Exact exchange-correlation potential of a ionic Hubbard model with a free surface

We use Lanczos exact diagonalization to compute the exact exchange-correlation (xc) potential of a Hubbard chain with large binding energy ("the bulk") followed by a chain with zero binding energy ("the vacuum"). Several results of density functional theory in the continuum (sometimes controversial) are verified in the lattice. In particular we show explicitly that the fundamental gap is given by the gap in the Kohn-Sham spectrum plus a contribution due to the jump of the xc-potential when a particle is added. The presence of a staggered potential and a nearest-neighbor interaction V allows to simulate a ionic solid. We show that in the ionic regime in the small hopping amplitude limit the xc-contribution to the gap equals V, while in the Mott regime it is determined by the Hubbard U interaction. In addition we show that correlations generates a new potential barrier at the surface

Relative entanglement entropies in 1 + 1-dimensional conformal field theories

We study the relative entanglement entropies of one interval between excited states of a 1+1 dimensional conformal field theory (CFT). To compute the relative entropy S(\u3c11\u2016\u3c10) between two given reduced density matrices \u3c11 and \u3c10 of a quantum field theory, we employ the replica trick which relies on the path integral representation of Tr(\u3c11\u3c1n 1210) and define a set of R\'enyi relative entropies Sn(\u3c11\u2016\u3c10). We compute these quantities for integer values of the parameter n and derive via the replica limit, the relative entropy between excited states generated by primary fields of a free massless bosonic field. In particular, we provide the relative entanglement entropy of the state described by the primary operator i 02\u3d5, both with respect to the ground state and to the state generated by chiral vertex operators. These predictions are tested against exact numerical calculations in the XX spin-chain finding perfect agreement. \ua9 2017, The Author(s)

Shared Genetics of Multiple System Atrophy and Inflammatory Bowel Disease

BACKGROUND: Multiple system atrophy (MSA) is a rare neurodegenerative disease characterized by intracellular accumulations of α-synuclein and nerve cell loss in striatonigral and olivopontocerebellar structures. Epidemiological and clinical studies have reported potential involvement of autoimmune mechanisms in MSA pathogenesis. However, genetic etiology of this interaction remains unknown. We aimed to investigate genetic overlap between MSA and 7 autoimmune diseases and to identify shared genetic loci. METHODS: Genome-wide association study summary statistics of MSA and 7 autoimmune diseases were combined in cross-trait conjunctional false discovery rate analysis to explore overlapping genetic background. Expression of selected candidate genes was compared in transgenic MSA mice and wild-type mice. Genetic variability of candidate genes was further investigated using independent whole-exome genotyping data from large cohorts of MSA and autoimmune disease patients and healthy controls. RESULTS: We observed substantial polygenic overlap between MSA and inflammatory bowel disease and identified 3 shared genetic loci with leading variants upstream of the DENND1B and RSP04 genes, and in intron of the C7 gene. Further, the C7 gene showed significantly dysregulated expression in the degenerating midbrain of transgenic MSA mice compared with wild-type mice and had elevated burden of protein-coding variants in independent MSA and inflammatory bowel disease cohorts. CONCLUSION: Our study provides evidence of shared genetic etiology between MSA and inflammatory bowel disease with an important role of the C7 gene in both phenotypes, with the implication of immune and gut dysfunction in MSA pathophysiology. © 2020 The Authors. Movement Disorders published by Wiley Periodicals LLC. on behalf of International Parkinson and Movement Disorder Society

Regulation of Heterochromatin Assembly on Unpaired Chromosomes during Caenorhabditis elegans Meiosis by Components of a Small RNA-Mediated Pathway

Many organisms have a mechanism for down regulating the expression of non-synapsed chromosomes and chromosomal regions during meiosis. This phenomenon is thought to function in genome defense. During early meiosis in Caenorhabditis elegans, unpaired chromosomes (e.g., the male X chromosome) become enriched for a modification associated with heterochromatin and transcriptional repression, dimethylation of histone H3 on lysine 9 (H3K9me2). This enrichment requires activity of the cellular RNA-directed RNA polymerase, EGO-1. Here we use genetic mutation, RNA interference, immunofluorescence microscopy, fluorescence in situ hybridization, and molecular cloning methods to identify and analyze three additional regulators of meiotic H3K9me2 distribution: CSR-1 (a Piwi/PAZ/Argonaute protein), EKL-1 (a Tudor domain protein), and DRH-3 (a DEAH/D-box helicase). In csr-1, ekl-1, and drh-3 mutant males, we observed a reduction in H3K9me2 accumulation on the unpaired X chromosome and an increase in H3K9me2 accumulation on paired autosomes relative to controls. We observed a similar shift in H3K9me2 pattern in hermaphrodites that carry unpaired chromosomes. Based on several assays, we conclude that ectopic H3K9me2 accumulates on paired and synapsed chromosomes in these mutants. We propose alternative models for how a small RNA-mediated pathway may regulate H3K9me2 accumulation during meiosis. We also describe the germline phenotypes of csr-1, ekl-1, and drh-3 mutants. Our genetic data suggest that these factors, together with EGO-1, participate in a regulatory network to promote diverse aspects of development

Visualization of C. elegans transgenic arrays by GFP

BACKGROUND: Targeting the green fluorescent protein (GFP) via the E. coli lac repressor (LacI) to a specific DNA sequence, the lac operator (lacO), allows visualization of chromosomes in yeast and mammalian cells. In principle this method of visualization could be used for genetic mosaic analysis, which requires cell-autonomous markers that can be scored easily and at single cell resolution. The C. elegans lin-3 gene encodes an epidermal growth factor family (EGF) growth factor. lin-3 is expressed in the gonadal anchor cell and acts through LET-23 (transmembrane protein tyrosine kinase and ortholog of EGF receptor) to signal the vulval precursor cells to generate vulval tissue. lin-3 is expressed in the vulval cells later, and recent evidence raises the possibility that lin-3 acts in the vulval cells as a relay signal during vulval induction. It is thus of interest to test the site of action of lin-3 by mosaic analysis. RESULTS: We visualized transgenes in living C. elegans by targeting the green fluorescent protein (GFP) via the E. coli lac repressor (LacI) to a specific 256 sequence repeat of the lac operator (lacO) incorporated into transgenes. We engineered animals to express a nuclear-localized GFP-LacI fusion protein. C. elegans cells having a lacO transgene result in nuclear-localized bright spots (i.e., GFP-LacI bound to lacO). Cells with diffuse nuclear fluorescence correspond to unbound nuclear localized GFP-LacI. We detected chromosomes in living animals by chromosomally integrating the array of the lacO repeat sequence and visualizing the integrated transgene with GFP-LacI. This detection system can be applied to determine polyploidy as well as investigating chromosome segregation. To assess the GFP-LacI•lacO system as a marker for mosaic analysis, we conducted genetic mosaic analysis of the epidermal growth factor lin-3, expressed in the anchor cell. We establish that lin-3 acts in the anchor cell to induce vulva development, demonstrating this method's utility in detecting the presence of a transgene. CONCLUSION: The GFP-LacI•lacO transgene detection system works in C. elegans for visualization of chromosomes and extrachromosomal transgenes. It can be used as a marker for genetic mosaic analysis. The lacO repeat sequence as an extrachromosomal array becomes a valuable technique allowing rapid, accurate determination of spontaneous loss of the array, thereby allowing high-resolution mosaic analysis. The lin-3 gene is required in the anchor cell to induce the epidermal vulval precursors cells to undergo vulval development

Progress and prospects toward our understanding of the evolution of dosage compensation

In many eukaryotic organisms, gender is determined by a pair of heteromorphic sex chromosomes. Degeneration of the non-recombining Y chromosome is a general facet of sex chromosome evolution. Selective pressure to restore expression levels of X-linked genes relative to autosomes accompanies Y-chromosome degeneration, thus driving the evolution of dosage compensation mechanisms. This review focuses on evolutionary aspects of dosage compensation, in light of recent advances in comparative and functional genomics that have substantially increased our understanding of the molecular mechanisms of dosage compensation and how it evolved. We review processes involved in sex chromosome evolution, and discuss the dynamic interaction between Y degeneration and the acquisition of dosage compensation. We compare mechanisms of dosage compensation and the origin of dosage compensation genes between different taxa and comment on sex chromosomes that apparently lack compensation mechanisms. Finally, we discuss how dosage compensation systems can also influence the evolution of well-established sex chromosomes

Towards the fast scrambling conjecture

Many proposed quantum mechanical models of black holes include highly nonlocal interactions. The time required for thermalization to occur in such models should reflect the relaxation times associated with classical black holes in general relativity. Moreover, the time required for a particularly strong form of thermalization to occur, sometimes known as scrambling, determines the time scale on which black holes should start to release information. It has been conjectured that black holes scramble in a time logarithmic in their entropy, and that no system in nature can scramble faster. In this article, we address the conjecture from two directions. First, we exhibit two examples of systems that do indeed scramble in logarithmic time: Brownian quantum circuits and the antiferromagnetic Ising model on a sparse random graph. Unfortunately, both fail to be truly ideal fast scramblers for reasons we discuss. Second, we use Lieb-Robinson techniques to prove a logarithmic lower bound on the scrambling time of systems with finite norm terms in their Hamiltonian. The bound holds in spite of any nonlocal structure in the Hamiltonian, which might permit every degree of freedom to interact directly with every other one.Comment: 34 pages. v2: typo correcte

The C. elegans H3K27 Demethylase UTX-1 Is Essential for Normal Development, Independent of Its Enzymatic Activity

Epigenetic modifications influence gene expression and provide a unique mechanism for fine-tuning cellular differentiation and development in multicellular organisms. Here we report on the biological functions of UTX-1, the Caenorhabditis elegans homologue of mammalian UTX, a histone demethylase specific for H3K27me2/3. We demonstrate that utx-1 is an essential gene that is required for correct embryonic and postembryonic development. Consistent with its homology to UTX, UTX-1 regulates global levels of H3K27me2/3 in C. elegans. Surprisingly, we found that the catalytic activity is not required for the developmental function of this protein. Biochemical analysis identified UTX-1 as a component of a complex that includes SET-16(MLL), and genetic analysis indicates that the defects associated with loss of UTX-1 are likely mediated by compromised SET-16/UTX-1 complex activity. Taken together, these results demonstrate that UTX-1 is required for many aspects of nematode development; but, unexpectedly, this function is independent of its enzymatic activity

Restricting Dosage Compensation Complex Binding to the X Chromosomes by H2A.Z/HTZ-1

Dosage compensation ensures similar levels of X-linked gene products in males (XY or XO) and females (XX), despite their different numbers of X chromosomes. In mammals, flies, and worms, dosage compensation is mediated by a specialized machinery that localizes to one or both of the X chromosomes in one sex resulting in a change in gene expression from the affected X chromosome(s). In mammals and flies, dosage compensation is associated with specific histone posttranslational modifications and replacement with variant histones. Until now, no specific histone modifications or histone variants have been implicated in Caenorhabditis elegans dosage compensation. Taking a candidate approach, we have looked at specific histone modifications and variants on the C. elegans dosage compensated X chromosomes. Using RNAi-based assays, we show that reducing levels of the histone H2A variant, H2A.Z (HTZ-1 in C. elegans), leads to partial disruption of dosage compensation. By immunofluorescence, we have observed that HTZ-1 is under-represented on the dosage compensated X chromosomes, but not on the non-dosage compensated male X chromosome. We find that reduction of HTZ-1 levels by RNA interference (RNAi) and mutation results in only a very modest change in dosage compensation complex protein levels. However, in these animals, the X chromosome–specific localization of the complex is partially disrupted, with some nuclei displaying DCC localization beyond the X chromosome territory. We propose a model in which HTZ-1, directly or indirectly, serves to restrict the dosage compensation complex to the X chromosome by acting as or regulating the activity of an autosomal repellant

The Germinal Center Kinase GCK-1 Is a Negative Regulator of MAP Kinase Activation and Apoptosis in the C. elegans Germline

The germinal center kinases (GCK) constitute a large, highly conserved family of proteins that has been implicated in a wide variety of cellular processes including cell growth and proliferation, polarity, migration, and stress responses. Although diverse, these functions have been attributed to an evolutionarily conserved role for GCKs in the activation of ERK, JNK, and p38 MAP kinase pathways. In addition, multiple GCKs from different species promote apoptotic cell death. In contrast to these paradigms, we found that a C. elegans GCK, GCK-1, functions to inhibit MAP kinase activation and apoptosis in the C. elegans germline. In the absence of GCK-1, a specific MAP kinase isoform is ectopically activated and oocytes undergo abnormal development. Moreover, GCK-1- deficient animals display a significant increase in germ cell death. Our results suggest that individual germinal center kinases act in mechanistically distinct ways and that these functions are likely to depend on organ- and developmental-specific contexts