Rational dilation problems associated with constrained algebras

It is shown that rational dilation fails on broad collection of distinguished varieties associated to constrained subalgebras of the disk algebra of the form C + B A(D), where B is a finite Blaschke product with two or more zeros. This is accomplished in part by finding a minimal set of test functions. In addition, an Agler-Pick interpolation theorem is given and it is proved that there exist Kaijser-Varopoulos style examples of non-contractive unital representations where the generators are contractions.Comment: Page proof corrections included in this version

Axoquant 2.0 quantifies neurite degeneration from quarter-field images of DRG explants.

<p>DRG explants are dissected from E13.5 mouse embryos and seeded on 6-well plates (two wells shown in A; NGF (top) & anti-NGF 24h (bottom), scale bar = 1 mm for 5x images and 10 μm for 40x images). To quantify the degree of degeneration following a phase of NGF withdrawal and to assess the effect of pharmacological or genetic manipulations on its progression, the entire culture is imaged (after fixation and tubulin cytoskeletal immunostaining) by automatic tile-scanning on a motorized microscope stage, and quarter-fields are cropped and saved according to embryo and treatment (A; fields containing axons from only a single DRG are chosen, indicated by dotted box and green checkmark). The user directs Axoquant 2.0 to the experimental parent folder, where subfolders organized by treatment and embryo are crawled and quantified automatically (B).</p

HBpF-proBDNF interacts with endogenous p75NTR and SorCS2 in PC12 cells.

<p>PC12 cells were stimulated with HBpF-proBDNF (100μg/ml) with or without 9μM GM6001 for 3h. BirA Ni-NTA eluate was used as control treatment. After stimulation, cells were lysed and HBpF-proBDNF and associated protein were recovered on SA beads. Cleavage with PP was performed for 16 hours and the resulting PP eluate was collected. Cell lysates (Input) and PP eluate samples were then analyzed by immunoblotting for p75NTR, SorCS2 and FLAG.</p

HBpF-proBDNF induces growth cone collapse.

<p>Following 2 days in culture, hippocampal neuronal culture were stimulated with different concentrations of HBpF-proBDNF or proBDNF (25ng/ml and 100ng/ml) for 1h. Ni-NTA eluate from cells expressing only BirA was used as a negative control. Cells were then fixed and immunostained against beta-III-tubulin (Tuj-1) and phalloidin (scale bar = 10μm). Quantification of growth cone-collapse was done on three independent experiments and 50 growth-cones were counted for each experiment (unpaired two-tailed <i>t</i>-test, * indicates a p-value < 0.05; bars indicate standard error).</p

HBpF-proBDNF can be isolated by a modified tandem affinity purification protocol.

<p>A. HEK293T cells were transfected with p75NTR, Sortilin, HBpF-proBDNF, and BirA expression plasmid as indicated. 48h after transfection, HEK293T cells were lysed (input) and pulled-down on Ni-NTA beads. The Ni-NTA eluate was then pulled-down on SA beads and then cleaved by PP overnight (PP eluate). Samples were analyzed by immunoblotting for p75NTR, sortilin, biotin and the Flag tag.</p

Endocytosis of HBpF-proBDNF in Hippocampal neurons.

<p>Primary hippocampal neurons cells were exposed to HBpF-proBDNF (250 ng/ml) conjugated to Streptavidin-Cy3 for 1h to 6h. After fixation and mounting, cells were analyzed by fluorescent microscopy. Hoechst staining was used as a nuclear marker. Quantification of fluorescence intensity was performed using ImageJ software on three independent experiments. 100 cells were measured for each experiment. (unpaired two-tailed <i>t</i>-test, * indicates a p-value < 0.05; bars indicate standard error).</p

A novel method for quantifying axon degeneration

<div><p>Axons normally degenerate during development of the mammalian nervous system, but dysregulation of the same genetically-encoded destructive cellular machinery can destroy crucial structures during adult neurodegenerative diseases. Nerve growth factor (NGF) withdrawal from dorsal root ganglia (DRG) axons is a well-established <i>in vitro</i> experimental model for biochemical and cell biological studies of developmental degeneration. Definitive methods for measuring axon degeneration have been lacking and here we report a novel method of axon degeneration quantification from bulk cultures of DRG that enables objective and automated measurement of axonal density over the entire field of radial axon outgrowth from the ganglion. As proof of principal, this new method, written as an R script called Axoquant 2.0, was used to examine the role of extracellular Ca²⁺ in the execution of cytoskeletal disassembly during degeneration of NGF-deprived DRG axons. This method can be easily applied to examine degenerative or neuroprotective effects of gene manipulations and pharmacological interventions.</p></div

Axoquant 2.0 workflow.

<p>The R script automatically crawls folders and opens each quarter-field image (A) and if necessary, auto-orients the explant centre to the origin (B). Images are converted to binary masks with adaptive thresholding (C), and the area of the substrate occupied by axons is measured in bins radiating from the explant centre (stylized in D). Axoquant 2.0 automatically saves a comma separated file (*.csv) to the experiment parent folder for import into graphing and statistical analysis software. Example axon density curves are shown as embryo means (E) and treatment means with standard error (F).</p

HBpF-proBDNF inhibits carbachol (CCh)-induced persistent firing in cortical pyramidal neurons.

<p>A. Representative trace of current-clamp recording from pyramidal neuron in layer V of the entorhinal cortex. Slices were perfused with 10μM CCh and the persistent activity was produced by a short depolarization (1s, 100pA). HBpF-proBDNF at 2ng/ml was next added in presence of 10μM CCh during 10 minutes (first cut in the trace) and cells were stimulated. HBpF-proBDNF was removed by perfusing a solution containing only 10μM CCh for 10 minutes (second cut in the trace) and before the stimulation of the cells. B. Quantification of the plateau amplitude and frequency of the persistent activity (unpaired two-tailed <i>t</i>-test, * indicates a p-value < 0.05; bars indicate standard error).</p

Secretome of the Free-living Mycelium from the Ectomycorrhizal Basidiomycete <i>Laccaria bicolor</i>

The ectomycorrhizal basidiomycete <i>Laccaria bicolor</i> has a dual lifestyle with a transitory soil saprotrophic phase and a longer mutualistic interaction with tree roots. Recent evidence suggests that secreted proteins play key roles in host plant colonisation and symbiosis development. However, a limited number of secreted proteins have been characterized, and the full spectrum of effectors involved in the mycobiont invasion and survival remains unknown. We analyzed the extracellular proteins secreted in growth medium by free-living mycelium of <i>L. bicolor</i> as a proxy for its saprotrophic phase. The proteomic analyses (two-dimensional electrophoresis and shotgun proteomics) were substantiated by whole-genome expression transcript profiling on ectomycorrhizal roots. Among the 224 proteins identified were carbohydrate-acting enzymes likely involved in the cell wall remodelling linked to hyphal growth as well as secreted proteases possibly digesting soil organic compounds and/or fending off competitors, pathogens, and predators. Evidence of gene expression was found in ectomycorrhizal roots for 210 of them. These findings provide the first global view of the secretome of a mutualistic symbiont and shed some light on the mechanisms controlling cell wall remodelling during the hyphal growth. They also revealed many novel putative secreted proteins of unknown function, including one mycorrhiza-induced small secreted protein