Dynamic visualization of membrane-inserted fraction of pHluorin-tagged channels using repetitive acidification technique.

Background Changes in neuronal excitability, synaptic efficacy and generally in cell signaling often result from insertion of key molecules into plasma membrane (PM). Many of the techniques used for monitoring PM insertion lack either spatial or temporal resolution. Results We improved the imaging method based on time-lapse total internal reflection fluorescence (TIRF) microscopy and pHluorin tagging by supplementing it with a repetitive extracellular acidification protocol. We illustrate the applicability of this method by showing that brief activation of NMDA receptors ("chemical LTP") in cultured hippocampal neurons induced a persistent PM insertion of glutamate receptors containing the pHluorin-tagged GluR-A(flip) subunits. Conclusion The repetitive acidification technique provides a more accurate way of monitoring the PM-inserted fraction of fluorescently tagged molecules and offers a good temporal and spatial resolution

Formal conserved quantities for isothermic surfaces

Isothermic surfaces in $S^n$ are characterised by the existence of a pencil $\nabla^t$ of flat connections. Such a surface is special of type $d$ if there is a family $p(t)$ of $\nabla^t$-parallel sections whose dependence on the spectral parameter $t$ is polynomial of degree $d$. We prove that any isothermic surface admits a family of $\nabla^t$-parallel sections which is a formal Laurent series in $t$. As an application, we give conformally invariant conditions for an isothermic surface in $S^3$ to be special.Comment: 13 page

NCS-1 Inhibits insulin stimulated GLUT4 translocation in 3T3L1 adipocytes through a phosphatidylinositol 4-kinase dependent pathway

Expression of NCS-1 (neuronal calcium sensor-1, also termed frequenin) in 3T3L1 adipocytes strongly inhibited insulin-stimulated translocation of GLUT4 and insulin-responsive aminopeptidase. The effect of NCS-1 was specific for GLUT4 and the insulin-responsive aminopeptidase translocation as there was no effect on the trafficking of the cation-independent mannose 6-phosphate receptor or the GLUT1 glucose transporter isoform. Moreover, NCS-1 showed partial colocalization with GLUT4-EGFP in the perinuclear region. The inhibitory action of NCS-1 was independent of calcium sequestration since neither treatment with ionomycin nor endothelin-1, both of which elevated the intracellular calcium concentration, restored insulin-stimulated GLUT4 translocation. Furthermore, NCS-1 did not alter the insulin-stimulated protein kinase B (PKB/Akt) phosphorylation or the recruitment of Cbl to the plasma membrane. In contrast, expression of the NCS-1 effector phosphatidylinositol 4-kinase (PI 4-kinase) inhibited insulin-stimulated GLUT4 translocation, whereas co-transfection with an inactive PI 4-kinase mutant prevented the NCS-1-induced inhibition. These data demonstrate that PI 4-kinase functions to negatively regulate GLUT4 translocation through its interaction with NCS-1

Constructing solutions to the Bj\"orling problem for isothermic surfaces by structure preserving discretization

In this article, we study an analog of the Bj\"orling problem for isothermic surfaces (that are more general than minimal surfaces): given a real analytic curve $\gamma$ in ${\mathbb R}^3$, and two analytic non-vanishing orthogonal vector fields $v$ and $w$ along $\gamma$, find an isothermic surface that is tangent to $\gamma$ and that has $v$ and $w$ as principal directions of curvature. We prove that solutions to that problem can be obtained by constructing a family of discrete isothermic surfaces (in the sense of Bobenko and Pinkall) from data that is sampled along $\gamma$, and passing to the limit of vanishing mesh size. The proof relies on a rephrasing of the Gauss-Codazzi-system as analytic Cauchy problem and an in-depth-analysis of its discretization which is induced from the geometry of discrete isothermic surfaces. The discrete-to-continuous limit is carried out for the Christoffel and the Darboux transformations as well.Comment: 29 pages, some figure

The PT-symmetric brachistochrone problem, Lorentz boosts and non-unitary operator equivalence classes

The PT-symmetric (PTS) quantum brachistochrone problem is reanalyzed as quantum system consisting of a non-Hermitian PTS component and a purely Hermitian component simultaneously. Interpreting this specific setup as subsystem of a larger Hermitian system, we find non-unitary operator equivalence classes (conjugacy classes) as natural ingredient which contain at least one Dirac-Hermitian representative. With the help of a geometric analysis the compatibility of the vanishing passage time solution of a PTS brachistochrone with the Anandan-Aharonov lower bound for passage times of Hermitian brachistochrones is demonstrated.Comment: 12 pages, 2 figures, strongly extended versio

Willmore Surfaces of Constant Moebius Curvature

We study Willmore surfaces of constant Moebius curvature $K$ in $S^4$. It is proved that such a surface in $S^3$ must be part of a minimal surface in $R^3$ or the Clifford torus. Another result in this paper is that an isotropic surface (hence also Willmore) in $S^4$ of constant $K$ could only be part of a complex curve in $C^2\cong R^4$ or the Veronese 2-sphere in $S^4$. It is conjectured that they are the only examples possible. The main ingredients of the proofs are over-determined systems and isoparametric functions.Comment: 16 pages. Mistakes occured in the proof to the main theorem (Thm 3.6) has been correcte

Generalized isothermic lattices

We study multidimensional quadrilateral lattices satisfying simultaneously two integrable constraints: a quadratic constraint and the projective Moutard constraint. When the lattice is two dimensional and the quadric under consideration is the Moebius sphere one obtains, after the stereographic projection, the discrete isothermic surfaces defined by Bobenko and Pinkall by an algebraic constraint imposed on the (complex) cross-ratio of the circular lattice. We derive the analogous condition for our generalized isthermic lattices using Steiner's projective structure of conics and we present basic geometric constructions which encode integrability of the lattice. In particular, we introduce the Darboux transformation of the generalized isothermic lattice and we derive the corresponding Bianchi permutability principle. Finally, we study two dimensional generalized isothermic lattices, in particular geometry of their initial boundary value problem.Comment: 19 pages, 11 figures; v2. some typos corrected; v3. new references added, higlighted similarities and differences with recent papers on the subjec

Connecting Cancer Pathways to Tumor Engines: A Stratification Tool for Colorectal Cancer Combining Human In Vitro Tissue Models with Boolean In Silico Models

To improve and focus preclinical testing, we combine tumor models based on a decellularized tissue matrix with bioinformatics to stratify tumors according to stage-specific mutations that are linked to central cancer pathways. We generated tissue models with BRAF-mutant colorectal cancer (CRC) cells (HROC24 and HROC87) and compared treatment responses to two-dimensional (2D) cultures and xenografts. As the BRAF inhibitor vemurafenib is—in contrast to melanoma—not effective in CRC, we combined it with the EGFR inhibitor gefitinib. In general, our 3D models showed higher chemoresistance and in contrast to 2D a more active HGFR after gefitinib and combination-therapy. In xenograft models murine HGF could not activate the human HGFR, stressing the importance of the human microenvironment. In order to stratify patient groups for targeted treatment options in CRC, an in silico topology with different stages including mutations and changes in common signaling pathways was developed. We applied the established topology for in silico simulations to predict new therapeutic options for BRAF-mutated CRC patients in advanced stages. Our in silico tool connects genome information with a deeper understanding of tumor engines in clinically relevant signaling networks which goes beyond the consideration of single drivers to improve CRC patient stratification