Extremal spacings between eigenphases of random unitary matrices and their tensor products

Extremal spacings between eigenvalues of random unitary matrices of size N pertaining to circular ensembles are investigated. Explicit probability distributions for the minimal spacing for various ensembles are derived for N = 4. We study ensembles of tensor product of k random unitary matrices of size n which describe independent evolution of a composite quantum system consisting of k subsystems. In the asymptotic case, as the total dimension N = n^k becomes large, the nearest neighbor distribution P(s) becomes Poissonian, but statistics of extreme spacings P(s_min) and P(s_max) reveal certain deviations from the Poissonian behavior

FOXA1 repression is associated with loss of BRCA1 and increased promoter methylation and chromatin silencing in breast cancer

FOXA1 expression correlates with the breast cancer luminal subtype and patient survival. RNA and protein analysis of a panel of breast cancer cell lines revealed that BRCA1 deficiency is associated with the downregulation of FOXA1 expression. Knockdown of BRCA1 resulted in the downregulation of FOXA1 expression and enhancement of FOXA1 promoter methylation in MCF-7 breast cancer cells, whereas the reconstitution of BRCA1 in Brca1-deficent mouse mammary epithelial cells (MMECs) promoted Foxa1 expression and methylation. These data suggest that BRCA1 suppresses FOXA1 hypermethylation and silencing. Consistently, the treatment of MMECs with the DNA methylation inhibitor 5-aza-2'-deoxycitydine induced Foxa1 mRNA expression. Furthermore, treatment with GSK126, an inhibitor of EZH2 methyltransferase activity, induced FOXA1 expression in BRCA1-deficient but not in BRCA1-reconstituted MMECs. Likewise, the depletion of EZH2 by small interfering RNA enhanced FOXA1 mRNA expression. Chromatin immunoprecipitation (ChIP) analysis demonstrated that BRCA1, EZH2, DNA methyltransferases (DNMT)1/3a/3b and H3K27me3 are recruited to the endogenous FOXA1 promoter, further supporting the hypothesis that these proteins interact to modulate FOXA1 methylation and repression. Further co-immunoprecipitation and ChIP analysis showed that both BRCA1 and DNMT3b form complexes with EZH2 but not with each other, consistent with the notion that BRCA1 binds to EZH2 and negatively regulates its methyltransferase activity. We also found that EZH2 promotes and BRCA1 impairs the deposit of the gene silencing histone mark H3K27me3 on the FOXA1 promoter. These associations were validated in a familial breast cancer patient cohort. Integrated analysis of the global gene methylation and expression profiles of a set of 33 familial breast tumours revealed that FOXA1 promoter methylation is inversely correlated with the transcriptional expression of FOXA1 and that BRCA1 mutation breast cancer is significantly associated with FOXA1 methylation and downregulation of FOXA1 expression, providing physiological evidence to our findings that FOXA1 expression is regulated by methylation and chromatin silencing and that BRCA1 maintains FOXA1 expression through suppressing FOXA1 gene methylation in breast cancer.Oncogene advance online publication, 22 December 2014; doi:10.1038/onc.2014.421.published_or_final_versio

Structure−Activity Relationship and Multidrug Resistance Study of NewS-trityl-l-Cysteine Derivatives As Inhibitors of Eg5

The mitotic spindle is a validated target for cancer chemotherapy. Drugs such as taxanes and vinca alkaloids specifically target microtubules and cause the mitotic spindle to collapse. However, toxicity and resistance are problems associated with these drugs. Thus, alternative approaches to inhibiting the mitotic spindle are being pursued. These include targeting Eg5, a human kinesin involved in the formation of the bipolar spindle. We previously identified S-trityl-L-cysteine (STLC) as a potent allosteric inhibitor of Eg5. Here, we report the synthesis of a new series of STLC-like compounds with in vitro inhibition in the low nanomolar range. We also performed a multidrug resistance study in cell lines overexpressing P-glycoprotein and showed that some of these inhibitors may have the potential to overcome susceptibility to this efflux pump. Finally, we performed molecular docking of the compounds and determined the structures of two Eg5-inhibitor complexes to explain the structure-activity relationship of these compound