Finding large average submatrices in high dimensional data

The search for sample-variable associations is an important problem in the exploratory analysis of high dimensional data. Biclustering methods search for sample-variable associations in the form of distinguished submatrices of the data matrix. (The rows and columns of a submatrix need not be contiguous.) In this paper we propose and evaluate a statistically motivated biclustering procedure (LAS) that finds large average submatrices within a given real-valued data matrix. The procedure operates in an iterative-residual fashion, and is driven by a Bonferroni-based significance score that effectively trades off between submatrix size and average value. We examine the performance and potential utility of LAS, and compare it with a number of existing methods, through an extensive three-part validation study using two gene expression datasets. The validation study examines quantitative properties of biclusters, biological and clinical assessments using auxiliary information, and classification of disease subtypes using bicluster membership. In addition, we carry out a simulation study to assess the effectiveness and noise sensitivity of the LAS search procedure. These results suggest that LAS is an effective exploratory tool for the discovery of biologically relevant structures in high dimensional data. Software is available at https://genome.unc.edu/las/.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS239 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Non Linear Sigma Model and Spin Ladders

The well known Haldane map from spin chains into the $O(3)$ non linear sigma model is generalized to the case of spin ladders. This map allows us to explain the different qualitative behaviour between even and odd ladders, exactly in the same way it explains the difference between integer and half-integer spin chains. Namely, for even ladders the topological term in the sigma model action is absent, while for odd ladders the $\theta$ parameter, which multiplies the topological term, is equal to $2 \pi S$, where $S$ is the spin of the ladder. Hence even ladders should have a dynamically generated spin gap, while odd ladders with half-integer spin should stay gapless, and physically equivalent to a perturbed $SU(2)_1$ Wess-Zumino -Witten model in the infrared regime. We also derive some consequences from the dependence of the sigma model coupling constant on the ladder Heisenberg couplings constants.Comment: Latex file, 14 pages, no figure

EGFR associated expression profiles vary with breast tumor subtype

<p>Abstract</p> <p>Background</p> <p>The epidermal growth factor receptor (EGFR/HER1) and its downstream signaling events are important for regulating cell growth and behavior in many epithelial tumors types. In breast cancer, the role of EGFR is complex and appears to vary relative to important clinical features including estrogen receptor (ER) status. To investigate EGFR-signaling using a genomics approach, several breast basal-like and luminal epithelial cell lines were examined for sensitivity to EGFR inhibitors. An EGFR-associated gene expression signature was identified in the basal-like SUM102 cell line and was used to classify a diverse set of sporadic breast tumors.</p> <p>Results</p> <p><it>In vitro</it>, breast basal-like cell lines were more sensitive to EGFR inhibitors compared to luminal cell lines. The basal-like tumor derived lines were also the most sensitive to carboplatin, which acted synergistically with cetuximab. An EGFR-associated signature was developed <it>in vitro</it>, evaluated on 241 primary breast tumors; three distinct clusters of genes were evident <it>in vivo</it>, two of which were predictive of poor patient outcomes. These EGFR-associated poor prognostic signatures were highly expressed in almost all basal-like tumors and many of the HER2+/ER- and Luminal B tumors.</p> <p>Conclusion</p> <p>These results suggest that breast basal-like cell lines are sensitive to EGFR inhibitors and carboplatin, and this combination may also be synergistic. <it>In vivo</it>, the EGFR-signatures were of prognostic value, were associated with tumor subtype, and were uniquely associated with the high expression of distinct EGFR-RAS-MEK pathway genes.</p

On the Application of the Non Linear Sigma Model to Spin Chains and Spin Ladders

We review the non linear sigma model approach (NLSM) to spin chains and spin ladders, presenting new results. The generalization of the Haldane's map to ladders in the Hamiltonian approach, give rise to different values of the $\theta$ parameter depending on the spin S, the number of legs $n_{\ell}$ and the choice of blocks needed to built up the NLSM fields. For rectangular blocks we obtain $\theta = 0$ or $2 \pi S$ depending on wether $n_{\ell}$, is even or odd, while for diagonal blocks we obtain $\theta = 2 \pi S n_{\ell}$. Both results agree modulo $2 \pi$, and yield the same prediction, namely that even ( resp. odd) ladders are gapped (resp. gapless). For even legged ladders we show that the spin gap collapses exponentially with $n_{\ell}$ and we propose a finite size correction to the gap formula recently derived by Chakravarty using the 2+1 NSLM, which gives a good fit of numerical results. We show the existence of a Haldane phase in the two legged ladder using diagonal blocks and finally we consider the phase diagram of dimerized ladders.Comment: 25 pages, Latex, 7 figures in postscript files, Proc. of the 1996 El Escorial Summer School on "Strongly Correlated Magnetic and Superconducting Systems". Some more references are adde

Department of Pathology, Thomas Jefferson University, Identification of conserved gene expression features between murine mammary carcinoma models and human breast tumors.

BACKGROUND: Although numerous mouse models of breast carcinomas have been developed, we do not know the extent to which any faithfully represent clinically significant human phenotypes. To address this need, we characterized mammary tumor gene expression profiles from 13 different murine models using DNA microarrays and compared the resulting data to those from human breast tumors. RESULTS: Unsupervised hierarchical clustering analysis showed that six models (TgWAP-Myc, TgMMTV-Neu, TgMMTV-PyMT, TgWAP-Int3, TgWAP-Tag, and TgC3(1)-Tag) yielded tumors with distinctive and homogeneous expression patterns within each strain. However, in each of four other models (TgWAP-T121, TgMMTV-Wnt1, Brca1Co/Co;TgMMTV-Cre;p53+/- and DMBA-induced), tumors with a variety of histologies and expression profiles developed. In many models, similarities to human breast tumors were recognized, including proliferation and human breast tumor subtype signatures. Significantly, tumors of several models displayed characteristics of human basal-like breast tumors, including two models with induced Brca1 deficiencies. Tumors of other murine models shared features and trended towards significance of gene enrichment with human luminal tumors; however, these murine tumors lacked expression of estrogen receptor (ER) and ER-regulated genes. TgMMTV-Neu tumors did not have a significant gene overlap with the human HER2+/ER- subtype and were more similar to human luminal tumors. CONCLUSION: Many of the defining characteristics of human subtypes were conserved among the mouse models. Although no single mouse model recapitulated all the expression features of a given human subtype, these shared expression features provide a common framework for an improved integration of murine mammary tumor models with human breast tumors

Identification of conserved gene expression features between murine mammary carcinoma models and human breast tumors

Comparison of mammary tumor gene-expression profiles from thirteen murine models using microarrays and with that of human breast tumors showed that many of the defining characteristics of human subtypes were conserved among mouse models

Allele-specific copy number analysis of tumors

We present an allele-specific copy number analysis of the in vivo breast cancer genome. We describe a unique bioinformatics approach, ASCAT (allele-specific copy number analysis of tumors), to accurately dissect the allele-specific copy number of solid tumors, simultaneously estimating and adjusting for both tumor ploidy and nonaberrant cell admixture. This allows calculation of “ASCAT profiles” (genome-wide allele-specific copy-number profiles) from which gains, losses, copy number-neutral events, and loss of heterozygosity (LOH) can accurately be determined. In an early-stage breast carcinoma series, we observe aneuploidy (>2.7n) in 45% of the cases and an average nonaberrant cell admixture of 49%. By aggregation of ASCAT profiles across our series, we obtain genomic frequency distributions of gains and losses, as well as genome-wide views of LOH and copy number-neutral events in breast cancer. In addition, the ASCAT profiles reveal differences in aberrant tumor cell fraction, ploidy, gains, losses, LOH, and copy number-neutral events between the five previously identified molecular breast cancer subtypes. Basal-like breast carcinomas have a significantly higher frequency of LOH compared with other subtypes, and their ASCAT profiles show large-scale loss of genomic material during tumor development, followed by a whole-genome duplication, resulting in near-triploid genomes. Finally, from the ASCAT profiles, we construct a genome-wide map of allelic skewness in breast cancer, indicating loci where one allele is preferentially lost, whereas the other allele is preferentially gained. We hypothesize that these alternative alleles have a different influence on breast carcinoma development

Basal-like Breast cancer DNA copy number losses identify genes involved in genomic instability, response to therapy, and patient survival

Breast cancer is a heterogeneous disease with known expression-defined tumor subtypes. DNA copy number studies have suggested that tumors within gene expression subtypes share similar DNA Copy number aberrations (CNA) and that CNA can be used to further sub-divide expression classes. To gain further insights into the etiologies of the intrinsic subtypes, we classified tumors according to gene expression subtype and next identified subtype-associated CNA using a novel method called SWITCHdna, using a training set of 180 tumors and a validation set of 359 tumors. Fisher’s exact tests, Chi-square approximations, and Wilcoxon rank-sum tests were performed to evaluate differences in CNA by subtype. To assess the functional significance of loss of a specific chromosomal region, individual genes were knocked down by shRNA and drug sensitivity, and DNA repair foci assays performed. Most tumor subtypes exhibited specific CNA. The Basal-like subtype was the most distinct with common losses of the regions containing RB1, BRCA1, INPP4B, and the greatest overall genomic instability. One Basal-like subtype-associated CNA was loss of 5q11–35, which contains at least three genes important for BRCA1-dependent DNA repair (RAD17, RAD50, and RAP80); these genes were predominantly lost as a pair, or all three simultaneously. Loss of two or three of these genes was associated with significantly increased genomic instability and poor patient survival. RNAi knockdown of RAD17, or RAD17/RAD50, in immortalized human mammary epithelial cell lines caused increased sensitivity to a PARP inhibitor and carboplatin, and inhibited BRCA1 foci formation in response to DNA damage. These data suggest a possible genetic cause for genomic instability in Basal-like breast cancers and a biological rationale for the use of DNA repair inhibitor related therapeutics in this breast cancer subtype.Electronic supplementary materialThe online version of this article (doi:10.1007/s10549-011-1846-y) contains supplementary material, which is available to authorized users

HIF2alpha cooperates with RAS to promote lung tumorigenesis in mice.

Members of the hypoxia-inducible factor (HIF) family of transcription factors regulate the cellular response to hypoxia. In non-small cell lung cancer (NSCLC), high HIF2alpha levels correlate with decreased overall survival, and inhibition of either the protein encoded by the canonical HIF target gene VEGF or VEGFR2 improves clinical outcomes. However, whether HIF2alpha is causal in imparting this poor prognosis is unknown. Here, we generated mice that conditionally express both a nondegradable variant of HIF2alpha and a mutant form of Kras (KrasG12D) that induces lung tumors. Mice expressing both Hif2a and KrasG12D in the lungs developed larger tumors and had an increased tumor burden and decreased survival compared with mice expressing only KrasG12D. Additionally, tumors expressing both KrasG12D and Hif2a were more invasive, demonstrated features of epithelial- mesenchymal transition (EMT), and exhibited increased angiogenesis associated with mobilization of circulating endothelial progenitor cells. These results implicate HIF2alpha causally in the pathogenesis of lung cancer in mice, demonstrate in vivo that HIF2alpha can promote expression of markers of EMT, and define HIF2alpha as a promoter of tumor growth and progression in a solid tumor other than renal cell carcinoma. They further suggest a possible causal relationship between HIF2alpha and prognosis in patients with NSCLC