The resonance spectrum of the cusp map in the space of analytic functions

We prove that the Frobenius--Perron operator $U$ of the cusp map $F:[-1,1]\to[-1,1]$, $F(x)=1-2\sqrt{|x|}$ (which is an approximation of the Poincar\'e section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that for any $q\in(0,1)$ the spectrum of $U$ in the Hardy space in the disk \{z\in\C:|z-q|<1+q\} is the union of the segment $[0,1]$ and some finite or countably infinite set of isolated eigenvalues of finite multiplicity.Comment: Submitted to JMP; The description of the spectrum in some Hardy spaces is adde

Complete spectral data for analytic Anosov maps of the torus

Using analytic properties of Blaschke factors we construct a family of analytic hyperbolic diffeomorphisms of the torus for which the spectral properties of the associated transfer operator acting on a suitable Hilbert space can be computed explicitly. As a result, we obtain explicit expressions for the decay of correlations of analytic observables without resorting to any kind of perturbation argument.Comment: 19 pages, 4 figure

Nogo-B is associated with cytoskeletal structures in human monocyte-derived macrophages

<p>Abstract</p> <p>Background</p> <p>The reticulon Nogo-B participates in cellular and immunological processes in murine macrophages. Since leukocytes are an essential part of the immune system in health and disease, we decided to investigate the expression of Nogo-A, Nogo-B and Nogo-C in different human immune cell subpopulations. Furthermore, we analyzed the localization of Nogo-B in human monocyte-derived macrophages by indirect immunofluorescence stainings to gain further insight into its possible function.</p> <p>Findings</p> <p>We describe an association of Nogo-B with cytoskeletal structures and the base of filopodia, but not with focal or podosomal adhesion sites of monocyte-derived macrophages. Nogo-B positive structures are partially co-localized with RhoA staining and Rac1 positive membrane ruffles. Furthermore, Nogo-B is associated with the tubulin network, but not accumulated in the Golgi region. Although Nogo-B is present in the endoplasmic reticulum, it can also be translocated to large cell protrusions or the trailing end of migratory cells, where it is homogenously distributed.</p> <p>Conclusions</p> <p>Two different Nogo-B staining patterns can be distinguished in macrophages: firstly we observed ER-independent Nogo-B localization in cell protrusions and at the trailing end of migrating cells. Secondly, the localization of Nogo-B in actin/RhoA/Rac1 positive regions supports an influence on cytoskeletal organization. To our knowledge this is the first report on Nogo-B expression at the base of filopodia, thus providing further insight into the distribution of this protein.</p

Proteoglycan-Specific Molecular Switch for RPTPσ Clustering and Neuronal Extension

Heparan and chondroitin sulfate proteoglycans (HSPGs and CSPGs, respectively) regulate numerous cell surface signaling events, with typically opposite effects on cell function. CSPGs inhibit nerve regeneration through receptor protein tyrosine phosphatase sigma (RPTPσ). Here we report that RPTPσ acts bimodally in sensory neuron extension, mediating CSPG inhibition and HSPG growth promotion. Crystallographic analyses of a shared HSPG-CSPG binding site reveal a conformational plasticity that can accommodate diverse glycosaminoglycans with comparable affinities. Heparan sulfate and analogs induced RPTPσ ectodomain oligomerization in solution, which was inhibited by chondroitin sulfate. RPTPσ and HSPGs colocalize in puncta on sensory neurons in culture, whereas CSPGs occupy the extracellular matrix. These results lead to a model where proteoglycans can exert opposing effects on neuronal extension by competing to control the oligomerization of a common receptor

NGF Causes TrkA to Specifically Attract Microtubules to Lipid Rafts

Membrane protein sorting is mediated by interactions between proteins and lipids. One mechanism that contributes to sorting involves patches of lipids, termed lipid rafts, which are different from their surroundings in lipid and protein composition. Although the nerve growth factor (NGF) receptors, TrkA and p75NTR collaborate with each other at the plasma membrane to bind NGF, these two receptors are endocytosed separately and activate different cellular responses. We hypothesized that receptor localization in membrane rafts may play a role in endocytic sorting. TrkA and p75NTR both reside in detergent-resistant membranes (DRMs), yet they responded differently to a variety of conditions. The ganglioside, GM1, caused increased association of NGF, TrkA, and microtubules with DRMs, but a decrease in p75NTR. When microtubules were induced to polymerize and attach to DRMs by in vitro reactions, TrkA, but not p75NTR, was bound to microtubules in DRMs and in a detergent-resistant endosomal fraction. NGF enhanced the interaction between TrkA and microtubules in DRMs, yet tyrosine phosphorylated TrkA was entirely absent in DRMs under conditions where activated TrkA was detected in detergent-sensitive membranes and endosomes. These data indicate that TrkA and p75NTR partition into membrane rafts by different mechanisms, and that the fraction of TrkA that associates with DRMs is internalized but does not directly form signaling endosomes. Rather, by attracting microtubules to lipid rafts, TrkA may mediate other processes such as axon guidance