Averages of Fourier coefficients of Siegel modular forms and representation of binary quadratic forms by quadratic forms in four variables

Let $-d$ be a a negative discriminant and let $T$ vary over a set of representatives of the integral equivalence classes of integral binary quadratic forms of discriminant $-d$. We prove an asymptotic formula for $d \to \infty$ for the average over $T$ of the number of representations of $T$ by an integral positive definite quaternary quadratic form and obtain results on averages of Fourier coefficients of linear combinations of Siegel theta series. We also find an asymptotic bound from below on the number of binary forms of fixed discriminant $-d$ which are represented by a given quaternary form. In particular, we can show that for growing $d$ a positive proportion of the binary quadratic forms of discriminant $-d$ is represented by the given quaternary quadratic form.Comment: v5: Some typos correcte

Crystal structure, site selectivity, and electronic structure of layered chalcogenide LaOBiPbS3

We have investigated the crystal structure of LaOBiPbS3 using neutron diffraction and synchrotron X-ray diffraction. From structural refinements, we found that the two metal sites, occupied by Bi and Pb, were differently surrounded by the sulfur atoms. Calculated bond valence sum suggested that one metal site was nearly trivalent and the other was nearly divalent. Neutron diffraction also revealed site selectivity of Bi and Pb in the LaOBiPbS3 structure. These results suggested that the crystal structure of LaOBiPbS3 can be regarded as alternate stacks of the rock-salt-type Pb-rich sulfide layers and the LaOBiS2-type Bi-rich layers. From band calculations for an ideal (LaOBiS2)(PbS) system, we found that the S bands of the PbS layer were hybridized with the Bi bands of the BiS plane at around the Fermi energy, which resulted in the electronic characteristics different from that of LaOBiS2. Stacking the rock-salt type sulfide (chalcogenide) layers and the BiS2-based layered structure could be a new strategy to exploration of new BiS2-based layered compounds, exotic two-dimensional electronic states, or novel functionality.Comment: 11 pages, 5 figure

Sturmian bases for two-electron systems in hyperspherical coordinates

We give a detailed account of an $\it{ab}$ $\it{initio}$ spectral approach for the calculation of energy spectra of two active electron atoms in a system of hyperspherical coordinates. In this system of coordinates, the Hamiltonian has the same structure as the one of atomic hydrogen with the Coulomb potential expressed in terms of a hyperradius and the nuclear charge replaced by an angle dependent effective charge. The simplest spectral approach consists in expanding the hyperangular wave function in a basis of hyperspherical harmonics. This expansion however, is known to be very slowly converging. Instead, we introduce new hyperangular sturmian functions. These functions do not have an analytical expression but they treat the first term of the multipole expansion of the electron-electron interaction potential, namely the radial electron correlation, exactly. The properties of these new functions are discussed in detail. For the basis functions of the hyperradius, several choices are possible. In the present case, we use Coulomb sturmian functions of half integer angular momentum. We show that, in the case of H$^-$, the accuracy of the energy and the width of the resonance states obtained through a single diagonalization of the Hamiltonian, is comparable to the values given by state-of-the-art methods while using a much smaller basis set. In addition, we show that precise values of the electric-dipole oscillator strengths for $S\rightarrow P$ transitions in helium are obtained thereby confirming the accuracy of the bound state wave functions generated with the present method.Comment: 28 pages, 4 figure

Genetic Heterogeneity of Hepatitis C Virus in Association with Antiviral Therapy Determined by Ultra-Deep Sequencing

The hepatitis C virus (HCV) invariably shows wide heterogeneity in infected patients, referred to as a quasispecies population. Massive amounts of genetic information due to the abundance of HCV variants could be an obstacle to evaluate the viral genetic heterogeneity in detail.Using a newly developed massive-parallel ultra-deep sequencing technique, we investigated the viral genetic heterogeneity in 27 chronic hepatitis C patients receiving peg-interferon (IFN) α2b plus ribavirin therapy.Ultra-deep sequencing determined a total of more than 10 million nucleotides of the HCV genome, corresponding to a mean of more than 1000 clones in each specimen, and unveiled extremely high genetic heterogeneity in the genotype 1b HCV population. There was no significant difference in the level of viral complexity between immediate virologic responders and non-responders at baseline (p = 0.39). Immediate virologic responders (n = 8) showed a significant reduction in the genetic complexity spanning all the viral genetic regions at the early phase of IFN administration (p = 0.037). In contrast, non-virologic responders (n = 8) showed no significant changes in the level of viral quasispecies (p = 0.12), indicating that very few viral clones are sensitive to IFN treatment. We also demonstrated that clones resistant to direct-acting antivirals for HCV, such as viral protease and polymerase inhibitors, preexist with various abundances in all 27 treatment-naïve patients, suggesting the risk of the development of drug resistance against these agents.Use of the ultra-deep sequencing technology revealed massive genetic heterogeneity of HCV, which has important implications regarding the treatment response and outcome of antiviral therapy

Characterization of antibody-mediated neutralization directed against the hypervariable region 1 of hepatitis C virus E2 glycoprotein

The hypervariable region 1 (HVR1) comprising the first 27 aa of E2 glycoprotein is a target for neutralizing antibodies against hepatitis C virus (HCV), but the mechanisms of this neutralization in the cell-culture-infectious genotype 2a strain JFH1 HCV virus (HCVcc) system are unknown. Two rabbit polyclonal sera, R1020 and R140, recognizing the HVR1 of the genotype 1a isolates H77c and Glasgow (Gla), respectively, and a Gla HVR1-specific mouse mAb AP213 have been described previously. However, attempts to generate of antibodies to the JFH1 HVR1 were unsuccessful. Therefore, this study produced chimeric JFH1 HCVcc viruses harbouring the H77c or Gla HVR1 to assess the reactivity of antibodies to this region and their effects on virus infectivity. The inter-genotypic HVR1 swap did not significantly affect virus infectivity. The genotype 1a HVR1-specific antibodies neutralized chimeric viruses in an isolate-dependent manner, underlining the role of HVR1 in HCV infection. The neutralizing antibodies reacted mainly with the C-terminal portion of HVR1, and detailed mapping identified A17, F20 and Q21 in the Gla HVR1 sequence and T21 (and possibly L20) in the corresponding H77c sequence as key epitope residues for AP213 and R140, and R1020, respectively. Importantly, none of the antibodies inhibited in vitro binding of viral envelope glycoproteins to the best-characterized HCV receptor, CD81, or to the glycosaminoglycan attachment factors. However, the HVR1 antibodies were capable of post-attachment neutralization. Overall, this study emphasizes the role of HVR1 in HCVcc entry and provides new tools to study this region further in the context of complete virions

Identification of tuberculosis-associated proteins in whole blood supernatant

<p>Abstract</p> <p>Background</p> <p>Biological parameters are useful tools for understanding and monitoring complicated disease processes. In this study, we attempted to identify proteins associated with active pulmonary tuberculosis (TB) using a proteomic approach.</p> <p>Methods</p> <p>To assess TB-associated changes in the composition of human proteins, whole blood supernatants were collected from patients with active TB and healthy control subjects. Two-dimensional difference gel electrophoresis (2D-DIGE) was performed to analyze proteins with high molecular weights (approximately >20 kDa). Baseline protein levels were initially compared between patients with active TB and control subjects. Possible changes of protein patterns in active TB were also compared <it>ex vivo </it>between whole blood samples incubated with <it>Mycobacterium tuberculosis </it>(<it>Mtb</it>)-specific antigens (stimulated condition) and under unstimulated conditions. Immunoblot and enzyme-linked immunosorbent assays (ELISA) were performed to confirm differences in identified proteins.</p> <p>Results</p> <p>Under the baseline condition, we found that the levels of retinol-binding protein 4 (RBP4), fetuin-A (also called α-HS-glycoprotein), and vitamin D-binding protein differed between patients with active TB and control subjects on 2D gels. Immunoblotting results confirmed differential expression of RBP4 and fetuin-A. ELISA results further confirmed significantly lower levels of these two proteins in samples from patients with active TB than in control subjects (<it>P </it>< 0.0001). <it>Mtb</it>-specific antigen stimulation <it>ex vivo </it>altered clusterin expression in whole blood samples collected from patients with active TB.</p> <p>Conclusions</p> <p>We identified TB-associated proteins in whole blood supernatants. The dynamics of protein expression during disease progression may improve our understanding of the pathogenesis of TB.</p

RAPID: Resource of Asian Primary Immunodeficiency Diseases

Availability of a freely accessible, dynamic and integrated database for primary immunodeficiency diseases (PID) is important both for researchers as well as clinicians. To build a PID informational platform and also as a part of action to initiate a network of PID research in Asia, we have constructed a web-based compendium of molecular alterations in PID, named Resource of Asian Primary Immunodeficiency Diseases (RAPID), which is available as a worldwide web resource at http://rapid.rcai.riken.jp/. It hosts information on sequence variations and expression at the mRNA and protein levels of all genes reported to be involved in PID patients. The main objective of this database is to provide detailed information pertaining to genes and proteins involved in primary immunodeficiency diseases along with other relevant information about protein–protein interactions, mouse studies and microarray gene-expression profiles in various organs and cells of the immune system. RAPID also hosts a tool, mutation viewer, to predict deleterious and novel mutations and also to obtain mutation-based 3D structures for PID genes. Thus, information contained in this database should help physicians and other biomedical investigators to further investigate the role of these molecules in PID