Signal and Noise in Correlation Matrix

Using random matrix technique we determine an exact relation between the eigenvalue spectrum of the covariance matrix and of its estimator. This relation can be used in practice to compute eigenvalue invariants of the covariance (correlation) matrix. Results can be applied in various problems where one experimentally estimates correlations in a system with many degrees of freedom, like in statistical physics, lattice measurements of field theory, genetics, quantitative finance and other applications of multivariate statistics.Comment: 17 pages, 3 figures, corrected typos, revtex style changed to elsar

ℤ 2 × ℤ 2-Cordial Cycle-Free Hypergraphs

Hovey introduced A-cordial labelings as a generalization of cordial and harmonious labelings [7]. If A is an Abelian group, then a labeling f: V(G) → A of the vertices of some graph G induces an edge labeling on G; the edge uv receives the label f(u)+f(v). A graph G is A-cordial if there is a vertex-labeling such that (1) the vertex label classes differ in size by at most one and (2) the induced edge label classes differ in size by at most one. The problem of A-cordial labelings of graphs can be naturally extended for hypergraphs. It was shown that not every 2-uniform hypertree (i.e., tree) admits a ℤ 2 × ℤ 2-cordial labeling [8]. The situation changes if we consider p-uniform hypertrees for a bigger p. We prove that a p-uniform hypertree is ℤ 2 × ℤ 2-cordial for any p > 2, and so is every path hypergraph in which all edges have size at least 3. The property is not valid universally in the class of hypergraphs of maximum degree 1, for which we provide a necessary and sufficient condition. © Sylwia Cichacz et al., published by Sciendo 2019

The permeability of reconstituted nuclear pores provides direct evidence for the selective phase model.

Nuclear pore complexes (NPCs) maintain a permeability barrier between the nucleus and the cytoplasm through FG-repeat-containing nucleoporins (Nups). We previously proposed a “selective phase model” in which the FG repeats interact with one another to form a sieve-like barrier that can be locally disrupted by the binding of nuclear transport receptors (NTRs), but not by inert macromolecules, allowing selective passage of NTRs and associated cargo. Here, we provide direct evidence for this model in a physiological context. By using NPCs reconstituted from Xenopus laevis egg extracts, we show that Nup98 is essential for maintaining the permeability barrier. Specifically, the multivalent cohesion between FG repeats is required, including cohesive FG repeats close to the anchorage point to the NPC scaffold. Our data exclude alternative models that are based solely on an interaction between the FG repeats and NTRs and indicate that the barrier is formed by a sieve-like FG hydrogel

Acetylation of importin-α nuclear import factors by CBP/p300.

Histone acetylases were originally identified because of their ability to acetylate histone substrates 1, 2 and 3. Acetylases can also target other proteins such as transcription factors 4, 5, 6 and 7. We asked whether the acetylase CREB-binding protein (CBP) could acetylate proteins not directly involved in transcription. A large panel of proteins, involved in a variety of cellular processes, were tested as substrates for recombinant CBP. This screen identified two proteins involved in nuclear import, Rch1 (human importin-α) and importin-α7, as targets for CBP. The acetylation site within Rch1 was mapped to a single residue, Lys22. By comparing the context of Lys22 with the sequences of other known substrates of CBP and the closely related acetylase p300, we identified G/SK (in the single-letter amino acid code) as a consensus acetylation motif. Mutagenesis of the glycine, as well as the lysine, severely impaired Rch1 acetylation, supporting the view that GK is part of a recognition motif for acetylation by CBP/p300. Using an antibody raised against an acetylated Rch1 peptide, we show that Rch1 was acetylated at Lys22 in vivo and that CBP or p300 could mediate this reaction. Lys22 lies within the binding site for a second nuclear import factor, importin-β. Acetylation of Lys22 promoted interaction with importin-β in vitro. Collectively, these results demonstrate that acetylation is not unique to proteins involved in transcription. Acetylation may regulate a variety of biological processes, including nuclear import

Properties of dynamical fractal geometries in the model of Causal Dynamical Triangulations

We investigate the geometry of a quantum universe with the topology of the four-torus. The study of non-contractible geodesic loops reveals that a typical quantum geometry consists of a small semi-classical toroidal bulk part, dressed with many outgrowths, which contain most of the four-volume and which have almost spherical topologies, but nevertheless are quite fractal.Comment: 16 pages, 16 figure

Nuclear import of HIV‐1 intracellular reverse transcription complexes is mediated by importin 7.

Human immunodeficiency virus type 1 (HIV‐1), like other lentiviruses, can infect non‐dividing cells. This property depends on the active nuclear import of its intracellular reverse transcription complex (RTC). We have studied nuclear import of purified HIV‐1 RTCs in primary macrophages and found that importin 7, an import receptor for ribosomal proteins and histone H1, is involved in the process. Nuclear import of RTCs requires, in addition, energy and the com ponents of the Ran system. Depletion of importin 7 from cultured cells by small interfering RNA inhibits HIV‐1 infection. These results provide a new insight into the molecular mechanism for HIV‐1 nuclear import and reveal potential targets for therapeutic intervention

The Identification of Proteins in the Proximity of Signal-Anchor Sequences during Their Targeting to and Insertion into the Membrane of the ER

Using a photocross-linking approach we have investigated the cytosolic and membrane components involved in the targeting and insertion of signalanchor proteins into the membrane of the ER. The nascent chains of both type I and type II signal-anchor proteins can be cross-linked to the 54-kD subunit of the signal recognition particle. Upon addition of rough microsomes the type I and type II signal-anchor proteins interact with a number of components. Both types of protein interact with an integral membrane protein, the signal sequence receptor, previously identified by its proximity to preprolactin during its translocation (Wiedmann, M., T. V. Kurzchalia, E. Hartmann, and T. A. Rapoport. 1987. Nature lLond.] 328: 830-833). Three proteins, previously unidentified, were found to be cross-linked to the nascent chains of the signal-anchor proteins. Among them was a 37-kD protein that was found to be the main component interacting with the type I SA protein used. These proteins were not seen in the absence of membranes suggesting they are components of the ER. The ability of the nascent chains to be cross-linked to these identiffed proteins was shown to be abolished by prior treatment with agents known to disrupt translocation intermediates or ribosomes. We propose that the newly identified proteins function either in the membrane insertion of only a subset of proteins or only at a specific stage of insertion

Barrier-properties of Nup98 FG phases ruled by FG motif identity and inter-FG spacer length

Nup98 FG repeat domains comprise hydrophobic FG motifs linked through uncharged spacers. FG motifs capture nuclear transport receptors (NTRs) during nuclear pore complex (NPC) passage, confer inter-repeat cohesion, and condense the domains into a selective phase with NPC-typical barrier properties. We found that shortening inter-FG spacers enhances cohesion, increases phase density, and tightens such barrier – consistent with a sieve-like phase. Phase separation tolerated mutations of Nup98-typical GLFG motifs, provided the domain-hydrophobicity remained preserved. NTR-entry, however, was sensitive to (certain) deviations from canonical FG motifs, suggesting a co-evolutionary adaptation. Unexpectedly, we found that arginines promote efficient FG-phase entry also by means other than cation-π interactions. Although incompatible with NTR·cargo complexes, a YG phase displayed remarkable transport selectivity, particularly for evolved GFPNTR-variants. GLFG to FSFG mutations made the FG phase hypercohesive, precluding NTR-entry. Longer spacers relieved this hypercohesive phenotype. The antagonism between cohesion and NTR·FG interactions appears thus key to transport selectivity