Hypergraph containers

We develop a notion of containment for independent sets in hypergraphs. For every $r$-uniform hypergraph $G$, we find a relatively small collection $C$ of vertex subsets, such that every independent set of $G$ is contained within a member of $C$, and no member of $C$ is large; the collection, which is in various respects optimal, reveals an underlying structure to the independent sets. The containers offer a straightforward and unified approach to many combinatorial questions concerned (usually implicitly) with independence. With regard to colouring, it follows that simple $r$-uniform hypergraphs of average degree $d$ have list chromatic number at least $(1/(r-1)^2 + o(1)) \log_r d$. For $r = 2$ this improves a bound due to Alon and is tight. For $r \ge 3$, previous bounds were weak but the present inequality is close to optimal. In the context of extremal graph theory, it follows that, for each $\ell$-uniform hypergraph $H$ of order $k$, there is a collection $C$ of $\ell$-uniform hypergraphs of order $n$ each with $o(n^k)$ copies of $H$, such that every $H$-free $\ell$-uniform hypergraph of order $n$ is a subgraph of a hypergraph in $C$, and $\log |C| \le c n^{\ell-1/m(H)} \log n$ where $m(H)$ is a standard parameter (there is a similar statement for induced subgraphs). This yields simple proofs, for example, for the number of $H$-free hypergraphs, and for the sparsity theorems of Conlon-Gowers and Schacht. A slight variant yields a counting version of the K{\L}R conjecture. Likewise, for systems of linear equations the containers supply, for example, bounds on the number of solution-free sets, and the existence of solutions in sparse random subsets. Balogh, Morris and Samotij have independently obtained related results.The first author was supported by a grant from the EPSRC.This is the author accepted manuscript. The final version is available from Springer at http://dx.doi.org/10.1007/s00222-014-0562-

mTOR Signaling in Growth, Metabolism, and Disease

© 2017 Elsevier Inc. The mechanistic target of rapamycin (mTOR) coordinates eukaryotic cell growth and metabolism with environmental inputs, including nutrients and growth factors. Extensive research over the past two decades has established a central role for mTOR in regulating many fundamental cell processes, from protein synthesis to autophagy, and deregulated mTOR signaling is implicated in the progression of cancer and diabetes, as well as the aging process. Here, we review recent advances in our understanding of mTOR function, regulation, and importance in mammalian physiology. We also highlight how the mTOR signaling network contributes to human disease and discuss the current and future prospects for therapeutically targeting mTOR in the clinic

First Results from the XMM-Newton Slew Survey

We have attempted to analyse all the available data taken by XMM-Newton as it slews between targets. This slew survey, the resultant source catalogue and the analysis procedures used are described in an accompanying paper. In this letter we present the initial science results from the survey. To date, detailed source-searching has been performed in three X-ray bands (soft, hard and total) in the EPIC-pn 0.2-12 keV band over ~6300 sq.degrees (~15% of the sky), and of order 4000 X-ray sources have been detected (~55% of which have IDs). A great variety of sources are seen, including AGN, galaxies, clusters and groups, active stars, SNRs, low- and high-mass XRBs and white dwarfs. In particular, as this survey constitutes the deepest ever hard-band 2-12 keV all-sky survey, a large number of hard sources are detected. Furthermore, the great sensitivity and low-background of the EPIC-pn camera are especially suited to emission from extended sources, and interesting spatial structure is observed in many supernova remnants and clusters of galaxies. The instrument is very adept at mapping large areas of the X-ray sky. Also, as the slew survey is well matched to the ROSAT all-sky survey, long-term variability studies are possible, and a number of extremely variable X-ray sources, some possibly due to the tidal disruption of stars by central supermassive black holes, have been discovered.Comment: 4 Pages, 3 Figs, to appear in PASJ (2006) 58, No 6. Colour version available at http://www.star.le.ac.uk/~amr30/publications.htm

Was the soft X-ray flare in NGC 3599 due to an AGN disc instability or a delayed tidal disruption event?

We present unpublished data from a tidal disruption candidate in NGC 3599 which show that the galaxy was already X-ray bright 18 months before the measurement which led to its classification. This removes the possibility that the flare was caused by a classical, fast-rising, short-peaked, tidal disruption event. Recent relativistic simulations indicate that the majority of disruptions will actually take months or years to rise to a peak, which will then be maintained for longer than previously thought. NGC 3599 could be one of the first identified examples of such an event. The optical spectra of NGC 3599 indicate that it is a low-luminosity Seyfert/LINER with L_bol~10^40 ergs/s The flare may alternatively be explained by a thermal instability in the accretion disc, which propagates through the inner region at the sound speed, causing an increase of the disc scale height and local accretion rate. This can explain the <9 years rise time of the flare. If this mechanism is correct then the flare may repeat on a timescale of several decades as the inner disc is emptied and refilled.Comment: Resubmitted due to typo in author nam

Mechanism of arginine sensing by CASTOR1 upstream of mTORC1

The mechanistic Target of Rapamycin Complex 1 (mTORC1) is a major regulator of eukaryotic growth that coordinates anabolic and catabolic cellular processes with inputs such as growth factors and nutrients, including amino acids. In mammals arginine is particularly important, promoting diverse physiological effects such as immune cell activation, insulin secretion, and muscle growth, largely mediated through activation of mTORC1 (refs 4, 5, 6, 7).Arginine activates mTORC1 upstream of the Rag family of GTPases, through either the lysosomal amino acid transporter SLC38A9 or the GATOR2-interacting Cellular Arginine Sensor for mTORC1 (CASTOR1). However, the mechanism by which the mTORC1 pathway detects and transmits this arginine signal has been elusive. Here, we present the 1.8 Å crystal structure of arginine-bound CASTOR1. Homodimeric CASTOR1 binds arginine at the interface of two Aspartate kinase, Chorismate mutase, TyrA (ACT) domains, enabling allosteric control of the adjacent GATOR2-binding site to trigger dissociation from GATOR2 and downstream activation of mTORC1. Our data reveal that CASTOR1 shares substantial structural homology with the lysine-binding regulatory domain of prokaryotic aspartate kinases, suggesting that the mTORC1 pathway exploited an ancient, amino-acid-dependent allosteric mechanism to acquire arginine sensitivity. Together, these results establish a structural basis for arginine sensing by the mTORC1 pathway and provide insights into the evolution of a mammalian nutrient sensor.National Institutes of Health (U.S.) (Grant R01CA103866)National Institutes of Health (U.S.) (Grant AI47389)United States. Department of Defense (Award W81XWH-07-0448)National Institutes of Health (U.S.) (Grant F31 CA180271

Sestrin2 is a leucine sensor for the mTORC1 pathway

Leucine is a proteogenic amino acid that also regulates many aspects of mammalian physiology, in large part by activating the mTOR complex 1 (mTORC1) protein kinase, a master growth controller. Amino acids signal to mTORC1 through the Rag guanosine triphosphatases (GTPases). Several factors regulate the Rags, including GATOR1, aGTPase-activating protein; GATOR2, a positive regulator of unknown function; and Sestrin2, a GATOR2-interacting protein that inhibits mTORC1 signaling. We find that leucine, but not arginine, disrupts the Sestrin2-GATOR2 interaction by binding to Sestrin2 with a dissociation constant of 20 micromolar, which is the leucine concentration that half-maximally activates mTORC1. The leucine-binding capacity of Sestrin2 is required for leucine to activate mTORC1 in cells. These results indicate that Sestrin2 is a leucine sensor for the mTORC1 pathway.United States. National Institutes of Health (R01CA103866)United States. National Institutes of Health (AI47389)United States. Department of Defense (W81XWH-07-0448)United States. National Institutes of Health (T32 GM007753)United States. National Institutes of Health (F30 CA189333)United States. National Institutes of Health (F31 CA180271

The CASTOR Proteins Are Arginine Sensors for the mTORC1 Pathway

Amino acids signal to the mTOR complex I (mTORC1) growth pathway through the Rag GTPases. Multiple distinct complexes regulate the Rags, including GATOR1, a GTPase activating protein (GAP), and GATOR2, a positive regulator of unknown molecular function. Arginine stimulation of cells activates mTORC1, but how it is sensed is not well understood. Recently, SLC38A9 was identified as a putative lysosomal arginine sensor required for arginine to activate mTORC1 but how arginine deprivation represses mTORC1 is unknown. Here, we show that CASTOR1, a previously uncharacterized protein, interacts with GATOR2 and is required for arginine deprivation to inhibit mTORC1. CASTOR1 homodimerizes and can also heterodimerize with the related protein, CASTOR2. Arginine disrupts the CASTOR1-GATOR2 complex by binding to CASTOR1 with a dissociation constant of ∼30 μM, and its arginine-binding capacity is required for arginine to activate mTORC1 in cells. Collectively, these results establish CASTOR1 as an arginine sensor for the mTORC1 pathway.United States. National Institutes of Health (R01CA103866)United States. National Institutes of Health (AI47389)United States. Department of Energy (W81XWH-07-0448)United States. National Institutes of Health (F31 CA180271)United States. National Institutes of Health (F31 CA189437

Use of a scanning optical profilometer for toolmark characterization

An optical profilometer has been used to obtain 3-dimensional data for use in two research projects concerning toolmark quantification and identification. In the first study quantitative comparisons between toolmarks made using data from the optical system proved superior to similar data obtained using a stylus profilometer. In the second study the ability of the instrument to obtain accurate data from two surfaces intersecting at a high angle (approximately 90 degrees) is demonstrated by obtaining measurements from the tip of a flat screwdriver. The data obtained was used to produce a computer generated virtual tool, which was then employed to create virtual tool marks. How these experiments were conducted and the results obtained will be presented and discussed

Structural basis for leucine sensing by the Sestrin2-mTORC1 pathway

Eukaryotic cells coordinate growth with the availability of nutrients through the mechanistic target of rapamycin complex 1 (mTORC1), a master growth regulator. Leucine is of particular importance and activates mTORC1 via the Rag guanosine triphosphatases and their regulators GATOR1 and GATOR2. Sestrin2 interacts with GATOR2 and is a leucine sensor. Here we present the 2.7 angstrom crystal structure of Sestrin2 in complex with leucine. Leucine binds through a single pocket that coordinates its charged functional groups and confers specificity for the hydrophobic side chain. A loop encloses leucine and forms a lid-latch mechanism required for binding. A structure-guided mutation in Sestrin2 that decreases its affinity for leucine leads to a concomitant increase in the leucine concentration required for mTORC1 activation in cells. These results provide a structural mechanism of amino acid sensing by the mTORC1 pathway.United States. Department of Defense (W81XWH-07- 0448)Damon Runyon Cancer Research Foundation (DRG-112-12)National Institutes of Health (U.S.) (Predoctoral Training Grant T32GM007287)National Institutes of Health (U.S.) (Grants R01CA103866, AI47389, T32 GM007753, F30 CA189333, F31 CA180271, and F31 CA189437)United States. Dept. of Defense. Breast Cancer Research Program (Postdoctoral Fellowship BC120208)Massachusetts Institute of Technology. Office of the Dean for Graduate Education (Whitaker Health Sciences Fund Fellowship)Damon Runyon Cancer Research Foundation (Sally Gordon Fellowship DRG-112-12

Serum response factor cleavage by caspases 3 and 7 linked to apoptosis in human BJAB cells

Apoptosis involves the cessation of cellular processes, the breakdown of intracellular organelles, and, finally, the nonphlogistic clearance of apoptotic cells from the body. Important for these events is a family of proteases, caspases, which are activated by a proteolytic cleavage cascade and drive apoptosis by targeting key proteins within the cell. Here, we demonstrate that serum response factor (SRF), a transcription factor essential for proliferative gene expression, is cleaved by caspases and that this cleavage occurs in proliferating murine fibroblasts and can be induced in the human B-cell line BJAB. We identify the two major sites at which SRF cleavage occurs as Asp245 and Asp254, the caspases responsible for the cleavage and generate a mutant of SRF resistant to cleavage in BJAB cells. Investigation of the physiological and functional significance of SRF cleavage reveals that it correlates with the loss of e-fos expression, whereby neither SRF cleavage fragment retains transcriptional activity. Moreover, the expression of a noncleavable SRF in BJAB cells suppresses apoptosis induced by Fas cross-linking. These results suggest that for apoptosis to proceed, the transcriptional events promoting cell survival and proliferation, in which SRF is involved, must first be inactivated