On the Geometry of the Nodal Lines of Eigenfunctions of the Two-Dimensional Torus

The width of a convex curve in the plane is the minimal distance between a pair of parallel supporting lines of the curve. In this paper we study the width of nodal lines of eigenfunctions of the Laplacian on the standard flat torus. We prove a variety of results on the width, some having stronger versions assuming a conjecture of Cilleruelo and Granville asserting a uniform bound for the number of lattice points on the circle lying in short arcs.Comment: 4 figures. Added some comments about total curvature and other detail

SNX19 restricts endolysosome motility through contacts with the endoplasmic reticulum.

The ability of endolysosomal organelles to move within the cytoplasm is essential for the performance of their functions. Long-range movement involves coupling of the endolysosomes to motor proteins that carry them along microtubule tracks. This movement is influenced by interactions with other organelles, but the mechanisms involved are incompletely understood. Herein we show that the sorting nexin SNX19 tethers endolysosomes to the endoplasmic reticulum (ER), decreasing their motility and contributing to their concentration in the perinuclear area of the cell. Tethering depends on two N-terminal transmembrane domains that anchor SNX19 to the ER, and a PX domain that binds to phosphatidylinositol 3-phosphate on the endolysosomal membrane. Two other domains named PXA and PXC negatively regulate the interaction of SNX19 with endolysosomes. These studies thus identify a mechanism for controlling the motility and positioning of endolysosomes that involves tethering to the ER by a sorting nexin

Acute Loss of Iron-Sulfur Clusters Results in Metabolic Reprogramming and Generation of Lipid Droplets in Mammalian Cells

Iron–sulfur (Fe-S) clusters are ancient cofactors in cells and participate in diverse biochemical functions, including electron transfer and enzymatic catalysis. Although cell lines derived from individuals carrying mutations in the Fe-S cluster biogenesis pathway or siRNA-mediated knockdown of the Fe-S assembly components provide excellent models for investigating Fe-S cluster formation in mammalian cells, these experimental strategies focus on the consequences of prolonged impairment of Fe-S assembly. Here, we constructed and expressed dominant–negative variants of the primary Fe-S biogenesis scaffold protein iron–sulfur cluster assembly enzyme 2 (ISCU2) in human HEK293 cells. This approach enabled us to study the early metabolic reprogramming associated with loss of Fe-S–containing proteins in several major cellular compartments. Using multiple metabolomics platforms, we observed a ∼12-fold increase in intracellular citrate content in Fe-S–deficient cells, a surge that was due to loss of aconitase activity. The excess citrate was generated from glucose-derived acetyl-CoA, and global analysis of cellular lipids revealed that fatty acid biosynthesis increased markedly relative to cellular proliferation rates in Fe-S–deficient cells. We also observed intracellular lipid droplet accumulation in both acutely Fe-S–deficient cells and iron-starved cells. We conclude that deficient Fe-S biogenesis and acute iron deficiency rapidly increase cellular citrate concentrations, leading to fatty acid synthesis and cytosolic lipid droplet formation. Our findings uncover a potential cause of cellular steatosis in nonadipose tissues

A keratin scaffold regulates epidermal barrier formation, mitochondrial lipid composition, and activity.

Keratin intermediate filaments (KIFs) protect the epidermis against mechanical force, support strong adhesion, help barrier formation, and regulate growth. The mechanisms by which type I and II keratins contribute to these functions remain incompletely understood. Here, we report that mice lacking all type I or type II keratins display severe barrier defects and fragile skin, leading to perinatal mortality with full penetrance. Comparative proteomics of cornified envelopes (CEs) from prenatal KtyI(-/-) and KtyII(-/-)(K8) mice demonstrates that absence of KIF causes dysregulation of many CE constituents, including downregulation of desmoglein 1. Despite persistence of loricrin expression and upregulation of many Nrf2 targets, including CE components Sprr2d and Sprr2h, extensive barrier defects persist, identifying keratins as essential CE scaffolds. Furthermore, we show that KIFs control mitochondrial lipid composition and activity in a cell-intrinsic manner. Therefore, our study explains the complexity of keratinopathies accompanied by barrier disorders by linking keratin scaffolds to mitochondria, adhesion, and CE formation

LKB1/AMPK and PKA Control ABCB11 Trafficking and Polarization in Hepatocytes.

Polarization of hepatocytes is manifested by bile canalicular network formation and activation of LKB1 and AMPK, which control cellular energy metabolism. The bile acid, taurocholate, also regulates development of the canalicular network through activation of AMPK. In the present study, we used collagen sandwich hepatocyte cultures from control and liver-specific LKB1 knockout mice to examine the role of LKB1 in trafficking of ABCB11, the canalicular bile acid transporter. In polarized hepatocytes, ABCB11 traffics from Golgi to the apical plasma membrane and endogenously cycles through the rab 11a-myosin Vb recycling endosomal system. LKB1 knockout mice were jaundiced, lost weight and manifested impaired bile canalicular formation and intracellular trafficking of ABCB11, and died within three weeks. Using live cell imaging, fluorescence recovery after photobleaching (FRAP), particle tracking, and biochemistry, we found that LKB1 activity is required for microtubule-dependent trafficking of ABCB11 to the canalicular membrane. In control hepatocytes, ABCB11 trafficking was accelerated by taurocholate and cAMP; however, in LKB1 knockout hepatocytes, ABCB11 trafficking to the apical membrane was greatly reduced and restored only by cAMP, but not taurocholate. cAMP acted through a PKA-mediated pathway which did not activate AMPK. Our studies establish a regulatory role for LKB1 in ABCB11 trafficking to the canalicular membrane, hepatocyte polarization, and canalicular network formation

Analyses of carnivore microsatellites and their intimate association with tRNA-derived SINEs

BACKGROUND: The popularity of microsatellites has greatly increased in the last decade on account of their many applications. However, little is currently understood about the factors that influence their genesis and distribution among and within species genomes. In this work, we analyzed carnivore microsatellite clones from GenBank to study their association with interspersed repeats and elucidate the role of the latter in microsatellite genesis and distribution. RESULTS: We constructed a comprehensive carnivore microsatellite database comprising 1236 clones from GenBank. Thirty-three species of 11 out of 12 carnivore families were represented, although two distantly related species, the domestic dog and cat, were clearly overrepresented. Of these clones, 330 contained tRNA(Lys)-derived SINEs and 357 contained other interspersed repeats. Our rough estimates of tRNA SINE copies per haploid genome were much higher than published ones. Our results also revealed a distinct juxtaposition of AG and A-rich repeats and tRNA(Lys)-derived SINEs suggesting their coevolution. Both microsatellites arose repeatedly in two regions of the insterspersed repeat. Moreover, microsatellites associated with tRNA(Lys)-derived SINEs showed the highest complexity and less potential instability. CONCLUSION: Our results suggest that tRNA(Lys)-derived SINEs are a significant source for microsatellite generation in carnivores, especially for AG and A-rich repeat motifs. These observations indicate two modes of microsatellite generation: the expansion and variation of pre-existing tandem repeats and the conversion of sequences with high cryptic simplicity into a repeat array; mechanisms which are not specific to tRNA(Lys)-derived SINEs. Microsatellite and interspersed repeat coevolution could also explain different distribution of repeat types among and within species genomes. Finally, due to their higher complexity and lower potential informative content of microsatellites associated with tRNA(Lys)-derived SINEs, we recommend avoiding their use as genetic markers

Poly(ADP-Ribose) Polymerase 1 (PARP-1) Regulates Ribosomal Biogenesis in Drosophila Nucleoli

Poly(ADP-ribose) polymerase 1 (PARP1), a nuclear protein, utilizes NAD to synthesize poly(AD-Pribose) (pADPr), resulting in both automodification and the modification of acceptor proteins. Substantial amounts of PARP1 and pADPr (up to 50%) are localized to the nucleolus, a subnuclear organelle known as a region for ribosome biogenesis and maturation. At present, the functional significance of PARP1 protein inside the nucleolus remains unclear. Using PARP1 mutants, we investigated the function of PARP1, pADPr, and PARP1-interacting proteins in the maintenance of nucleolus structure and functions. Our analysis shows that disruption of PARP1 enzymatic activity caused nucleolar disintegration and aberrant localization of nucleolar-specific proteins. Additionally, PARP1 mutants have increased accumulation of rRNA intermediates and a decrease in ribosome levels. Together, our data suggests that PARP1 enzymatic activity is required for targeting nucleolar proteins to the proximity of precursor rRNA; hence, PARP1 controls precursor rRNA processing, post-transcriptional modification, and pre-ribosome assembly. Based on these findings, we propose a model that explains how PARP1 activity impacts nucleolar functions and, consequently, ribosomal biogenesis