Scattering theory on graphs (2): the Friedel sum rule

We consider the Friedel sum rule in the context of the scattering theory for the Schr\"odinger operator -\Dc_x^2+V(x) on graphs made of one-dimensional wires connected to external leads. We generalize the Smith formula for graphs. We give several examples of graphs where the state counting method given by the Friedel sum rule is not working. The reason for the failure of the Friedel sum rule to count the states is the existence of states localized in the graph and not coupled to the leads, which occurs if the spectrum is degenerate and the number of leads too small.Comment: 20 pages, LaTeX, 6 eps figure

Effects of bone marrow-derived cells on monocrotaline- and hypoxia-induced pulmonary hypertension in mice

BACKGROUND: Bone marrow -derived cells (BMDCs) can either limit or contribute to the process of pulmonary vascular remodeling. Whether the difference in their effects depends on the mechanism of pulmonary hypertension (PH) remains unknown. OBJECTIVES: We investigated the effect of BMDCs on PH induced in mice by either monocrotaline or exposure to chronic hypoxia. METHODS: Intravenous administration of the active monocrotaline metabolite (monocrotaline pyrrole, MCTp) to C57BL/6 mice induced PH within 15 days, due to remodeling of small distal vessels. Three days after the MCTp injection, the mice were injected with BMDCs harvested from femurs and tibias of donor mice treated with 5-fluorouracil (3.5 mg IP/animal) to deplete mature cells and to allow proliferation of progenitor cells. RESULTS: BMDCs significantly attenuated PH as assessed by reductions in right ventricular systolic pressure (20 ± 1 mmHg vs. 27 ± 1 mmHg, P ≤ 0.01), right ventricle weight/left ventricle+septum weight ratio (0.29 ± 0.02 vs. 0.36 ± 0.01, P ≤ 0.03), and percentage of muscularized vessels (26.4% vs. 33.5%, P ≤ 0.05), compared to control animals treated with irradiated BMDCs. Tracking cells from constitutive GFP-expressing male donor mice with anti-GFP antibodies or chromosome Y level measurement by quantitative real-time PCR showed BMDCs in the lung. In contrast, chronically hypoxic mice subjected to the same procedure failed to show improvement in PH. CONCLUSION: These results show that BMDCs limit pulmonary vascular remodeling induced by vascular injury but not by hypoxia

Enhanced Osteogenesis of Adipose-Derived Stem Cells by Regulating Bone Morphogenetic Protein Signaling Antagonists and Agonists

Although adipose-derived stem cells (ASCs) are an attractive cell source for bone tissue engineering, direct use of ASCs alone has had limited success in the treatment of large bone defects. Although bone morphogenetic proteins (BMPs) are believed to be the most potent osteoinductive factors to promote osteogenic differentiation of ASCs, their clinical applications require supraphysiological dosage, leading to high medical burden and adverse side effects. In the present study, we demonstrated an alternative approach that can effectively complement the BMP activity to maximize the osteogenesis of ASCs without exogenous application of BMPs by regulating levels of antagonists and agonists to BMP signaling. Treatment of ASCs with the amiloride derivative phenamil, a positive regulator of BMP signaling, combined with gene manipulation to suppress the BMP antagonist noggin, significantly enhanced osteogenic differentiation of ASCs through increased BMP–Smad signaling in vitro. Furthermore, the combination approach of noggin suppression and phenamil stimulation enhanced the BMP signaling and bone repair in a mouse calvarial defect model by adding noggin knockdown ASCs to apatite-coated poly(lactic-coglycolic acid) scaffolds loaded with phenamil. These results suggest novel complementary osteoinductive strategies that could maximize activity of the BMP pathway in ASC bone repair while reducing potential adverse effects of current BMP-based therapeutics. SIGNIFICANCE: Although stem cell-based tissue engineering strategy offers a promising alternative to repair damaged bone, direct use of stem cells alone is not adequate for challenging healing environments such as in large bone defects. This study demonstrates a novel strategy to maximize bone formation pathways in osteogenic differentiation of mesenchymal stem cells and functional bone formation by combining gene manipulation with a small molecule activator toward osteogenesis. The findings indicate promising stem cell-based therapy for treating bone defects that can effectively complement or replace current osteoinductive therapeutics

Calcium-dependent modulation and plasma membrane targeting of the AKT2 potassium channel by the CBL4/CIPK6 calcium sensor/protein kinase complex

Potassium (K+) channel function is fundamental to many physiological processes. However, components and mechanisms regulating the activity of plant K+ channels remain poorly understood. Here, we show that the calcium (Ca2+) sensor CBL4 together with the interacting protein kinase CIPK6 modulates the activity and plasma membrane (PM) targeting of the K+ channel AKT2 from Arabidopsis thaliana by mediating translocation of AKT2 to the PM in plant cells and enhancing AKT2 activity in oocytes. Accordingly, akt2, cbl4 and cipk6 mutants share similar developmental and delayed flowering phenotypes. Moreover, the isolated regulatory C-terminal domain of CIPK6 is sufficient for mediating CBL4- and Ca2+-dependent channel translocation from the endoplasmic reticulum membrane to the PM by a novel targeting pathway that is dependent on dual lipid modifications of CBL4 by myristoylation and palmitoylation. Thus, we describe a critical mechanism of ion-channel regulation where a Ca2+ sensor modulates K+ channel activity by promoting a kinase interaction-dependent but phosphorylation-independent translocation of the channel to the PM