Grassmannians,Calibrations and Five-Brane Intersections

We present a geometric construction of a new class of hyper-Kahler manifolds with torsion. This involves the superposition of the four-dimensional hyper-Kahler geometry with torsion associated with the NS-5-brane along quaternionic planes in quaternionic k-space, \bH^k. We find the moduli space of these geometries and show that it can be constructed using the bundle space of the canonical quaternionic line bundle over a quaternionic projective space. We also investigate several special cases which are associated with certain classes of quaternionic planes in \bH^k. We then show that the eight-dimensional geometries we have found can be constructed using quaternionic calibrations. We generalize our construction to superpose the same four-dimensional hyper-Kahler geometry with torsion along complex planes in \bC^{2k}. We find that the resulting geometry is Kahler with torsion. The moduli space of these geometries is also investigated. In addition, the applications of these new geometries to M-theory and sigma models are presented. In particular, we find new solutions of IIA supergravity with the interpretation of intersecting NS-5-branes at Sp(2)-angles on a string and show that they preserve 3/32, 1/8, 5/32 and 3/16 of supersymmetry. We also show that two-dimensional sigma models with target spaces the above manifolds have (p,q) extended supersymmetry.Comment: 39 pages, phyzzx; a previously undetermined fraction of supersymmetry has now been fixed; a table has been replaced; version submitted for publication in CM

Instantons at Angles

We interpret a class of 4k-dimensional instanton solutions found by Ward, Corrigan, Goddard and Kent as four-dimensional instantons at angles. The superposition of each pair of four-dimensional instantons is associated with four angles which depend on some of the ADHM parameters. All these solutions are associated with the group $Sp(k)$ and are examples of Hermitian-Einstein connections on \bE^{4k}. We show that the eight-dimensional solutions preserve 3/16 of the ten-dimensional N=1 supersymmetry. We argue that under the correspondence between the BPS states of Yang-Mills theory and those of M-theory that arises in the context of Matrix models, the instantons at angles configuration corresponds to the longitudinal intersecting 5-branes on a string at angles configuration of M-theory.Comment: 17 pages, phyzzx, many changes and a new section was adde

Stochastic epigenetic outliers can define field defects in cancer

BACKGROUND: There is growing evidence that DNA methylation alterations may contribute to carcinogenesis. Recent data also suggest that DNA methylation field defects in normal pre-neoplastic tissue represent infrequent stochastic “outlier” events. This presents a statistical challenge for standard feature selection algorithms, which assume frequent alterations in a disease phenotype. Although differential variability has emerged as a novel feature selection paradigm for the discovery of outliers, a growing concern is that these could result from technical confounders, in principle thus favouring algorithms which are robust to outliers. RESULTS: Here we evaluate five differential variability algorithms in over 700 DNA methylomes, including two of the largest cohorts profiling precursor cancer lesions, and demonstrate that most of the novel proposed algorithms lack the sensitivity to detect epigenetic field defects at genome-wide significance. In contrast, algorithms which recognise heterogeneous outlier DNA methylation patterns are able to identify many sites in pre-neoplastic lesions, which display progression in invasive cancer. Thus, we show that many DNA methylation outliers are not technical artefacts, but define epigenetic field defects which are selected for during cancer progression. CONCLUSIONS: Given that cancer studies aiming to find epigenetic field defects are likely to be limited by sample size, adopting the novel feature selection paradigm advocated here will be critical to increase assay sensitivity

Prognostic gene network modules in breast cancer hold promise

A substantial proportion of lymph node-negative patients who receive adjuvant chemotherapy do not derive any benefit from this aggressive and potentially toxic treatment. However, standard histopathological indices cannot reliably detect patients at low risk of relapse or distant metastasis. In the past few years several prognostic gene expression signatures have been developed and shown to potentially outperform histopathological factors in identifying low-risk patients in specific breast cancer subgroups with predictive values of around 90%, and therefore hold promise for clinical application. We envisage that further improvements and insights may come from integrative expression pathway analyses that dissect prognostic signatures into modules related to cancer hallmarks

Increased entropy of signal transduction in the cancer metastasis phenotype

Studies into the statistical properties of biological networks have led to important biological insights, such as the presence of hubs and hierarchical modularity. There is also a growing interest in studying the statistical properties of networks in the context of cancer genomics. However, relatively little is known as to what network features differ between the cancer and normal cell physiologies, or between different cancer cell phenotypes. Based on the observation that frequent genomic alterations underlie a more aggressive cancer phenotype, we asked if such an effect could be detectable as an increase in the randomness of local gene expression patterns. Using a breast cancer gene expression data set and a model network of protein interactions we derive constrained weighted networks defined by a stochastic information flux matrix reflecting expression correlations between interacting proteins. Based on this stochastic matrix we propose and compute an entropy measure that quantifies the degree of randomness in the local pattern of information flux around single genes. By comparing the local entropies in the non-metastatic versus metastatic breast cancer networks, we here show that breast cancers that metastasize are characterised by a small yet significant increase in the degree of randomness of local expression patterns. We validate this result in three additional breast cancer expression data sets and demonstrate that local entropy better characterises the metastatic phenotype than other non-entropy based measures. We show that increases in entropy can be used to identify genes and signalling pathways implicated in breast cancer metastasis. Further exploration of such integrated cancer expression and protein interaction networks will therefore be a fruitful endeavour.Comment: 5 figures, 2 Supplementary Figures and Table

Multi-angle Five-Brane Intersections

We find new solutions of IIA supergravity which have the interpretation of intersecting NS-5-branes at $Sp(2)$-angles on a string preserving at least 3/32 of supersymmetry. We show that the relative position of every pair of NS-5-branes involved in the superposition is determined by four angles. In addition we explore the related configurations in IIB strings and M-theory.Comment: 18 pages,phyzzx; reference added; version to appear in PL

The multi-omic landscape of transcription factor inactivation in cancer

BACKGROUND: Hypermethylation of transcription factor promoters bivalently marked in stem cells is a cancer hallmark. However, the biological significance of this observation for carcinogenesis is unclear given that most of these transcription factors are not expressed in any given normal tissue. METHODS: We analysed the dynamics of gene expression between human embryonic stem cells, fetal and adult normal tissue, as well as six different matching cancer types. In addition, we performed an integrative multi-omic analysis of matched DNA methylation, copy number, mutational and transcriptomic data for these six cancer types. RESULTS: We here demonstrate that bivalently and PRC2 marked transcription factors highly expressed in a normal tissue are more likely to be silenced in the corresponding tumour type compared with non-housekeeping genes that are also highly expressed in the same normal tissue. Integrative multi-omic analysis of matched DNA methylation, copy number, mutational and transcriptomic data for six different matching cancer types reveals that in-cis promoter hypermethylation, and not in-cis genomic loss or genetic mutation, emerges as the predominant mechanism associated with silencing of these transcription factors in cancer. However, we also observe that some silenced bivalently/PRC2 marked transcription factors are more prone to copy number loss than promoter hypermethylation, pointing towards distinct, mutually exclusive inactivation patterns. CONCLUSIONS: These data provide statistical evidence that inactivation of cell fate-specifying transcription factors in cancer is an important step in carcinogenesis and that it occurs predominantly through a mechanism associated with promoter hypermethylation

Corruption of the Intra-Gene DNA Methylation Architecture Is a Hallmark of Cancer

Epigenetic processes - including DNA methylation - are increasingly seen as having a fundamental role in chronic diseases like cancer. It is well known that methylation levels at particular genes or loci differ between normal and diseased tissue. Here we investigate whether the intra-gene methylation architecture is corrupted in cancer and whether the variability of levels of methylation of individual CpGs within a defined gene is able to discriminate cancerous from normal tissue, and is associated with heterogeneous tumour phenotype, as defined by gene expression. We analysed 270985 CpGs annotated to 18272 genes, in 3284 cancerous and 681 normal samples, corresponding to 14 different cancer types. In doing so, we found novel differences in intra-gene methylation pattern across phenotypes, particularly in those genes which are crucial for stem cell biology; our measures of intra-gene methylation architecture are a better determinant of phenotype than measures based on mean methylation level alone (K-S test [Formula: see text] in all 14 diseases tested). These per-gene methylation measures also represent a considerable reduction in complexity, compared to conventional per-CpG beta-values. Our findings strongly support the view that intra-gene methylation architecture has great clinical potential for the development of DNA-based cancer biomarkers