Asymptotic forms for hard and soft edge general β\beta conditional gap probabilities

An infinite log-gas formalism, due to Dyson, and independently Fogler and Shklovskii, is applied to the computation of conditioned gap probabilities at the hard and soft edges of random matrix $\beta$-ensembles. The conditioning is that there are $n$ eigenvalues in the gap, with $n \ll |t|$, $t$ denoting the end point of the gap. It is found that the entropy term in the formalism must be replaced by a term involving the potential drop to obtain results consistent with known asymptotic expansions in the case $n=0$. With this modification made for general $n$, the derived expansions - which are for the logarithm of the gap probabilities - are conjectured to be correct up to and including terms O$(\log|t|)$. They are shown to satisfy various consistency conditions, including an asymptotic duality formula relating $\beta$ to $4/\beta$.Comment: Replaces v2 which contains typographical errors arising from a previous unpublished draf

Non-canonical functions of the RB protein in cancer

The canonical model of RB-mediated tumour suppression developed over the past 30 years is based on the regulation of E2F transcription factors to restrict cell cycle progression. Several additional functions have been proposed for RB, on the basis of which a non-canonical RB pathway can be described. Mechanistically, the non-canonical RB pathway promotes histone modification and regulates chromosome structure in a manner distinct from cell cycle regulation. These functions have implications for chemotherapy response and resistance to targeted anticancer agents. This Opinion offers a framework to guide future studies of RB in basic and clinical research

In Vivo Regulation of E2F1 by Polycomb Group Genes in Drosophila

The E2F transcription factors are important regulators of the cell cycle whose function is commonly misregulated in cancer. To identify novel regulators of E2F1 activity in vivo, we used Drosophila to conduct genetic screens. For this, we generated transgenic lines that allow the tissue-specific depletion of dE2F1 by RNAi. Expression of these transgenes using Gal4 drivers in the eyes and wings generated reliable and modifiable phenotypes. We then conducted genetic screens testing the capacity of Exelixis deficiencies to modify these E2F1-RNAi phenotypes. From these screens, we identified mutant alleles of Suppressor of zeste 2 [Su(z)2] and multiple Polycomb group genes as strong suppressors of the E2F1-RNA interference phenotypes. In validation of our genetic data, we find that depleting Su(z)2 in cultured Drosophila cells restores the cell-proliferation defects caused by reduction of dE2F1 by elevating the level of dE2f1. Furthermore, analyses of methylation status of histone H3 lysine 27 (H3K27me) from the published modENCODE data sets suggest that the genomic regions harboring dE2f1 gene and certain dE2f1 target genes display H3K27me during development and in several Drosophila cell lines. These in vivo observations suggest that the Polycomb group may regulate cell proliferation by repressing the transcription of dE2f1 and certain dE2F1 target genes. This mechanism may play an important role in coordinating cellular differentiation and proliferation during Drosophila development

Tumor Induction and Tissue Atrophy in Mice Lacking E2F-1

AbstractThe retinoblastoma tumor suppressor protein (pRB) is a transcriptional repressor that regulates gene expression by physically associating with transcription factors such as E2F family members. Although pRB and its upstream regulators are commonly mutated in human cancer, the physiological role of the pRB–E2F pathway is unknown. To address the function of E2F-1 and pRB/E2F-1 complexes in vivo, we have produced mice homozygous for a nonfunctional E2F-1 allele. Mice lacking E2F-1 are viable and fertile, yet experience testicular atrophy and exocrine gland dysplasia. Surprisingly, mice lacking E2F-1 develop a broad and unusual spectrum of tumors. Although overexpression of E2F-1 in tissue culture cells can stimulate cell proliferation and be oncogenic, loss of E2F-1 in mice results in tumorigenesis, demonstrating that E2F-1 also functions as a tumor suppressor

dREAM co-operates with insulator-binding proteins and regulates expression at divergently paired genes

dREAM complexes represent the predominant form of E2F/RBF repressor complexes in Drosophila. dREAM associates with thousands of sites in the fly genome but its mechanism of action is unknown. To understand the genomic context in which dREAM acts we examined the distribution and localization of Drosophila E2F and dREAM proteins. Here we report a striking and unexpected overlap between dE2F2/dREAM sites and binding sites for the insulator-binding proteins CP190 and Beaf-32. Genetic assays show that these components functionally co-operate and chromatin immunoprecipitation experiments on mutant animals demonstrate that dE2F2 is important for association of CP190 with chromatin. dE2F2/dREAM binding sites are enriched at divergently transcribed genes, and the majority of genes upregulated by dE2F2 depletion represent the repressed half of a differentially expressed, divergently transcribed pair of genes. Analysis of mutant animals confirms that dREAM and CP190 are similarly required for transcriptional integrity at these gene pairs and suggest that dREAM functions in concert with CP190 to establish boundaries between repressed/activated genes. Consistent with the idea that dREAM co-operates with insulator-binding proteins, genomic regions bound by dREAM possess enhancer-blocking activity that depends on multiple dREAM components. These findings suggest that dREAM functions in the organization of transcriptional domains

E2F and p53 Induce Apoptosis Independently during Drosophila Development but Intersect in the Context of DNA Damage

In mammalian cells, RB/E2F and p53 are intimately connected, and crosstalk between these pathways is critical for the induction of cell cycle arrest or cell death in response to cellular stresses. Here we have investigated the genetic interactions between RBF/E2F and p53 pathways during Drosophila development. Unexpectedly, we find that the pro-apoptotic activities of E2F and p53 are independent of one another when examined in the context of Drosophila development: apoptosis induced by the deregulation of dE2F1, or by the overexpression of dE2F1, is unaffected by the elimination of dp53; conversely, dp53-induced phenotypes are unaffected by the elimination of dE2F activity. However, dE2F and dp53 converge in the context of a DNA damage response. Both dE2F1/dDP and dp53 are required for DNA damage-induced cell death, and the analysis of rbf1 mutant eye discs indicates that dE2F1/dDP and dp53 cooperatively promote cell death in irradiated discs. In this context, the further deregulation in the expression of pro-apoptotic genes generates an additional sensitivity to apoptosis that requires both dE2F/dDP and dp53 activity. This sensitivity differs from DNA damage-induced apoptosis in wild-type discs (and from dE2F/dDP-induced apoptosis in un-irradiated rbf1 mutant eye discs) by being dependent on both hid and reaper. These results show that pro-apoptotic activities of dE2F1 and dp53 are surprisingly separable: dp53 is required for dE2F-dependent apoptosis in the response to DNA damage, but it is not required for dE2F-dependent apoptosis caused simply by the inactivation of rbf1

Mean-field driven first-order phase transitions in systems with long-range interactions

We consider a class of spin systems on $\Z^d$ with vector valued spins (\bS_x) that interact via the pair-potentials J_{x,y} \bS_x\cdot\bS_y. The interactions are generally spread-out in the sense that the $J_{x,y}$'s exhibit either exponential or power-law fall-off. Under the technical condition of reflection positivity and for sufficiently spread out interactions, we prove that the model exhibits a first-order phase transition whenever the associated mean-field theory signals such a transition. As a consequence, e.g., in dimensions $d\ge3$, we can finally provide examples of the 3-state Potts model with spread-out, exponentially decaying interactions, which undergoes a first-order phase transition as the temperature varies. Similar transitions are established in dimensions $d=1,2$ for power-law decaying interactions and in high dimensions for next-nearest neighbor couplings. In addition, we also investigate the limit of infinitely spread-out interactions. Specifically, we show that once the mean-field theory is in a unique ``state,'' then in any sequence of translation-invariant Gibbs states various observables converge to their mean-field values and the states themselves converge to a product measure.Comment: 57 pages; uses a (modified) jstatphys class fil

Key Roles for E2F1 in Signaling p53-Dependent Apoptosis and in Cell Division within Developing Tumors

AbstractApoptosis induced by the p53 tumor suppressor can attenuate cancer growth in preclinical animal models. Inactivation of the pRb proteins in mouse brain epithelium by the T121 oncogene induces aberrant proliferation and p53-dependent apoptosis. p53 inactivation causes aggressive tumor growth due to an 85% reduction in apoptosis. Here, we show that E2F1 signals p53-dependent apoptosis since E2F1 deficiency causes an 80% apoptosis reduction. E2F1 acts upstream of p53 since transcriptional activation of p53 target genes is also impaired. Yet, E2F1 deficiency does not accelerate tumor growth. Unlike normal cells, tumor cell proliferation is impaired without E2F1, counterbalancing the effect of apoptosis reduction. These studies may explain the apparent paradox that E2F1 can act as both an oncogene and a tumor suppressor in experimental systems

A novel retinoblastoma therapy from genomic and epigenetic analyses.

Retinoblastoma is an aggressive childhood cancer of the developing retina that is initiated by the biallelic loss of RB1. Tumours progress very quickly following RB1 inactivation but the underlying mechanism is not known. Here we show that the retinoblastoma genome is stable, but that multiple cancer pathways can be epigenetically deregulated. To identify the mutations that cooperate with RB1 loss, we performed whole-genome sequencing of retinoblastomas. The overall mutational rate was very low; RB1 was the only known cancer gene mutated. We then evaluated the role of RB1 in genome stability and considered non-genetic mechanisms of cancer pathway deregulation. For example, the proto-oncogene SYK is upregulated in retinoblastoma and is required for tumour cell survival. Targeting SYK with a small-molecule inhibitor induced retinoblastoma tumour cell death in vitro and in vivo. Thus, retinoblastomas may develop quickly as a result of the epigenetic deregulation of key cancer pathways as a direct or indirect result of RB1 loss