A class of Schrodinger operators with decaying oscillatory potentials

We discuss Schr\"odinger operators on a half-line with decaying oscillatory potentials, such as products of an almost periodic function and a decaying function. We provide sufficient conditions for preservation of absolutely continuous spectrum and give bounds on the Hausdorff dimension of the singular part of the spectral measure. We also discuss the analogs for orthogonal polynomials on the real line and unit circle.Comment: 18 page

A Mathematical Model of Liver Cell Aggregation In Vitro

The behavior of mammalian cells within three-dimensional structures is an area of intense biological research and underpins the efforts of tissue engineers to regenerate human tissues for clinical applications. In the particular case of hepatocytes (liver cells), the formation of spheroidal multicellular aggregates has been shown to improve cell viability and functionality compared to traditional monolayer culture techniques. We propose a simple mathematical model for the early stages of this aggregation process, when cell clusters form on the surface of the extracellular matrix (ECM) layer on which they are seeded. We focus on interactions between the cells and the viscoelastic ECM substrate. Governing equations for the cells, culture medium, and ECM are derived using the principles of mass and momentum balance. The model is then reduced to a system of four partial differential equations, which are investigated analytically and numerically. The model predicts that provided cells are seeded at a suitable density, aggregates with clearly defined boundaries and a spatially uniform cell density on the interior will form. While the mechanical properties of the ECM do not appear to have a significant effect, strong cell-ECM interactions can inhibit, or possibly prevent, the formation of aggregates. The paper concludes with a discussion of our key findings and suggestions for future work

Signaling via a novel integral plasma membrane pool of a serine/threonine protein kinase PRK1 in mammalian cells

10.1096/fj.04-1876fjeFASEB Journal18141722-1724FAJO

Angiostatin effects on endothelial cells mediated by ceramide and RhoA

Angiostatin is a cleavage product of plasminogen that has anti-angiogenic properties. We investigated whether the effects of angiostatin on endothelial cells are mediated by ceramide, a lipid implicated in endothelial cell signaling. Our results demonstrate that angiostatin produces a transient increase in ceramide that correlates with actin stress fiber reorganization, detachment and death. DNA array expression analysis performed on ceramide-treated human endothelial cells demonstrated induction of certain genes involved in cytoskeleton organization. Specifically, we report that treatment with angiostatin or ceramide results in the activation of RhoA, an important effector of cytoskeletal structure. We also show that treatment of endothelial cells with the antioxidant N-acetylcysteine abrogates morphological changes and cytotoxic effects of treatment with angiostatin or ceramide. These findings support a model in which angiostatin induces a transient rise in ceramide, RhoA activation and free radical production

ag) Isolation and characterization of hepatic stem cells, or "oval cells," from rat livers.

The pace of research on the potential therapeutic uses of liver stem cells or "oval cells" has accelerated significantly in recent years. Concurrent advancements in techniques for the isolation and characterization of these cells have helped fuel this research. Several models now exist for the induction of oval cell proliferation in rodents. Protocols for the isolation and culture of these cells have evolved to the point that they may be set up in any laboratory equipped for cell culture. The advent of magnetic cell sorting has eliminated reliance on expensive flow cytometric sorting equipment to generate highly enriched populations of oval cells. Our laboratory has had much success in using the oval cell surface marker Thy-1 in combination with magnetic sorting to produce material suitable for testing the influence of a myriad of chemical signaling molecules on the oval cell phenotype. This chapter will describe our basic strategy for oval cell induction and isolation. Additionally, two in vitro procedures are described which the reader may find useful in the early stages of developing an oval cell research project