On Markov operators preserving polynomials

The paper is concerned with a special class of positive linear operators acting on the space C(K) of all continuous functions defined on a convex compact subset K of R^d, d \geq 1, having non-empty interior. Actually, this class consists of all positive linear operators T on C(K) which leave invariant the polynomials of degree at most 1 and which, in addition, map polynomials into polynomials of the same degree. Among other things, we discuss the existence of such operators in the special case where K is strictly convex by also characterizing them within the class of positive projections. In particular we show that such operators exist if and only if ∂K is an ellipsoid. Furthermore, a characterization of balls of R^d in terms of a special class of them is furnished. Additional results and illustrative examples are presented as well

Tamoxifen induces oxidative stress and apoptosis in oestrogen receptor-negative human cancer cell lines

Recent data have demonstrated that the anti-oestrogen tamoxifen (TAM) is able to facilitate apoptosis in cancer cells not expressing oestrogen receptor (ER). In an attempt to identify the biochemical pathway for this phenomenon, we investigated the role of TAM as an oxidative stress agent. In two ER-negative human cancer cell lines, namely T-leukaemic Jurkat and ovarian A2780 cancer cells, we have demonstrated that TAM is able to generate oxidative stress, thereby causing thiol depletion and activation of the transcriptional factor NF-κB. As described for other oxidative agents, TAM was able to induce either cell proliferation or apoptosis depending on the dose. When used at the lowest dose tested (0.1 μM), a slight proliferative effect of TAM was noticed in terms of cell counts and DNA synthesis rate, whereas at higher doses (10 μM) a consistent occurrence of apoptosis was detected. Importantly, the induction of apoptosis by TAM is not linked to down-regulation or functional inactivation by phosphorylation of the antiapoptotic bcl-2 protein. © 1999 Cancer Research Campaig

AIB1 gene amplification and the instability of polyQ encoding sequence in breast cancer cell lines

BACKGROUND: The poly Q polymorphism in AIB1 (amplified in breast cancer) gene is usually assessed by fragment length analysis which does not reveal the actual sequence variation. The purpose of this study is to investigate the sequence variation of poly Q encoding region in breast cancer cell lines at single molecule level, and to determine if the sequence variation is related to AIB1 gene amplification. METHODS: The polymorphic poly Q encoding region of AIB1 gene was investigated at the single molecule level by PCR cloning/sequencing. The amplification of AIB1 gene in various breast cancer cell lines were studied by real-time quantitative PCR. RESULTS: Significant amplifications (5–23 folds) of AIB1 gene were found in 2 out of 9 (22%) ER positive cell lines (in BT-474 and MCF-7 but not in BT-20, ZR-75-1, T47D, BT483, MDA-MB-361, MDA-MB-468 and MDA-MB-330). The AIB1 gene was not amplified in any of the ER negative cell lines. Different passages of MCF-7 cell lines and their derivatives maintained the feature of AIB1 amplification. When the cells were selected for hormone independence (LCC1) and resistance to 4-hydroxy tamoxifen (4-OH TAM) (LCC2 and R27), ICI 182,780 (LCC9) or 4-OH TAM, KEO and LY 117018 (LY-2), AIB1 copy number decreased but still remained highly amplified. Sequencing analysis of poly Q encoding region of AIB1 gene did not reveal specific patterns that could be correlated with AIB1 gene amplification. However, about 72% of the breast cancer cell lines had at least one under represented (<20%) extra poly Q encoding sequence patterns that were derived from the original allele, presumably due to somatic instability. Although all MCF-7 cells and their variants had the same predominant poly Q encoding sequence pattern of (CAG)(3)CAA(CAG)(9)(CAACAG)(3)(CAACAGCAG)(2)CAA of the original cell line, a number of altered poly Q encoding sequences were found in the derivatives of MCF-7 cell lines. CONCLUSION: These data suggest that poly Q encoding region of AIB1 gene is somatic unstable in breast cancer cell lines. The instability and the sequence characteristics, however, do not appear to be associated with the level of the gene amplification

A Mutation in Intracellular Loop 4 Affects the Drug-Efflux Activity of the Yeast Multidrug Resistance ABC Transporter Pdr5p

Multidrug resistance protein Pdr5p is a yeast ATP-binding cassette (ABC) transporter in the plasma membrane. It confers multidrug resistance by active efflux of intracellular drugs. However, the highly polymorphic Pdr5p from clinical strain YJM789 loses its ability to expel azole and cyclohexmide. To investigate the role of amino acid changes in this functional change, PDR5 chimeras were constructed by segmental replacement of homologous BY4741 PDR5 fragments. Functions of PDR5 chimeras were evaluated by fluconazole and cycloheximide resistance assays. Their expression, ATPase activity, and efflux efficiency for other substrates were also analyzed. Using multiple lines of evidence, we show that an alanine-to-methionine mutation at position 1352 located in the predicted short intracellular loop 4 significantly contributes to the observed transport deficiency. The degree of impairment is likely correlated to the size of the mutant residue

Prognostic impact of multidrug resistance gene expression on the management of breast cancer in the context of adjuvant therapy based on a series of 171 patients

Study of the prognostic impact of multidrug resistance gene expression in the management of breast cancer in the context of adjuvant therapy. This study involved 171 patients treated by surgery, adjuvant chemotherapy±radiotherapy±hormonal therapy (mean follow-up: 55 months). We studied the expression of multidrug resistance gene 1 (MDR1), multidrug resistance-associated protein (MRP1), and glutathione-S-transferase P1 (GSTP1) using a standardised, semiquantitative rt–PCR method performed on frozen samples of breast cancer tissue. Patients were classified as presenting low or high levels of expression of these three genes. rt-PCR values were correlated with T stage, N stage, Scarff–Bloom–Richardson (SBR) grade, age and hormonal status. The impact of gene expression levels on 5-year disease-free survival (DFS) and overall survival (OS) was studied by univariate and multivariate Cox analysis. No statistically significant correlation was demonstrated between MDR1, MRP1 and GSTP1 expressions. On univariate analysis, DFS was significantly decreased in a context of low GSTP1 expression (P=0.0005) and high SBR grade (P=0.003), size ⩾5 cm (P=0.038), high T stage (P=0.013), presence of intravascular embolus (P=0.034), and >3 N+ (P=0.05). On multivariate analysis, GSTP1 expression and the presence of ER remained independent prognostic factors for DFS. GSTP1 expression did not affect OS. The levels of MDR1 and MRP1 expression had no significant influence on DFS or OS. GSTP1 expression can be considered to be an independent prognostic factor for DFS in patients receiving adjuvant chemotherapy for breast cancer

Suppression of Her2/neu expression through ILK inhibition is regulated by a pathway involving TWIST and YB-1

In a previous study it was found that the therapeutic effects of QLT0267, a small molecule inhibitor of integrin-linked kinase (ILK), were influenced by Her2/neu expression. To understand how inhibition or silencing of ILK influences Her2/neu expression, Her2/neu signaling was evaluated in six Her2/neu-positive breast cancer cell lines (LCC6Her2, MCF7Her2, SKBR3, BT474, JIMT-1 and KPL-4). Treatment with QLT0267 engendered suppression (32–87%) of total Her2/neu protein in these cells. Suppression of Her2/neu was also observed following small interfering RNA-mediated silencing of ILK expression. Time course studies suggest that ILK inhibition or silencing caused transient decreases in P-AKTser473, which were not temporally related to Her2/neu downregulation. Attenuation of ILK activity or expression was, however, associated with decreases in YB-1 (Y-box binding protein-1) protein and transcript levels. YB-1 is a known transcriptional regulator of Her2/neu expression, and in this study it is demonstrated that inhibition of ILK activity using QLT0267 decreased YB-1 promoter activity by 50.6%. ILK inhibition was associated with changes in YB-1 localization, as reflected by localization of cytoplasmic YB-1 into stress granules. ILK inhibition also suppressed TWIST (a regulator of YB-1 expression) protein expression. To confirm the role of ILK on YB-1 and TWIST, cells were engineered to overexpress ILK. This was associated with a fourfold increase in the level of YB-1 in the nucleus, and a 2- and 1.5-fold increase in TWIST and Her2/neu protein levels, respectively. Taken together, these data indicate that ILK regulates the expression of Her2/neu through TWIST and YB-1, lending support to the use of ILK inhibitors in the treatment of aggressive Her2/neu-positive tumors

Continuous selections of Borel measures, positive operators and degenerate evolution problems

In this paper we continue the study of a sequence of positive lin- ear operators which we have introduced in [9] and which are associated with a continuous selection of Borel measures on the unit interval. We show that the iterates of these operators converge to a Markov semigroup whose generator is a degenerate second-order elliptic differential operator on the unit interval. Some qualitative properties of the semigroup, or equivalently, of the solutions of the corresponding degenerate evolution problems, are also investigated

An invitation to the study of evolution equations by means of positive linear operators

This paper provides a detailed survey on a series of methods and results which are centered around the problem of the constructive approximation of the positive semigroups generated by degenerate second order differential operators by means of iterates of positive linear operators. This problem, first states in [7], has been tackled n the last fifteen years from different angles and in different settings such us spaces of bounded and unbounded continuous functions on real intervals as well as on multidimensional convex compact subsets. For the sake of simplicity the presentation is restricted in the framework of compact intervals. The exposition includes several applications as well ad several references for further possible deepening and developments