Algorithmic decidability of Engel's property for automaton groups

We consider decidability problems associated with Engel's identity ($[\cdots[[x,y],y],\dots,y]=1$ for a long enough commutator sequence) in groups generated by an automaton. We give a partial algorithm that decides, given $x,y$, whether an Engel identity is satisfied. It succeeds, importantly, in proving that Grigorchuk's $2$-group is not Engel. We consider next the problem of recognizing Engel elements, namely elements $y$ such that the map $x\mapsto[x,y]$ attracts to $\{1\}$. Although this problem seems intractable in general, we prove that it is decidable for Grigorchuk's group: Engel elements are precisely those of order at most $2$. Our computations were implemented using the package FR within the computer algebra system GAP

Fission of Tubular Endosomes Triggers Endosomal Acidification and Movement

The early endosome acts as a sorting station for internalized molecules destined for recycling or degradation. While recycled molecules are sorted and delivered to tubular endosomes, residual compartments containing molecules to be degraded undergo “maturation” before final degradation in the lysosome. This maturation involves acidification, microtubule-dependent motility, and perinuclear localization. It is currently unknown how sorting and the processes of maturation cooperate with each other. Here, we show that fission of a tubular endosome triggers the maturation of the residual endosome, leading to degradation. Use of the dynamin inhibitor dynasore to block tubular endosome fission inhibited acidification, endosomal motility along microtubules, perinuclear localization, and degradation. However, tubular endosome fission was not affected by inhibiting endosomal acidification or by depolymerizing the microtubules. These results demonstrate that the fission of recycling tubules is the first important step in endosomal maturation and degradation in the lysosome. We believe this to be the first evidence of a cascade from sorting to degradation

Quantitative Analysis of Lipid Droplet Fusion: Inefficient Steady State Fusion but Rapid Stimulation by Chemical Fusogens

Lipid droplets (LDs) are dynamic cytoplasmic organelles containing neutral lipids and bounded by a phospholipid monolayer. Previous studies have suggested that LDs can undergo constitutive homotypic fusion, a process linked to the inhibitory effects of fatty acids on glucose transporter trafficking. Using strict quantitative criteria for LD fusion together with refined light microscopic methods and real-time analysis, we now show that LDs in diverse cell types show low constitutive fusogenic activity under normal growth conditions. To investigate the possible modulation of LD fusion, we screened for agents that can trigger fusion. A number of pharmacological agents caused homotypic fusion of lipid droplets in a variety of cell types. This provided a novel cell system to study rapid regulated fusion between homotypic phospholipid monolayers. LD fusion involved an initial step in which the two adjacent membranes became continuous (<10 s), followed by the slower merging (100 s) of the neutral lipid cores to produce a single spherical LD. These fusion events were accompanied by changes to the LD surface organization. Measurements of LDs undergoing homotypic fusion showed that fused LDs maintained their initial volume, with a corresponding decrease in surface area suggesting rapid removal of membrane from the fused LD. This study provides estimates for the level of constitutive LD fusion in cells and questions the role of LD fusion in vivo. In addition, it highlights the extent of LD restructuring which occurs when homotypic LD fusion is triggered in a variety of cell types

Analysis of Endocytic Pathways in Drosophila Cells Reveals a Conserved Role for GBF1 in Internalization via GEECs

In mammalian cells, endocytosis of the fluid phase and glycosylphosphatidylinositol-anchored proteins (GPI-APs) forms GEECs (GPI-AP enriched early endosomal compartments) via an Arf1- and Cdc42-mediated, dynamin independent mechanism. Here we use four different fluorescently labeled probes and several markers in combination with quantitative kinetic assays, RNA interference and high resolution imaging to delineate major endocytic routes in Drosophila cultured cells. We find that the hallmarks of the pinocytic GEEC pathway are conserved in Drosophila and identify garz, the fly ortholog of the GTP exchange factor GBF1, as a novel component of this pathway. Live confocal and TIRF imaging reveals that a fraction of GBF1 GFP dynamically associates with ABD RFP (a sensor for activated Arf1 present on nascent pinosomes). Correspondingly, a GTP exchange mutant of GBF1 has altered ABD RFP localization in the evanescent field and is impaired in fluid phase uptake. Furthermore, GBF1 activation is required for the GEEC pathway even in the presence of Brefeldin A, implying that, like Arf1, it has a role in endocytosis that is separable from its role in secretion

A Potential New Pathway for Staphylococcus aureus Dissemination: The Silent Survival of S. aureus Phagocytosed by Human Monocyte-Derived Macrophages

Although considered to be an extracellular pathogen, Staphylococcus aureus is able to invade a variety of mammalian, non-professional phagocytes and can also survive engulfment by professional phagocytes such as neutrophils and monocytes. In both of these cell types S. aureus promptly escapes from the endosomes/phagosomes and proliferates within the cytoplasm, which quickly leads to host cell death. In this report we show that S. aureus interacted with human monocyte-derived macrophages in a very different way to those of other mammalian cells. Upon phagocytosis by macrophages, S. aureus persisted intracellularly in vacuoles for 3–4 days before escaping into the cytoplasm and causing host cell lysis. Until the point of host cell lysis the infected macrophages showed no signs of apoptosis or necrosis and were functional. They were able to eliminate intracellular staphylococci if prestimulated with interferon-γ at concentrations equivalent to human therapeutic doses. S. aureus survival was dependent on the alternative sigma factor B as well as the global regulator agr, but not SarA. Furthermore, isogenic mutants deficient in α-toxin, the metalloprotease aureolysin, protein A, and sortase A were efficiently killed by macrophages upon phagocytosis, although with different kinetics. In particular α-toxin was a key effector molecule that was essential for S. aureus intracellular survival in macrophages. Together, our data indicate that the ability of S. aureus to survive phagocytosis by macrophages is determined by multiple virulence factors in a way that differs considerably from its interactions with other cell types. S. aureus persists inside macrophages for several days without affecting the viability of these mobile cells which may serve as vehicles for the dissemination of infection

On the absence of cohomological finiteness in wreath products

The wreath product W = A wreath product T, where A ≠ 1, is of type F P2 if and only if T is finite and A is of type FP2