enhancers based on histone marks or p300 sites from a single cell line, we trained EnhancerFinder on hundreds of experimentally verified human developmental enhancers from the VISTA Enhancer Browser. We comprehensively evaluated EnhancerFinder using cross validation and found that our integrative method improves the identification of enhancers over approaches that consider a single type of data, such as sequence motifs, evolutionary conservation, or the binding of enhancer-associated proteins. We find that VISTA enhancers active in embryonic heart are easier to identify than enhancers active in several other embryonic tissues, likely due to their uniquely high GC content. We applied EnhancerFinder to the entire human genome and predicted 84,301 developmental enhancers and their tissue specificity. These predictions provide specific functional annotations for large amounts of human non-coding DNA, and are significantly enriched near genes with annotated roles in their predicted tissues and lead SNPs from genome-wide association studies. We demonstrate the utility of EnhancerFinder predictions through in vivo validation of novel embryonic gene regulatory enhancers from three developmental transcription factor loci. Our genome-wide developmental enhancer predictions are freely available as a UCSC Genome Browser track, which we hope will enable researchers to further investigate questions in developmental biology. © 2014 Erwin et al

Solvent-selective routing for centrifugally automated solid-phase purification of RNA

The final publication is available at Springer via https://doi.org/10.1007/s10404-014-1477-9.We present a disc-based module for rotationally controlled solid-phase purification of RNA from cell lysate. To this end, multi-stage routing of a sequence of aqueous and organic liquids into designated waste and elution reservoirs is implemented by a network of strategically placed, solvent-selective composite valves. Using a bead-based stationary phase at the entrance of the router, we show that total RNA is purified with high integrity from cultured MCF7 and T47D cell lines, human leucocytes and Haemophilus influenzae cell lysates. Furthermore, we demonstrate the broad applicability of the device through the in vitro amplification of RNA purified on-disc using RT-PCR and NASBA. Our novel router will be at the pivot of a forthcoming, fully integrated and automated sample preparation system for RNA-based analysis.Peer reviewe

Spatiotemporal DNA methylome dynamics of the developing mouse fetus

Cytosine DNA methylation is essential for mammalian development but understanding of its spatiotemporal distribution in the developing embryo remains limited. Here, as part of the mouse Encyclopedia of DNA Elements (ENCODE) project, we profiled 168 methylomes from 12 mouse tissues or organs at 9 developmental stages from embryogenesis to adulthood. We identified 1,808,810 genomic regions that showed variations in CG methylation by comparing the methylomes of different tissues or organs from different developmental stages. These DNA elements predominantly lose CG methylation during fetal development, whereas the trend is reversed after birth. During late stages of fetal development, non-CG methylation accumulated within the bodies of key developmental transcription factor genes, coinciding with their transcriptional repression. Integration of genome-wide DNA methylation, histone modification and chromatin accessibility data enabled us to predict 461,141 putative developmental tissue-specific enhancers, the human orthologues of which were enriched for disease-associated genetic variants. These spatiotemporal epigenome maps provide a resource for studies of gene regulation during tissue or organ progression, and a starting point for investigating regulatory elements that are involved in human developmental disorders

SOX10 directly modulates ERBB3 transcription via an intronic neural crest enhancer

<p>Abstract</p> <p>Background</p> <p>The <it>ERBB3 </it>gene is essential for the proper development of the neural crest (NC) and its derivative populations such as Schwann cells. As with all cell fate decisions, transcriptional regulatory control plays a significant role in the progressive restriction and specification of NC derived lineages during development. However, little is known about the sequences mediating transcriptional regulation of <it>ERBB3 </it>or the factors that bind them.</p> <p>Results</p> <p>In this study we identified three transcriptional enhancers at the <it>ERBB3 </it>locus and evaluated their regulatory potential <it>in vitro </it>in NC-derived cell types and <it>in vivo </it>in transgenic zebrafish. One enhancer, termed <it>ERBB3</it>_MCS6, which lies within the first intron of <it>ERBB3</it>, directs the highest reporter expression <it>in vitro </it>and also demonstrates epigenetic marks consistent with enhancer activity. We identify a consensus SOX10 binding site within <it>ERBB3</it>_MCS6 and demonstrate, <it>in vitro</it>, its necessity and sufficiency for the activity of this enhancer. Additionally, we demonstrate that transcription from the endogenous <it>Erbb3 </it>locus is dependent on Sox10. Further we demonstrate <it>in vitro </it>that Sox10 physically interacts with that <it>ERBB3</it>_MCS6. Consistent with its <it>in vitro </it>activity, we also show that <it>ERBB3</it>_MCS6 drives reporter expression in NC cells and a subset of its derivative lineages <it>in vivo </it>in zebrafish in a manner consistent with <it>erbb3b </it>expression. We also demonstrate, using morpholino analysis, that Sox10 is necessary for <it>ERBB3</it>_MCS6 expression <it>in vivo </it>in zebrafish.</p> <p>Conclusions</p> <p>Taken collectively, our data suggest that <it>ERBB3 </it>may be directly regulated by SOX10, and that this control may in part be facilitated by <it>ERBB3</it>_MCS6.</p