On the shape of spectra for non-self-adjoint periodic Schr\"odinger operators

The spectra of the Schr\"odinger operators with periodic potentials are studied. When the potential is real and periodic, the spectrum consists of at most countably many line segments (energy bands) on the real line, while when the potential is complex and periodic, the spectrum consists of at most countably many analytic arcs in the complex plane. In some recent papers, such operators with complex $\mathcal{PT}$-symmetric periodic potentials are studied. In particular, the authors argued that some energy bands would appear and disappear under perturbations. Here, we show that appearance and disappearance of such energy bands imply existence of nonreal spectra. This is a consequence of a more general result, describing the local shape of the spectrum.Comment: 5 pages, 2 figure

Biorthogonal Quantum Systems

Models of PT symmetric quantum mechanics provide examples of biorthogonal quantum systems. The latter incorporporate all the structure of PT symmetric models, and allow for generalizations, especially in situations where the PT construction of the dual space fails. The formalism is illustrated by a few exact results for models of the form H=(p+\nu)^2+\sum_{k>0}\mu_{k}exp(ikx). In some non-trivial cases, equivalent hermitian theories are obtained and shown to be very simple: They are just free (chiral) particles. Field theory extensions are briefly considered.Comment: 34 pages, 5 eps figures; references added and other changes made to conform to journal versio

The Rhodococcus equi virulence protein VapA disrupts endolysosome function and stimulates lysosome biogenesis

Rhodococcus equi (R. equi) is an important pulmonary pathogen in foals that often leads to the death of the horse. The bacterium harbors a virulence plasmid that encodes numerous virulence-associated proteins (Vaps) including VapA that is essential for intracellular survival inside macrophages. However, little is known about the precise function of VapA. Here, we demonstrate that VapA causes perturbation to late endocytic organelles with swollen endolysosome organelles having reduced Cathepsin B activity and an accumulation of LBPA, LC3 and Rab7. The data are indicative of a loss of endolysosomal function, which leads cells to upregulate lysosome biogenesis to compensate for the loss of functional endolysosomes. Although there is a high degree of homology of the core region of VapA to other Vap proteins, only the highly conserved core region of VapA, and not VapD of VapG, gives the observed effects on endolysosomes. This is the first demonstration of how VapA works and implies that VapA aids R. equi survival by reducing the impact of lysosomes on phagocytosed bacteria

On the structure of eigenfunctions corresponding to embedded eigenvalues of locally perturbed periodic graph operators

The article is devoted to the following question. Consider a periodic self-adjoint difference (differential) operator on a graph (quantum graph) G with a co-compact free action of the integer lattice Z^n. It is known that a local perturbation of the operator might embed an eigenvalue into the continuous spectrum (a feature uncommon for periodic elliptic operators of second order). In all known constructions of such examples, the corresponding eigenfunction is compactly supported. One wonders whether this must always be the case. The paper answers this question affirmatively. What is more surprising, one can estimate that the eigenmode must be localized not far away from the perturbation (in a neighborhood of the perturbation's support, the width of the neighborhood determined by the unperturbed operator only). The validity of this result requires the condition of irreducibility of the Fermi (Floquet) surface of the periodic operator, which is expected to be satisfied for instance for periodic Schroedinger operators.Comment: Submitted for publicatio

Metallothionein in human oesophagus, Barrett's epithelium and adenocarcinoma

The potential of the metal-binding protein, metallothionein, in assessing the progression of normal oesophagus through Barrett's to adenocarcinoma was investigated. Metallothionein was quantitatively determined in resected tissues from patients undergoing oesophagectomy for high grade dysplasia/adenocarcinoma and in biopsies from patients with Barrett's syndrome. In 10 cancer patients, metallothionein concentrations in adenocarcinoma were not significantly different from normal oesophagus, although six had elevated metallothionein concentrations in the metaplastic tissue bordering the adenocarcinoma. In 17 out of 20 non-cancer patients with Barrett's epithelium, metallothionein was significantly increased by 108% (P<0.004). There was no association between the metallothionein levels in Barrett's epithelium and the presence of inflammatory cells, metaplasia or dysplasia. Metallothionein is a marker of progression from normal to Barrett's epithelium but is not increased in oesophageal adenocarcinoma

Adipose atrophy in cancer cachexia:morphologic and molecular analysis of adipose tissue in tumour-bearing mice

Extensive loss of adipose tissue is a hallmark of cancer cachexia but the cellular and molecular basis remains unclear. This study has examined morphologic and molecular characteristics of white adipose tissue in mice bearing a cachexia-inducing tumour, MAC16. Adipose tissue from tumour-bearing mice contained shrunken adipocytes that were heterogeneous in size. Increased fibrosis was evident by strong collagen-fibril staining in the tissue matrix. Ultrastructure of 'slimmed' adipocytes revealed severe delipidation and modifications in cell membrane conformation. There were major reductions in mRNA levels of adipogenic transcription factors including CCAAT/enhancer binding protein alpha (C/EBPα), CCAAT/enhancer binding protein beta, peroxisome proliferator-activated receptor gamma, and sterol regulatory element binding protein-1c (SREBP-1c) in adipose tissue, which was accompanied by reduced protein content of C/EBPα and SREBP-1. mRNA levels of SREBP-1c targets, fatty acid synthase, acetyl CoA carboxylase, stearoyl CoA desaturase 1 and glycerol-3-phosphate acyl transferase, also fell as did glucose transporter-4 and leptin. In contrast, mRNA levels of peroxisome proliferators-activated receptor gamma coactivator-1alpha and uncoupling protein-2 were increased in white fat of tumour-bearing mice. These results suggest that the tumour-induced impairment in the formation and lipid storing capacity of adipose tissue occurs in mice with cancer cachexia. © 2006 Cancer Research UK