Exact Inverse Scattering Theory

The concepts of reference wave slowness (reciprocal of velocity) and an associated free reference space Green\u27s function slowness spectrum are introduced. A modified Kirchoff surface integral, containing only the imaginary part of this free reference space Green\u27s function slowness spectrum, is formulated, yielding an integral equation for the unknown fields and sources in the interior of a closed surface on which the (remotely sensed) fields are known. A well-posed, analytic closed form solution of this integral equation is obtained

HIGHER-ORDER REGULARITY FOR THE SOLUTIONS OF SOME DEGENERATE QUASI-LINEAR ELLIPTIC-EQUATIONS IN THE PLANE

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The stability for the Cauchy problem for elliptic equations

We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse boundary value problems modeled by elliptic equations. We provide essentially optimal stability results, in wide generality and under substantially minimal assumptions. As a general scheme in our arguments, we show that all such stability results can be derived by the use of a single building brick, the three-spheres inequality.Comment: 57 pages, review articl

Calcium Ions Promote Formation of Amyloid β-Peptide (1–40) Oligomers Causally Implicated in Neuronal Toxicity of Alzheimer's Disease

Amyloid β-peptide (Aβ) is directly linked to Alzheimer's disease (AD). In its monomeric form, Aβ aggregates to produce fibrils and a range of oligomers, the latter being the most neurotoxic. Dysregulation of Ca2+ homeostasis in aging brains and in neurodegenerative disorders plays a crucial role in numerous processes and contributes to cell dysfunction and death. Here we postulated that calcium may enable or accelerate the aggregation of Aβ. We compared the aggregation pattern of Aβ(1–40) and that of Aβ(1–40)E22G, an amyloid peptide carrying the Arctic mutation that causes early onset of the disease. We found that in the presence of Ca2+, Aβ(1–40) preferentially formed oligomers similar to those formed by Aβ(1–40)E22G with or without added Ca2+, whereas in the absence of added Ca2+ the Aβ(1–40) aggregated to form fibrils. Morphological similarities of the oligomers were confirmed by contact mode atomic force microscopy imaging. The distribution of oligomeric and fibrillar species in different samples was detected by gel electrophoresis and Western blot analysis, the results of which were further supported by thioflavin T fluorescence experiments. In the samples without Ca2+, Fourier transform infrared spectroscopy revealed conversion of oligomers from an anti-parallel β-sheet to the parallel β-sheet conformation characteristic of fibrils. Overall, these results led us to conclude that calcium ions stimulate the formation of oligomers of Aβ(1–40), that have been implicated in the pathogenesis of AD

Oral and Fecal Campylobacter concisus Strains Perturb Barrier Function by Apoptosis Induction in HT-29/B6 Intestinal Epithelial Cells

Campylobacter concisus infections of the gastrointestinal tract can be accompanied by diarrhea and inflammation, whereas colonization of the human oral cavity might have a commensal nature. We focus on the pathophysiology of C. concisus and the effects of different clinical oral and fecal C. concisus strains on human HT-29/B6 colon cells. Six oral and eight fecal strains of C. concisus were isolated. Mucus-producing HT-29/B6 epithelial monolayers were infected with the C. concisus strains. Transepithelial electrical resistance (Rt) and tracer fluxes of different molecule size were measured in Ussing chambers. Tight junction (TJ) protein expression was determined by Western blotting, and subcellular TJ distribution was analyzed by confocal laser-scanning microscopy. Apoptosis induction was examined by TUNEL-staining and Western blot of caspase-3 activation. All strains invaded confluent HT-29/B6 cells and impaired epithelial barrier function, characterized by a time- and dose-dependent decrease in Rt either after infection from the apical side but even more from the basolateral compartment. TJ protein expression changes were sparse, only in apoptotic areas of infected monolayers TJ proteins were redistributed. Solely the barrier-forming TJ protein claudin-5 showed a reduced expression level to 66±8% (P<0.05), by expression regulation from the gene. Concomitantly, Lactate dehydrogenase release was elevated to 3.1±0.3% versus 0.7±0.1% in control (P<0.001), suggesting cytotoxic effects. Furthermore, oral and fecal C. concisus strains elevated apoptotic events to 5-fold. C. concisus-infected monolayers revealed an increased permeability for 332 Da fluorescein (1.74±0.13 vs. 0.56±0.17 10−6 cm/s in control, P<0.05) but showed no difference in permeability for 4 kDa FITC-dextran (FD-4). The same was true in camptothecin-exposed monolayers, where camptothecin was used for apoptosis induction

MAGUKs, scaffolding proteins at cell junctions, are substrates of different proteases during apoptosis

A major feature of apoptotic cell death is gross structural changes, one of which is the loss of cell–cell contacts. The caspases, executioners of apoptosis, were shown to cleave several proteins involved in the formation of cell junctions. The membrane-associated guanylate kinases (MAGUKs), which are typically associated with cell junctions, have a major role in the organization of protein–protein complexes at plasma membranes and are therefore potentially important caspase targets during apoptosis. We report here that MAGUKs are cleaved and/or degraded by executioner caspases, granzyme B and several cysteine cathepsins in vitro. When apoptosis was induced by UV-irradiation and staurosporine in different epithelial cell lines, caspases were found to efficiently cleave MAGUKs in these cell models, as the cleavages could be prevented by a pan-caspase inhibitor N-benzyloxycarbonyl-Val-Ala-Asp(OMe)fluoromethylketone. Using a selective lysosomal disrupting agent -leucyl--leucine methyl ester, which induces apoptosis through the lysosomal pathway, it was further shown that MAGUKs are also cleaved by the cathepsins in HaCaT and CaCo-2 cells. Immunohistological data showed rapid loss of MAGUKs at the sites of cell–cell contacts, preceding actual cell detachment, suggesting that cleavage of MAGUKs is an important step in fast and efficient cell detachment