Quantum convolutional data-syndrome codes

We consider performance of a simple quantum convolutional code in a fault-tolerant regime using several syndrome measurement/decoding strategies and three different error models, including the circuit model.Comment: Abstract submitted for The 20th IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC 2019

Percolation Transitions on Finite Transitive Hyperbolic Graphs

Edge percolation on finite transitive graphs is studied analytically and numerically. The results are made rigorous by considering a sequence of finite graphs $(\mathcal{G}_t)_t$ covered by an infinite graph $\mathcal{H}$, and weakly convergent to $\mathcal{H}$. The covering maps are used to classify $1$-cycles on graphs $\mathcal{G}_t$ as homologically trivial or nontrivial, and to define several thresholds associated with the rank of the first homology group on the open subgraphs. The growth of the homological distance $d_t$, the smallest size of a non-trivial cycle on $\mathcal{G}_t$, is identified as the main factor determining the location of homology changing thresholds. In particular, the giant cycle erasure threshold $p_E^0$ (related to the conventional erasure threshold for the corresponding sequence of generalized toric codes) coincides with the edge percolation threshold $p_c(\mathcal{H})$ if the ratio $d_t/\ln n_t$ diverges, where $n_t$ is the number of edges of $\mathcal{G}_t$, and evidence is given that p_E^0 < p_c(\mathcal{H}) in several cases where this ratio remains bounded, which is necessarily the case if $\mathcal{H}$ is non-amenable. Numerically, finite graphs are constructed with up to $10^5$ edges from several families of locally-planar graphs covered by infinite transitive planar graphs parameterized by Schl\"afli symbols $\{f,d\}$ with $fd/(f+d)\ge 2$, where $d$ regular $f$-gonal faces meet in each vertex. Specifically, considered are the planar regular tiling $\{4,4\}$, regular hyperbolic tilings $\{3,7\}$, $\{3,8\}$, $\{4,5\}$, $\{4,6\}$, $\{5,5\}$, and $\{5,6\}$, their duals with $f$ and $d$ interchanged, as well as random graphs of degree $d=5$---this latter family converges to an infinite tree of the same degree. Conventional and homological percolation are analyzed in these graphs, and the accuracy of several finite-size scaling methods designed calculate the cycle erasure threshold $p_E^0$, the conventional percolation threshold $p_c(\mathcal{H})$, and the giant cluster threshold $p_G$ compared. In particular, the cluster ratio method, one of the most commonly used techniques to locate percolation thresholds, shows rather poor convergence for hyperbolic graphs of this type

Quantum convolutional data-syndrome codes

We consider performance of a simple quantum convolutional code in a fault-tolerant regime using several syndrome measurement/decoding strategies and three different error models, including the circuit model

Inter-Cellular Exchange of Cellular Components via VE-Cadherin-Dependent Trans-Endocytosis

<div><p>Cell-cell communications typically involve receptor-mediated signaling initiated by soluble or cell-bound ligands. Here, we report a unique mode of endocytosis: proteins originating from cell-cell junctions and cytosolic cellular components from the neighboring cell are internalized, leading to direct exchange of cellular components between two adjacent endothelial cells. VE-cadherins form transcellular bridges between two endothelial cells that are the basis of adherence junctions. At such adherens junction sites, we observed the movement of the entire VE-cadherin molecule from one endothelial cell into the other with junctional and cytoplasmic components. This phenomenon, here termed trans-endocytosis, requires the establishment of a VE-cadherin homodimer <i>in trans</i> with internalization proceeding in a Rac1-, and actomyosin-dependent manner. Importantly, the trans-endocytosis is not dependent on any known endocytic pathway including clathrin-dependent endocytosis, macropinocytosis or phagocytosis. This novel form of cell-cell communications, leading to a direct exchange of cellular components, was observed in 2D and 3D-cultured endothelial cells as well as in the developing zebrafish vasculature.</p></div

VEC trans-endocytosis is Rac1 dependent.

<p>(<b>A</b>) Co-culture of HUVECs expressing VEC-EGFP and HUVECs expressing iRFP with 100 µM of NSC23766. NSC23766, a specific inhibitor for Rac1 activation, inhibited trans-endocytosis of VEC-EGFP, though cell-cell junctions remained intact. Arrow shows intact cell-cell junction. Cells were first pre-treated for an hour with 100 µM of NSC23766 before co-culture, then were mixed and incubated for 4 hours with 100 µM of NSC23766. Scale bar  = 10 µm. (<b>B</b>) Quantitative analysis of the number of trans-endocytosed structures with Rac1 or Cdc42 inhibitors. ML141, a specific inhibitor of Cdc42, and NSC23766 were used at concentrations around their IC₅₀ values. The IC₅₀ values of ML141 and NSC23766 are 2.6 µM and 50 µM, respectively. NSC23766 inhibited trans-endocytosis of VEC in a dose-dependent manner. The number of trans-endocytosed structures was counted for over 10-13 different fields of view per time point; n = 24-35 (ML141) and n = 19-38 (NSC23766). *, p<0.01 vs DMSO. Data were expressed as mean ± SD. (<b>C</b>) Co-culture of HUVECs expressing PA-Rac1-CA and HUVECs expressing VEC-EGFP. PA-Rac1-CA was accumulated at cell-cell junctions and co-localized with VEC-EGFP after its activation at 0 time point. Arrowheads show co-localization of PA-Rac1-CA with VEC-EGFP at cell-cell junctions. Scale bar  = 10 µm. See also <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0090736#pone.0090736.s010" target="_blank">Movie S4</a>. (<b>D</b>) Co-culture of HUVECs expressing PA-Rac1-DN and HUVECs expressing VEC-EGFP. PA-Rac1-DN was not accumulated at cell-cell junctions, nor co-localized with VEC-EGFP after its activation at 0 time point. Scale bar  = 10 µm. See also <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0090736#pone.0090736.s010" target="_blank">Movie S4</a>.</p

VEC trans-endocytosis mediates transport of junctional proteins.

<p>(<b>A</b>) Co-culture of HUVECs expressing VEC-Y658E-EGFP and HUVECs expressing VEC-Y658F-TagRFPT. Arrow heads show VEC-Y658F-TagRFPT molecules were trans-endocytosed by VEC-Y658E-EGFP expressing cells. (<b>B</b>) Co-culture of HUVECs expressing p120-EGFP and HUVECs expressing VEC-TagRFPT. Arrow shows p120-EGFP molecules were trans-endocytosed by VEC-TagRFPT expressing cells. (<b>C</b>) Co-culture of HUVECs expressing β-catenin-EGFP and HUVECs expressing VEC-TagRFPT. Arrows show β-catenin -EGFP molecules were trans-endocytosed by VEC-TagRFPT expressing cells. (<b>D</b>) Co-culture of HUVECs expressing VEC-EGFP and HUVECs expressing VEC/α-catenin-FLAG. Arrowheads show VEC/α-catenin-FLAG molecules were trans-endocytosed by VEC-EGFP expressing cells. (<b>E</b>) Co-culture of HUVECs expressing EGFP and HUVECs expressing VEC-TagRFPT. Arrow shows EGFP molecules were trans-endocytosed and co-localized with VEC-TagRFPT in the recipient cell. (<b>F</b>) Co-culture of HUVECs labeled with iRFP and VEC-EGFP expressing HUVECs transfected with Cy3-labeled scramble siRNA. Arrowhead shows siRNA molecules were trans-endocytosed and co-localized with VEC-EGFP in the recipient cell. (<b>A–F</b>) Lower images are higher magnification of the indicated area in upper images. Scale bars  = 20 µm, upper images; 5 µm, lower images.</p

VEC molecules are internalized by adjacent cells via trans-endocytosis.

<p>(<b>A</b>) Co-culture of primary microvascular endothelial cells from mice lungs. The primary microvascular endothelial cells were isolated separately from VEC-EGFP knock-in mice and Rosa26-mTmG mice expressing mTomato fluorescent protein in all cells and fixed after 24 hours of the co-culture. The trans-endocytosed VEC-EGFP molecules in mTomato fluorescent protein expressing cells were stained by anti-GFP antibody without (upper images) and with permeabilization (lower images). (<b>B</b>) Higher magnification of images of the indicated area in A. Arrows in upper images show VEC-EGFP molecule could not be stained by anti-GFP antibody in non-permeabilized cells. Arrowheads in lower images show VEC-EGFP molecule stained by anti-GFP antibody in permeabilized cells. (<b>C</b>) Co-culture of HUVECs expressing VEC-EGFP and HUVECs expressing VEC-TagRFPT. Trans-endocytosis of VEC occurred in HUVECs (scale bar  = 20 µm). (<b>D</b>) Higher magnification of the indicated area in C. Arrow shows VEC-EGFP molecules were trans-endocytosed by VEC-TagRFPT expressing cells. Asterisks show the extended filopodia or adherens junctions from the neighboring cell. Arrow heads show VEC-TagRFPT molecules were trans-endocytosed by VEC-EGFP expressing cells. Scale bar  = 5 µm.</p

VEC trans-endocytosis is not dependent on known endocytic pathway.

<p>(<b>A</b>) Co-culture of HUVECs expressing VEC-EGFP and HUVECs expressing VEC-TagRFPT, then stained with anti-Rab5 antibody. The trans-endocytosed VEC molecules by the adjacent cell co-localized with Rab5 in the recipient cells to a low extent. Lower images are higher magnification of the indicated area in upper images. Scale bars  = 20 µm, upper images; 5 µm, lower images. (<b>B</b>) Quantitative analysis of the number of trans-endocytosed VEC molecules co-localized with Rab5 in the recipient cells. About 15–20% of trans-endocytosed VEC molecules co-localized with Rab5 in the recipient cells. The percentage of Rab5 co-localization with VEC-TagRFPT was counted over 6-9 different fields of view for each time point; n = 6 (3 h), n = 8 (5 h) and n = 10 (7 h). Data were expressed as mean ± SD. (<b>C</b>) Co-culture of COS7 cells expressing VEC-EGFP and COS7 cells expressing VEC-TagRFPT with or without various inhibitors. Arrows show the trans-endocytosed VEC-EGFP molecules by VEC-TagRFPT expressing cells. Arrowheads show trans-endocytosed VEC-TagRFPT molecules by VEC-EGFP expressing cells. The trans-endocytosis occurred even with several inhibitors for clathrin-dependent endocytosis, macropinocytosis or phagocytosis. Dynasore (20 µM), an inhibitor for clathrin/dynamin dependent endocytosis, 5-(N-ethyl-N-isopropyl) amiloride (25 µM), the macropinocytosis inhibitor, Y27632 (10 µM), ROCK inhibitor, and bafilomycin A1 (200 nM), a specific inhibitor of the vacuolar type H(+)-ATPase for phagocytosis were used. Scale bars  = 20 µm. (<b>D</b>) Quantification of the number of trans-endocytosis positive cells with indicated inhibitors. The percentage of trans-endocytosis positive cells was counted over 10 different fields of view for each inhibitor; n = 88 (DMSO), n = 65 (dynasore), n = 57 (amiloride), n = 63 (Y27632) and n = 57 (bafilomycin A1). Data were expressed as mean ± SD.</p