Zero area singularities in general relativity and inverse mean curvature flow

First we restate the definition of a Zero Area Singularity, recently introduced by H. Bray. We then consider several definitions of mass for these singularities. We use the Inverse Mean Curvature Flow to prove some new results about the mass of a singularity, the ADM mass of the manifold, and the capacity of the singularity.Comment: 13 page

Available potential energy for mode eddies

Also published as: Journal of Physical Oceanography 11 (1981): 30-47Available potential energy (APE) is defined as the difference between total potential plus internal energy of a fluid in a gravity field and a corresponding reference field in which the fluid is redistributed (leveled) adiabatically to have constant stably-stratified densities along geopotential surfaces. Potential energy changes result from local shifts of flu id mass relative to geopotential surfaces that are accompanied by local changes of enthalpy and internal energy and global shifts of mass (because volumes of fluid elements are not conserved) that do not change enthalpy or internal energy. The potential energy changes are examined separately by computing available gravitational potential energy (GPE) per unit mass and total GPE (TGPE) per unit area. A technique for estimating GPE in the ocean is developed by introducirtg a reference density field (or an equivalent specific volume anomaly field) that is a function of pressure only and is connected to the observed field by adiabatic vertical displacements. The full empirical equation of state for seawater is used in the computational algorithm. The accuracy of the estimate is limited by the data and sampling and not by the algorithm itself, which can be made as precise as desired. The reference density field defined locally for an ocean region allows redefinition of dynamic height ΔD (potential energy per unit mass) relative to the reference field. TGPE per unit area becomes simply the horizontal average of dynamic height integrated over depth in the region considered. The reference density surfaces provide a precise approximation to material surfaces for tracing conservative variables such as salinity and potential temperature and for estimating vortex stretching between surfaces. The procedure is applied to the MODE density data collected in 1973. For each group of stations within five 2-week time windows (designated Groups A-E) the estimated GPE is compared with the net APE based on the Boussinesq approximation and to the low-frequency kinetic energy measured from moored buoys. Changes of potential energy of the reference field from one time window to the next are large compared with the GPE within each window, indicating the presence of scales larger than the station grid. An analysis of errors has been made to show the sensitivity of the estimates to data accuracy and sampling frequency.Prepared for the Office of Naval Research under Contract N00014-76-C-0197

Schizophrenia genomics: convergence on synaptic development, adult synaptic plasticity, or both?

Large-scale genomic studies of schizophrenia have identified hundreds of genetic loci conferring risk to the disorder. This progress offers an important route towards defining the biological basis of the condition and potentially developing new treatments. In this review, we discuss insights from recent genome-wide association study (GWAS), copy number variant (CNV) and exome sequencing analyses of schizophrenia, together with functional genomics data from the pre- and post-natal brain, in relation to synaptic development and function. These data provide strong support for the view that synaptic dysfunction within glutamatergic and GABAergic neurons of the cerebral cortex, hippocampus and other limbic structures is a central component of schizophrenia pathophysiology. Implicated genes and functional genomic data suggest that disturbances in synaptic connectivity associated with susceptibility to schizophrenia begin in utero but continue throughout development, with some alleles conferring risk to the disorder through direct effects on synaptic function in adulthood. This model implies that novel interventions for schizophrenia could include broad preventative approaches aimed at enhancing synaptic health during development as well as more targeted treatments aimed at correcting synaptic function in affected adults

Enhancer Priming Enables Fast and Sustained Transcriptional Responses to Notch Signaling.

Information from developmental signaling pathways must be accurately decoded to generate transcriptional outcomes. In the case of Notch, the intracellular domain (NICD) transduces the signal directly to the nucleus. How enhancers decipher NICD in the real time of developmental decisions is not known. Using the MS2-MCP system to visualize nascent transcripts in single cells in Drosophila embryos, we reveal how two target enhancers read Notch activity to produce synchronized and sustained profiles of transcription. By manipulating the levels of NICD and altering specific motifs within the enhancers, we uncover two key principles. First, increased NICD levels alter transcription by increasing duration rather than frequency of transcriptional bursts. Second, priming of enhancers by tissue-specific transcription factors is required for NICD to confer synchronized and sustained activity; in their absence, transcription is stochastic and bursty. The dynamic response of an individual enhancer to NICD thus differs depending on the cellular context.Wellcome Trus

Multiple prebiotic metals mediate translation.

Today, Mg2+ is an essential cofactor with diverse structural and functional roles in life's oldest macromolecular machine, the translation system. We tested whether ancient Earth conditions (low O2, high Fe2+, and high Mn2+) can revert the ribosome to a functional ancestral state. First, SHAPE (selective 2'-hydroxyl acylation analyzed by primer extension) was used to compare the effect of Mg2+, Fe2+, and Mn2+ on the tertiary structure of rRNA. Then, we used in vitro translation reactions to test whether Fe2+ or Mn2+ could mediate protein production, and quantified ribosomal metal content. We found that (i) Mg2+, Fe2+, and Mn2+ had strikingly similar effects on rRNA folding; (ii) Fe2+ and Mn2+ can replace Mg2+ as the dominant divalent cation during translation of mRNA to functional protein; and (iii) Fe and Mn associate extensively with the ribosome. Given that the translation system originated and matured when Fe2+ and Mn2+ were abundant, these findings suggest that Fe2+ and Mn2+ played a role in early ribosomal evolution

Pain in malignant pleural mesothelioma: a prospective characterisation study.

INTRODUCTION: Malignant pleural mesothelioma (MPM) is associated with severe pain. The underlying neurobiology of this is complex. The primary aim of this study was to characterize pain in MPM. METHODS: This study was undertaken as part of a trial examining radiotherapy for the treatment of pain in MPM (ISRCTN 10644347). Patients had MPM with associated pain for which radiotherapy was planned and a worst pain score ≥ 4/10. The following assessments were undertaken: clinical neuropathic pain assessment, Brief Pain Inventory (BPI), Leeds Assessment of Neuropathic Symptoms and Signs (LANSS), Short form of the McGill Pain Questionnaire (SF-MPQ), and Quantitative Sensory Testing (QST). The relationship of these characteristics and response to radiotherapy was assessed. Unless stated, medians and interquartile range (IQR) are used. RESULTS: Thirty-seven patients were recruited. Average pain and worst pain was 4 (4-6) and 8 (6-8), respectively. Higher average pain and higher worst pain scores were associated with higher interference scores on the BPI, P < 0.001 and P < 0.0005. Twenty patients (54%) had a clinical diagnosis of neuropathic pain, and of these, only six patients (40%) screened positively for neuropathic pain using the LANSS. Patients with a high LANSS also had higher BPI and SF-MPQs. The presence of neuropathic pain (clinically or by LANSS) did not predict response to radiotherapy, P < 0.05. The SF-MPQ scores were higher in those with abnormal cool sensation on QST (P = 0.016). CONCLUSION: Pain in mesothelioma varies among patients and may have neuropathic components. An adequate pain assessment is necessary to guide the clinician in the appropriate choice of analgesics

Knockdown of the schizophrenia susceptibility gene TCF4 alters gene expression and proliferation of progenitor cells from the developing human neocortex

BACKGROUND: Common variants in the TCF4 gene are among the most robustly supported genetic risk factors for schizophrenia. Rare TCF4 deletions and loss-of-function point mutations cause Pitt-Hopkins syndrome, a developmental disorder associated with severe intellectual disability. METHODS: To explore molecular and cellular mechanisms by which TCF4 perturbation could interfere with human cortical development, we experimentally reduced the endogenous expression of TCF4 in a neural progenitor cell line derived from the developing human cerebral cortex using RNA interference. Effects on genome-wide gene expression were assessed by microarray, followed by Gene Ontology and pathway analysis of differentially expressed genes. We tested for genetic association between the set of differentially expressed genes and schizophrenia using genome-wide association study data from the Psychiatric Genomics Consortium and competitive gene set analysis (MAGMA). Effects on cell proliferation were assessed using high content imaging. RESULTS: Genes that were differentially expressed following TCF4 knockdown were highly enriched for involvement in the cell cycle. There was a nonsignificant trend for genetic association between the differentially expressed gene set and schizophrenia. Consistent with the gene expression data, TCF4 knockdown was associated with reduced proliferation of cortical progenitor cells in vitro. LIMITATIONS: A detailed mechanistic explanation of how TCF4 knockdown alters human neural progenitor cell proliferation is not provided by this study. CONCLUSION: Our data indicate effects of TCF4 perturbation on human cortical progenitor cell proliferation, a process that could contribute to cognitive deficits in individuals with Pitt-Hopkins Syndrome and risk for schizophrenia

Genome-wide significant schizophrenia risk variation on chromosome 10q24 is associated with altered cis-regulation of BORCS7, AS3MT, and NT5C2 in the human brain

Chromosome 10q24.32-q24.33 is one of the most robustly supported risk loci to emerge from genome-wide association studies (GWAS) of schizophrenia. However, extensive linkage disequilibrium makes it difficult to distinguish the actual susceptibility gene(s) at the locus, limiting its value for improving biological understanding of the condition. In the absence of coding changes that can account for the association, risk is likely conferred by altered regulation of one or more genes in the region. We, therefore, used highly sensitive measures of allele-specific expression to assess cis-regulatory effects associated with the two best-supported schizophrenia risk variants (SNP rs11191419 and indel ch10_104957618_I/rs202213518) on the primary positional candidates BORCS7, AS3MT, CNNM2, and NT5C2 in the human brain. Heterozygosity at rs11191419 was associated with increased allelic expression of BORCS7 and AS3MT in the fetal and adult brain, and with reduced allelic expression of NT5C2 in the adult brain. Heterozygosity at ch10_104957618_I was associated with reduced allelic expression of NT5C2 in both the fetal and adult brain. Comparisons between cDNA ratios in heterozygotes and homozygotes for the risk alleles indicated that cis-effects on NT5C2 expression in the adult dorsolateral prefrontal cortex could be largely accounted for by genotype at these two risk variants. While not excluding effects on other genes in the region, this study implicates altered neural expression of BORCS7, AS3MT, and NT5C2 in susceptibility to schizophrenia arising from genetic variation at the chromosome 10q24 locus

Structure of the hexameric HerA ATPase reveals a mechanism of translocation-coupled DNA-end processing in archaea.

The HerA ATPase cooperates with the NurA nuclease and the Mre11-Rad50 complex for the repair of double-strand DNA breaks in thermophilic archaea. Here we extend our structural knowledge of this minimal end-resection apparatus by presenting the first crystal structure of hexameric HerA. The full-length structure visualizes at atomic resolution the N-terminal HerA-ATP synthase domain and a conserved C-terminal extension, which acts as a physical brace between adjacent protomers. The brace also interacts in trans with nucleotide-binding residues of the neighbouring subunit. Our observations support a model in which the coaxial interaction of the HerA ring with the toroidal NurA dimer generates a continuous channel traversing the complex. HerA-driven translocation would propel the DNA towards the narrow annulus of NurA, leading to duplex melting and nucleolytic digestion. This system differs substantially from the bacterial end-resection paradigms. Our findings suggest a novel mode of DNA-end processing by this integrated archaeal helicase-nuclease machine.The SAXS data collection was supported by funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under BioStruct-X (grant agreement N°283570). Research in the N.P.R. laboratory is funded by the Medical Research Council [Career Development Award G0701443]. Research in the L.P. laboratory is funded by a Wellcome Trust Senior Fellowship Award in Basic Biomedical Sciences [grant number 08279/Z/07/Z]. Work in the L.P. and N.P.R. laboratories is also supported by an Isaac Newton Trust Research Grant, and S.M.B. is supported by a BBSRC Doctoral Training Grant.This is the author accepted manuscript. The final version is available from NPG via http://dx.doi.org/10.1038/ncomms650