Combinatorial formulas for Kazhdan-Lusztig polynomials with respect to W-graph ideals

In \cite{y1} Yin generalized the definition of $W$-graph ideal $E_J$ in weighted Coxeter groups and introduced the weighted Kazhdan-Lusztig polynomials $\left \{ P_{x,y} \mid x,y\in E_J\right \}$, where $J$ is a subset of simple generators $S$. In this paper, we study the combinatorial formulas for those polynomials, which extend the results of Deodhar \cite{v3} and Tagawa \cite{h1}.Comment: 16 page

Transcription factors whose consensus binding sequences are over-represented in the promoter region of genes down-regulated by either 8 nM or 80 nM DIG-MSK in A2780 human ovarian carcinoma cells.

a<p>According to TELiS database (<a href="http://www.telis.ucla.edu/" target="_blank">http://www.telis.ucla.edu/</a>).</p>b<p>AG: Number of genes analysed.</p>c<p>Ranking according to the <i>p</i>-value (<i>p</i><0.05) in incidence analyses.</p><p>//These transcription factors were not enriched in the promoters.</p

Cell cycle distribution and mechanisms of cell death.

<p>(A) Flow cytometry analysis of the time-dependent changes in cell cycle distribution of A2780 cells treated with either 8 nM or 80 nM DIG-MSK. Both adherent (attached) and detached (floating) cell populations were pooled together and their distribution in the different phases of the cell cycle quantified. (B) Analysis of cell death in A2780 human ovarian carcinoma cells treated with 8 nM or 80 nM DIG-MSK. This panel shows time-course bivariate flow cytometry analyses of control and DIG-MSK-treated cells stained with Annexin-V-Fluos and PI. Percentages of necrosis, apoptosis and secondary necrosis/apoptosis (double staining) are indicated inside the panels.</p

Immunoblotting analysis of protein levels.

<p>(A) Western blots showing changes in protein levels in A2780 cells treated with 80 nM DIG-MSK for the times indicated at the top of the panel. Experiments were performed in duplicate with similar results. (B) Quantification of the Western blots shown in panel A. It shows the time-dependent decrease in Sp1 and Sp3 (short isoform) protein levels, and the time-dependent enhancement of p53 and p21^WAF1 (CDKN1A) protein levels.</p

Chromatin immunoprecipitation analysis of Sp1 binding to the promoters of <i>XIAP</i>, <i>CRABP1</i>, <i>MDK</i> and <i>KCNMA1</i> genes in A2780 cells in the presence/absence of 80 nM DIG-MSK.

<p>ChIP was performed using an anti-Sp1 specific antibody. A DNA fragment that does not contain Sp1-binding sites was also immunoprecipitated as a negative control, as well as an unspecific immunoprecipitation using IgG (Mock). DNA in both the input and in the immunoprecipitated fractions was quantified by qRT-PCR. Data (mean ± SD from 3 independent experiments) are shown as the enrichment of input DNA in the immunoprecipitated fractions (**<i>p</i><0.01; Student’s t-test).</p

Analysis of gene expression in A2780 cells treated with DIG-MSK.

<p>(A) Venn diagrams representing genes affected, either up-regulated or down-regulated in microarray analysis by treatments with 8 nM or 80 nM DIG-MSK (1.5-fold changes, <i>p</i><0.05). Numbers inside the intersections correspond to genes influenced by both drug concentrations. (B) Quantitative real-time PCR measurements of a set of genes selected among those differentially expressed in A2780 cells treated with DIG-MSK. Compared to untreated cells, the expression of all these genes changed significantly upon treatment (<i>p</i><0.05). Histograms represent mean ± SD from 3 independent experiments (**<i>p</i><0.01, Student’s t-test comparison between treatments with either 8 nM or 80 nM DIG-MSK).</p

Gene Ontology (GO) categories affected by 8 nM DIG-MSK.

a<p>The GO analysis was undertaken on down-regulated genes by PANTHER 7.0.</p>b<p>Binomial test.</p

Chemical formulae of the mithramycin analogue DIG-MSK (demycarosyl-3D-β-D-digitoxosyl-mithramycin SK).

<p>DIG-MSK differs from the parental mithramycin A in the side chain linked to C-3 and the distal sugar in the trisaccharide moiety.</p

Effects of the treatment of A2780 cells with 8 nM or 80 nM DIG-MSK on a panel of genes characterized as being related to “ovarian neoplasm” and containing at least one putative Sp1-binding site in the proximal promoter region.

<p>(A) Hierarchical clustering of changes in gene expression for each treatment. Dendrograms show average-linkage hierarchical clustering based in Pearson correlation coefficients. For the sake of comparison, lowercase letters at the right side indicate “clusters” with shared characteristics that are detailed in Results. (B) Network generated by the Genomatix Pathway System (GePS) representing bibliographic relationships for Sp1 co-expressed gene profiles (<i>p</i> = 1.48E-03). Dashed lines indicate genes associated by co-citation, while continuous lines indicate genes associated by expert-curation. Filled diamonds and triangles indicate the promoter of gene “B” (the gene with the diamond/triangle) has a corresponding experimentally validated binding site for the transcription factor encoded by gene “A”. Open triangles indicate that the binding of a particular transcription factor to the gene promoter has not been described unambiguously. The sequence logo for the consensus Sp1 binding site, retrieved from JASPAR, is shown at the top right of panel B.</p

Assessment of cell proliferation.

<p>Effects of DIG-MSK on the proliferation of A2780 human ovarian carcinoma cells after 72-h continuous treatments. Data are mean ± SEM from 6 independent experiments.</p