Avoiding 3-Term Geometric Progressions in Non-Commutative Settings

Several recent papers have considered the Ramsey-theoretic problem of how large a subset of integers can be without containing any 3-term geometric progressions. This problem has also recently been generalized to number fields and \F_q[x]. We study the analogous problem in two noncommutative settings, quaternions and free groups, to see how lack of commutivity affected the problem. In the quaternion case, we show bounds for the supremum of upper densities of 3-term geometric progression avoiding sets. In the free groups case, we calculate the decay rate for the greedy set in $\langle x,y : x^2 = y^2 = 1\rangle$ avoiding 3-term geometric progressions.Comment: Version 1.0, 15 page

Insulin regulates Presenilin 1 localization via PI3K/Akt signaling.

Recently, insulin signaling has been highlighted in the pathology of Alzheimer's disease (AD). Although the association between insulin signaling and Tau pathology has been investigated in several studies, the interaction between insulin signaling and Presenilin 1 (PS1), a key molecule of amyloid beta (Abeta) pathology, has not been elucidated so far. In this study, we demonstrated that insulin inhibited PS1 phosphorylation at serine residues (serine 353, 357) via phosphatidylinositol 3-kinase (PI3K)/Akt signal pathway and strengthened the trimeric complex of PS1/N-cadherin/beta-catenin, consequently relocalizing PS1 to the cell surface. Since our recent report suggests that PS1/N-cadherin/beta-catenin complex regulates Abeta production, it is likely that insulin signaling affects Abeta pathology by regulating PS1 localization

Failure of DNA double-strand break repair by tau mediates Alzheimer’s disease pathology in vitro

DNA double-strand break (DSB) is the most severe form of DNA damage and accumulates with age, in which cytoskeletal proteins are polymerized to repair DSB in dividing cells. Since tau is a microtubule-associated protein, we investigate whether DSB is involved in tau pathologies in Alzheimer’s disease (AD). First, immunohistochemistry reveals the frequent coexistence of DSB and phosphorylated tau in the cortex of AD patients. In vitro studies using primary mouse cortical neurons show that non-p-tau accumulates perinuclearly together with the tubulin after DSB induction with etoposide, followed by the accumulation of phosphorylated tau. Moreover, the knockdown of endogenous tau exacerbates DSB in neurons, suggesting the protective role of tau on DNA repair. Interestingly, synergistic exposure of neurons to microtubule disassembly and the DSB strikingly augments aberrant p-tau aggregation and apoptosis. These data suggest that DSB plays a pivotal role in AD-tau pathology and that the failure of DSB repair leads to tauopathy

Loss of yata, a Novel Gene Regulating the Subcellular Localization of APPL, Induces Deterioration of Neural Tissues and Lifespan Shortening

Background: The subcellular localization of membrane and secreted proteins is finely and dynamically regulated through intracellular vesicular trafficking for permitting various biological processes. Drosophila Amyloid precursor protein like (APPL) and Hikaru genki (HIG) are examples of proteins that show differential subcellular localization among several developmental stages. Methodology/Principal Findings: During the study of the localization mechanisms of APPL and HIG, we isolated a novel mutant of the gene, CG1973, which we named yata. This molecule interacted genetically with Appl and is structurally similar to mouse NTKL/SCYL1, whose mutation was reported to cause neurodegeneration. yata null mutants showed phenotypes that included developmental abnormalities, progressive eye vacuolization, brain volume reduction, and lifespan shortening. Exogenous expression of Appl or hig in neurons partially rescued the mutant phenotypes of yata. Conversely, the phenotypes were exacerbated in double null mutants for yata and Appl. We also examined the subcellular localization of endogenous APPL and exogenously pulse-induced APPL tagged with FLAG by immunostaining the pupal brain and larval motor neurons in yata mutants. Our data revealed that yata mutants showed impaired subcellular localization of APPL. Finally, yata mutant pupal brains occasionally showed aberrant accumulation of Sec23p, a component of the COPII coat of secretory vesicles traveling from the endoplasmic reticulum (ER) to the Golgi

Conformational change of RNA-helicase DHX30 by ALS/FTD-linked FUS induces mitochondrial dysfunction and cytosolic aggregates.

Genetic mutations in fused in sarcoma (FUS) cause amyotrophic lateral sclerosis (ALS). Although mitochondrial dysfunction and stress granule have been crucially implicated in FUS proteinopathy, the molecular basis remains unclear. Here, we show that DHX30, a component of mitochondrial RNA granules required for mitochondrial ribosome assembly, interacts with FUS, and plays a crucial role in ALS-FUS. WT FUS did not affect mitochondrial localization of DHX30, but the mutant FUS lowered the signal of mitochondrial DHX30 and promoted the colocalization of cytosolic FUS aggregates and stress granule markers. The immunohistochemistry of the spinal cord from an ALS-FUS patient also confirmed the colocalization, and the immunoelectron microscope demonstrated decreased mitochondrial DHX30 signal in the spinal motor neurons. Subcellular fractionation by the detergent-solubility and density-gradient ultracentrifugation revealed that mutant FUS also promoted cytosolic mislocalization of DHX30 and aggregate formation. Interestingly, the mutant FUS disrupted the DHX30 conformation with aberrant disulfide formation, leading to impaired mitochondrial translation. Moreover, blue-native gel electrophoresis revealed an OXPHOS assembly defect caused by the FUS mutant, which was similar to that caused by DHX30 knockdown. Collectively, our study proposes DHX30 as a pivotal molecule in which disulfide-mediated conformational change mediates mitochondrial dysfunction and cytosolic aggregate formation in ALS-FUS