Upper bound on the density of Ruelle resonances for Anosov flows

Using a semiclassical approach we show that the spectrum of a smooth Anosov vector field V on a compact manifold is discrete (in suitable anisotropic Sobolev spaces) and then we provide an upper bound for the density of eigenvalues of the operator (-i)V, called Ruelle resonances, close to the real axis and for large real parts.Comment: 57 page

Myosin Motors and Not Actin Comets Are Mediators of the Actin-based Golgi-to-Endoplasmic Reticulum Protein Transport

We have previously reported that actin filaments are involved in protein transport from the Golgi complex to the endoplasmic reticulum. Herein, we examined whether myosin motors or actin comets mediate this transport. To address this issue we have used, on one hand, a combination of specific inhibitors such as 2,3-butanedione monoxime (BDM) and 1-[5-isoquinoline sulfonyl]-2-methyl piperazine (ML7), which inhibit myosin and the phosphorylation of myosin II by the myosin light chain kinase, respectively; and a mutant of the nonmuscle myosin II regulatory light chain, which cannot be phosphorylated (MRLC2(AA)). On the other hand, actin comet tails were induced by the overexpression of phosphatidylinositol phosphate 5-kinase. Cells treated with BDM/ML7 or those that express the MRLC2(AA) mutant revealed a significant reduction in the brefeldin A (BFA)-induced fusion of Golgi enzymes with the endoplasmic reticulum (ER). This delay was not caused by an alteration in the formation of the BFA-induced tubules from the Golgi complex. In addition, the Shiga toxin fragment B transport from the Golgi complex to the ER was also altered. This impairment in the retrograde protein transport was not due to depletion of intracellular calcium stores or to the activation of Rho kinase. Neither the reassembly of the Golgi complex after BFA removal nor VSV-G transport from ER to the Golgi was altered in cells treated with BDM/ML7 or expressing MRLC2(AA). Finally, transport carriers containing Shiga toxin did not move into the cytosol at the tips of comet tails of polymerizing actin. Collectively, the results indicate that 1) myosin motors move to transport carriers from the Golgi complex to the ER along actin filaments; 2) nonmuscle myosin II mediates in this process; and 3) actin comets are not involved in retrograde transport

Regulation of Protein Transport from the Golgi Complex to the Endoplasmic Reticulum by CDC42 and N-WASP

Actin is involved in the organization of the Golgi complex and Golgi-to-ER protein transport in mammalian cells. Little, however, is known about the regulation of the Golgi-associated actin cytoskeleton. We provide evidence that Cdc42, a small GTPase that regulates actin dynamics, controls Golgi-to-ER protein transport. We located GFP-Cdc42 in the lateral portions of Golgi cisternae and in COPI-coated and noncoated Golgi-associated transport intermediates. Overexpression of Cdc42 and its activated form Cdc42V12 inhibited the retrograde transport of Shiga toxin from the Golgi complex to the ER, the redistribution of the KDEL receptor, and the ER accumulation of Golgi-resident proteins induced by the active GTP-bound mutant of Sar1 (Sar1[H79G]). Coexpression of wild-type or activated Cdc42 and N-WASP also inhibited Golgi-to-ER transport, but this was not the case in cells expressing Cdc42V12 and N-WASP(ΔWA), a mutant form of N-WASP that lacks Arp2/3 binding. Furthermore, Cdc42V12 recruited GFP-N-WASP to the Golgi complex. We therefore conclude that Cdc42 regulates Golgi-to-ER protein transport in an N-WASP–dependent manner