Correlation evolution and monogamy of two geometric quantum discords in multipartite systems

We explore two different geometric quantum discords defined respectively via the trace norm (GQD-1) and Hilbert-Schmidt norm (GQD-2) in multipartite systems. A rigorous hierarchy relation is revealed for the two GQDs in a class of symmetric two-qubit $X$-shape states. For multiqubit pure states, it is found that both GQDs are related to the entanglement concurrence, with the hierarchy relation being saturated. Furthermore, we look into a four-partite dynamical system consisting of two cavities interacting with independent reservoirs. It is found that the GQD-2 can exhibit various sudden change behaviours, while the GQD-1 only evolves asymptotically, with the two GQDs exhibiting different monogamous properties.Comment: 5 pages, 3 figure

The clathrin-binding motif and the J-domain of Drosophila Auxilin are essential for facilitating Notch ligand endocytosis

<p>Abstract</p> <p>Background</p> <p>Ligand endocytosis plays a critical role in regulating the activity of the Notch pathway. The <it>Drosophila </it>homolog of auxilin (<it>dAux</it>), a J-domain-containing protein best known for its role in the disassembly of clathrin coats from clathrin-coated vesicles, has recently been implicated in Notch signaling, although its exact mechanism remains poorly understood.</p> <p>Results</p> <p>To understand the role of auxilin in Notch ligand endocytosis, we have analyzed several point mutations affecting specific domains of dAux. In agreement with previous work, analysis using these stronger <it>dAux </it>alleles shows that dAux is required for several Notch-dependent processes, and its function during Notch signaling is required in the signaling cells. In support of the genetic evidences, the level of Delta appears elevated in <it>dAux </it>deficient cells, suggesting that the endocytosis of Notch ligand is disrupted. Deletion analysis shows that the clathrin-binding motif and the J-domain, when over-expressed, are sufficient for rescuing <it>dAux </it>phenotypes, implying that the recruitment of Hsc70 to clathrin is a critical role for dAux. However, surface labeling experiment shows that, in <it>dAux </it>mutant cells, Delta accumulates at the cell surface. In <it>dAux </it>mutant cells, clathrin appears to form large aggregates, although Delta is not enriched in these aberrant clathrin-positive structures.</p> <p>Conclusion</p> <p>Our data suggest that <it>dAux </it>mutations inhibit Notch ligand internalization at an early step during clathrin-mediated endocytosis, before the disassembly of clathrin-coated vesicles. Further, the inhibition of ligand endocytosis in <it>dAux </it>mutant cells possibly occurs due to depletion of cytosolic pools of clathrin via the formation of clathrin aggregates. Together, our observations argue that ligand endocytosis is critical for Notch signaling and auxilin participates in Notch signaling by facilitating ligand internalization.</p