Generalized qd algorithm and Markov–Bernstein inequalities for Jacobi weight

The Markov–Bernstein inequalities for the Jacobi measure remained to be studied in detail. Indeed the tools used for obtaining lower and upper bounds of the constant which appear in these inequalities, did not work, since it is linked with the smallest eigenvalue of a five diagonal positive definite symmetric matrix. The aim of this paper is to generalize the qd algorithm for positive definite symmetric band matrices and to give the mean to expand the determinant of a five diagonal symmetric matrix. After that these new tools are applied to the problem to produce effective lower and upper bounds of the Markov–Bernstein constant in the Jacobi case. In the last part we com pare, in the particular case of the Gegenbauer measure, the lower and upper bounds which can be deduced from this paper, with those given in Draux and Elhami (Comput J Appl Math 106:203–243, 1999) and Draux (Numer Algor 24:31–58, 2000).      

Rectangular matrix Padé approximants and square matrix orthogonal polynomials

In this paper we study Padé-type and Padé approximants for rectangular matrix formal power series, as well as the formal orthogonal polynomials which are a consequence of the definition of these matrix Padé approximants. Recurrence relations are given along a diagonal or two adjacent diagonals of the table of orthogonal polynomials and their adjacent ones. A matrix qd-algorithm is deduced from these relations. Recurrence relations are also proved for the associated polynomials. Finally a short presentation of right matrix Padé approximants gives a link between the degrees of orthogonal polynomials in right and left matrix Padé approximants in order to show that the latter are identical. This revised version was published online in June 2006 with corrections to the Cover Date.     

EGCG Inhibits Adipose-Derived Mesenchymal Stem Cells Differentiation into Adipocytes and Prevents a STAT3-Mediated Paracrine Oncogenic Control of Triple-Negative Breast Cancer Cell Invasive Phenotype

Obese subjects have an increased risk of developing triple-negative breast cancer (TNBC), in part associated with the chronic low-grade inflammation state. On the other hand, epidemiological data indicates that increased consumption of polyphenol-rich fruits and vegetables plays a key role in reducing incidence of some cancer types. Here, we tested whether green tea-derived epigallocatechin-3-gallate (EGCG) could alter adipose-derived mesenchymal stem cell differentiation into adipocytes, and how this impacts the secretome profile and paracrine regulation of the TNBC invasive phenotype. Here, cell differentiation was performed and conditioned media (CM) from preadipocytes and mature adipocytes harvested. Human TNBC-derived MDA-MB-231 real-time cell migration was performed using the exCELLigence system. Differential gene arrays and RT-qPCR were used to assess gene expression levels. Western blotting was used to assess protein expression and phosphorylation status levels. In vitro vasculogenic mimicry (VM) was assessed with Matrigel. EGCG was found to inhibit the induction of key adipogenic biomarkers, including lipoprotein lipase, adiponectin, leptin, fatty acid synthase, and fatty acid binding protein 4. Increased TNBC-derived MDA-MB-231 cell chemotaxis and vasculogenic mimicry were observed in response to mature adipocytes secretome, and this was correlated with increased STAT3 phosphorylation status. This invasive phenotype was prevented by EGCG, the JAK/STAT inhibitors Tofacitinib and AG490, as well as upon STAT3 gene silencing. In conclusion, dietary catechin-mediated interventions could, in part through the inhibition of adipogenesis and modulation of adipocytes secretome profile, prevent the onset of an obesogenic environment that favors TNBC development.     

1,2,4-trihydroxynaphthalene-2-O-β-D-glucopyranoside: A new powerful antioxidant and inhibitor of Aβ42 aggregation isolated from the leaves of Lawsonia inermis

Mounting evidence indicates free radicals as toxic species causing damage to human cells leading to the pathogenesis of many diseases such as neurodegenerative disease. Plant derived antioxidants are considered as promising strategy to prevent free radical toxicity. In this study, the crude extract (CE), 50%MeOH, Petroleum Ether (PE) and Ethyl acetate (EA) fractions of Lawsonia inermis leaves were investigated for their antioxidant activity and their ability to counteract amyloid-β₄₂ (Aβ₄₂) aggregation. Elution of the most bioactive fraction (EA) on silica gel column chromatography led to six sub-fractions. The most active sub-fraction (1) was further resolved on silica gel column chromatography. A new compound with powerful antioxidant and anti-Aβ₄₂ aggregation properties was purified and characterised by spectroscopic methods as 1,2,4-trihydroxynaphthalene-2-O-β-D-glucopyranoside (THNG). This finding suggests that the antioxidant and anti-Aβ₄₂ aggregation activities of L. inermis leaves are strongly correlated to this compound.     

Assessing multidrug resistance protein 1-mediated function in cancer cell multidrug resistance by scanning electrochemical microscopy and flow cytometry

Cancer cell multidrug resistance is a molecular signature that highly influences the outcome of chemotherapy treatment and for which there is currently no robust method to monitor in vitro its activity. Herein, we demonstrate that ferrocenemethanol (FcCH(2)OH) and its oxidized form ([FcCH(2)OH](+)) affect the redox state of cancer cells. Specifically, the interaction of FcCH(2)OH with the glutathione couple (GSH/GSSG) is shown in human adenocarcinoma cervical cancer cells HeLa and a multidrug resistant variant overexpressing the multidrug resistant associated protein 1 (MRP1) using bioanalytical techniques, such as flow cytometry and fluorescence microscopy. It is further demonstrated that the differential response to FcCH(2)OH in multidrug-resistant cells is in part due to MRP1's unspecific efflux. Scanning electrochemical microscopy confirmed the interaction between FcCH(2)OH and the cells, and the differential response was observed to depend on MRP1 expression. This newly established relation between FcCH(2)OH/[FcCH(2)OH](+), GSH/GSSG and multidrug resistance in human cancer cells enables than the acquisition of scanning electrochemical microscopy images.