Positive correlation between transcriptomic stemness and PI3K/AKT/mTOR signaling scores in breast cancer, and a counterintuitive relationship with PIK3CA genotype

A PI3Kα-selective inhibitor has recently been approved for use in breast tumors harboring mutations in PIK3CA, the gene encoding p110α. Preclinical studies have suggested that the PI3K/AKT/mTOR signaling pathway influences stemness, a dedifferentiation-related cellular phenotype associated with aggressive cancer. However, to date, no direct evidence for such a correlation has been demonstrated in human tumors. In two independent human breast cancer cohorts, encompassing nearly 3,000 tumor samples, transcriptional footprint-based analysis uncovered a positive linear association between transcriptionally-inferred PI3K/AKT/mTOR signaling scores and stemness scores. Unexpectedly, stratification of tumors according to PIK3CA genotype revealed a “biphasic” relationship of mutant PIK3CA allele dosage with these scores. Relative to tumor samples without PIK3CA mutations, the presence of a single copy of a hotspot PIK3CA variant was associated with lower PI3K/AKT/mTOR signaling and stemness scores, whereas the presence of multiple copies of PIK3CA hotspot mutations correlated with higher PI3K/AKT/mTOR signaling and stemness scores. This observation was recapitulated in a human cell model of heterozygous and homozygous PIK3CAH1047R expression. Collectively, our analysis (1) provides evidence for a signaling strength-dependent PI3K-stemness relationship in human breast cancer; (2) supports evaluation of the potential benefit of patient stratification based on a combination of conventional PI3K pathway genetic information with transcriptomic indices of PI3K signaling activation

Further properties on the core partial order and other matrix partial orders

This paper carries further the study of core partial order initiated by Baksalary and Trenkler [Core inverse of matrices, Linear Multilinear Algebra. 2010;58:681-697]. We have extensively studied the core partial order, and some new characterizations are obtained in this paper. In addition, simple expressions for the already known characterizations of the minus, the star (and one-sided star), the sharp (and one-sided sharp) and the diamond partial orders are also obtained by using a Hartwig-Spindelbck decomposition.This author was partially supported by Ministry of Education of Spain [grant number DGI MTM2010-18228] and by Universidad Nacional de La Pampa, Argentina, Facultad de Ingenieria [grant number Resol. No 049/11].Malik, SB.; Rueda, LC.; Thome, N. (2014). Further properties on the core partial order and other matrix partial orders. Linear and Multilinear Algebra. 62(12):1629-1648. https://doi.org/10.1080/03081087.2013.839676S162916486212Mitra, S. K., & Bhimasankaram, P. (2010). MATRIX PARTIAL ORDERS, SHORTED OPERATORS AND APPLICATIONS. SERIES IN ALGEBRA. doi:10.1142/9789812838452Baksalary, J. K., & Hauke, J. (1990). A further algebraic version of Cochran’s theorem and matrix partial orderings. Linear Algebra and its Applications, 127, 157-169. doi:10.1016/0024-3795(90)90341-9Baksalary, O. M., & Trenkler, G. (2010). Core inverse of matrices. Linear and Multilinear Algebra, 58(6), 681-697. doi:10.1080/03081080902778222Baksalary, J. K., Baksalary, O. M., & Liu, X. (2003). Further properties of the star, left-star, right-star, and minus partial orderings. Linear Algebra and its Applications, 375, 83-94. doi:10.1016/s0024-3795(03)00609-8Groβ, J., Hauke, J., & Markiewicz, A. (1999). Partial orderings, preorderings, and the polar decomposition of matrices. Linear Algebra and its Applications, 289(1-3), 161-168. doi:10.1016/s0024-3795(98)10108-8Mosić, D., & Djordjević, D. S. (2012). Reverse order law for the group inverse in rings. Applied Mathematics and Computation, 219(5), 2526-2534. doi:10.1016/j.amc.2012.08.088Patrício, P., & Costa, A. (2009). On the Drazin index of regular elements. Open Mathematics, 7(2). doi:10.2478/s11533-009-0015-6Rakić, D. S., & Djordjević, D. S. (2012). Space pre-order and minus partial order for operators on Banach spaces. Aequationes mathematicae, 85(3), 429-448. doi:10.1007/s00010-012-0133-2Tošić, M., & Cvetković-Ilić, D. S. (2012). Invertibility of a linear combination of two matrices and partial orderings. Applied Mathematics and Computation, 218(9), 4651-4657. doi:10.1016/j.amc.2011.10.052Hartwig, R. E., & Spindelböck, K. (1983). Matrices for whichA∗andA†commute. Linear and Multilinear Algebra, 14(3), 241-256. doi:10.1080/03081088308817561Baksalary, O. M., Styan, G. P. H., & Trenkler, G. (2009). On a matrix decomposition of Hartwig and Spindelböck. Linear Algebra and its Applications, 430(10), 2798-2812. doi:10.1016/j.laa.2009.01.015Mielniczuk, J. (2011). Note on the core matrix partial ordering. Discussiones Mathematicae Probability and Statistics, 31(1-2), 71. doi:10.7151/dmps.1134Meyer, C. (2000). Matrix Analysis and Applied Linear Algebra. doi:10.1137/1.978089871951

A response to Yu et al. "A forward-backward fragment assembling algorithm for the identification of genomic amplification and deletion breakpoints using high-density single nucleotide polymorphism (SNP) array", BMC Bioinformatics 2007, 8: 145

<p>Abstract</p> <p>Background</p> <p>Yu et al. (BMC Bioinformatics 2007,8: 145+) have recently compared the performance of several methods for the detection of genomic amplification and deletion breakpoints using data from high-density single nucleotide polymorphism arrays. One of the methods compared is our non-homogenous Hidden Markov Model approach. Our approach uses Markov Chain Monte Carlo for inference, but Yu et al. ran the sampler for a severely insufficient number of iterations for a Markov Chain Monte Carlo-based method. Moreover, they did not use the appropriate reference level for the non-altered state.</p> <p>Methods</p> <p>We rerun the analysis in Yu et al. using appropriate settings for both the Markov Chain Monte Carlo iterations and the reference level. Additionally, to show how easy it is to obtain answers to additional specific questions, we have added a new analysis targeted specifically to the detection of breakpoints.</p> <p>Results</p> <p>The reanalysis shows that the performance of our method is comparable to that of the other methods analyzed. In addition, we can provide probabilities of a given spot being a breakpoint, something unique among the methods examined.</p> <p>Conclusion</p> <p>Markov Chain Monte Carlo methods require using a sufficient number of iterations before they can be assumed to yield samples from the distribution of interest. Running our method with too small a number of iterations cannot be representative of its performance. Moreover, our analysis shows how our original approach can be easily adapted to answer specific additional questions (e.g., identify edges).</p

Detection of recurrent copy number alterations in the genome: taking among-subject heterogeneity seriously

Se adjunta un fichero pdf con los datos de investigación titulado "Supplementary Material for \Detection of Recurrent Copy Number Alterations in the Genome: taking among-subject heterogeneity seriously"Background: Alterations in the number of copies of genomic DNA that are common or recurrent among diseased individuals are likely to contain disease-critical genes. Unfortunately, defining common or recurrent copy number alteration (CNA) regions remains a challenge. Moreover, the heterogeneous nature of many diseases requires that we search for common or recurrent CNA regions that affect only some subsets of the samples (without knowledge of the regions and subsets affected), but this is neglected by most methods. Results: We have developed two methods to define recurrent CNA regions from aCGH data. Our methods are unique and qualitatively different from existing approaches: they detect regions over both the complete set of arrays and alterations that are common only to some subsets of the samples (i.e., alterations that might characterize previously unknown groups); they use probabilities of alteration as input and return probabilities of being a common region, thus allowing researchers to modify thresholds as needed; the two parameters of the methods have an immediate, straightforward, biological interpretation. Using data from previous studies, we show that we can detect patterns that other methods miss and that researchers can modify, as needed, thresholds of immediate interpretability and develop custom statistics to answer specific research questions. Conclusion: These methods represent a qualitative advance in the location of recurrent CNA regions, highlight the relevance of population heterogeneity for definitions of recurrence, and can facilitate the clustering of samples with respect to patterns of CNA. Ultimately, the methods developed can become important tools in the search for genomic regions harboring disease-critical genesFunding provided by Fundación de Investigación Médica Mutua Madrileña. Publication charges covered by projects CONSOLIDER: CSD2007-00050 of the Spanish Ministry of Science and Innovation and by RTIC COMBIOMED RD07/0067/0014 of the Spanish Health Ministr

Associations between genomic stratification of breast cancer and centrally reviewed tumour pathology in the METABRIC cohort.

The integration of genomic and transcriptomic profiles of 2000 breast tumours from the METABRIC [Molecular Taxonomy of Breast Cancer International Consortium] cohort revealed ten subtypes, termed integrative clusters (IntClust/s), characterised by distinct genomic drivers. Central histopathology (N = 1643) review was undertaken to explore the relationship between these ten molecular subtypes and traditional clinicopathological features. IntClust subtypes were significantly associated with histological type, tumour grade, receptor status, and lymphocytic infiltration (p < 0.0001). Lymph node status and Nottingham Prognostic Index [NPI] categories were also significantly associated with IntClust subtype. IntClust 3 was enriched for tubular and lobular carcinomas, the latter largely accounting for the association with CDH1 mutations in this cluster. Mucinous carcinomas were not present in IntClusts 5 or 10, but did not show an association with any of the remaining IntClusts. In contrast, medullary-like cancers were associated with IntClust 10 (15/26). Hormone receptor-positive tumours were scattered across all IntClusts. IntClust 5 was dominated by HER2 positivity (127/151), including both hormone receptor-positive (60/72) and hormone receptor-negative tumours (67/77). Triple-negative tumours comprised the majority of IntClust 10 (132/159) and around a quarter of IntClust 4 (52/217). Whilst the ten IntClust subtypes of breast cancer show characteristic patterns of association with traditional clinicopathological variables, no IntClust can be adequately identified by these variables alone. Hence, the addition of genomic stratification has the potential to enhance the biological relevance of the current clinical evaluation and facilitate genome-guided therapeutic strategies

A forward-backward fragment assembling algorithm for the identification of genomic amplification and deletion breakpoints using high-density single nucleotide polymorphism (SNP) array

<p>Abstract</p> <p>Background</p> <p>DNA copy number aberration (CNA) is one of the key characteristics of cancer cells. Recent studies demonstrated the feasibility of utilizing high density single nucleotide polymorphism (SNP) genotyping arrays to detect CNA. Compared with the two-color array-based comparative genomic hybridization (array-CGH), the SNP arrays offer much higher probe density and lower signal-to-noise ratio at the single SNP level. To accurately identify small segments of CNA from SNP array data, segmentation methods that are sensitive to CNA while resistant to noise are required.</p> <p>Results</p> <p>We have developed a highly sensitive algorithm for the edge detection of copy number data which is especially suitable for the SNP array-based copy number data. The method consists of an over-sensitive edge-detection step and a test-based forward-backward edge selection step.</p> <p>Conclusion</p> <p>Using simulations constructed from real experimental data, the method shows high sensitivity and specificity in detecting small copy number changes in focused regions. The method is implemented in an R package FASeg, which includes data processing and visualization utilities, as well as libraries for processing Affymetrix SNP array data.</p

Bayesian estimation of genomic copy number with single nucleotide polymorphism genotyping arrays

<p>Abstract</p> <p>Background</p> <p>The identification of copy number aberration in the human genome is an important area in cancer research. We develop a model for determining genomic copy numbers using high-density single nucleotide polymorphism genotyping microarrays. The method is based on a Bayesian spatial normal mixture model with an unknown number of components corresponding to true copy numbers. A reversible jump Markov chain Monte Carlo algorithm is used to implement the model and perform posterior inference.</p> <p>Results</p> <p>The performance of the algorithm is examined on both simulated and real cancer data, and it is compared with the popular CNAG algorithm for copy number detection.</p> <p>Conclusions</p> <p>We demonstrate that our Bayesian mixture model performs at least as well as the hidden Markov model based CNAG algorithm and in certain cases does better. One of the added advantages of our method is the flexibility of modeling normal cell contamination in tumor samples.</p

Detection of copy number variation from array intensity and sequencing read depth using a stepwise Bayesian model

Abstract Background Copy number variants (CNVs) have been demonstrated to occur at a high frequency and are now widely believed to make a significant contribution to the phenotypic variation in human populations. Array-based comparative genomic hybridization (array-CGH) and newly developed read-depth approach through ultrahigh throughput genomic sequencing both provide rapid, robust, and comprehensive methods to identify CNVs on a whole-genome scale. Results We developed a Bayesian statistical analysis algorithm for the detection of CNVs from both types of genomic data. The algorithm can analyze such data obtained from PCR-based bacterial artificial chromosome arrays, high-density oligonucleotide arrays, and more recently developed high-throughput DNA sequencing. Treating parameters--e.g., the number of CNVs, the position of each CNV, and the data noise level--that define the underlying data generating process as random variables, our approach derives the posterior distribution of the genomic CNV structure given the observed data. Sampling from the posterior distribution using a Markov chain Monte Carlo method, we get not only best estimates for these unknown parameters but also Bayesian credible intervals for the estimates. We illustrate the characteristics of our algorithm by applying it to both synthetic and experimental data sets in comparison to other segmentation algorithms. Conclusions In particular, the synthetic data comparison shows that our method is more sensitive than other approaches at low false positive rates. Furthermore, given its Bayesian origin, our method can also be seen as a technique to refine CNVs identified by fast point-estimate methods and also as a framework to integrate array-CGH and sequencing data with other CNV-related biological knowledge, all through informative priors.</p

A high-resolution integrated map of copy number polymorphisms within and between breeds of the modern domesticated dog

<p>Abstract</p> <p>Background</p> <p>Structural variation contributes to the rich genetic and phenotypic diversity of the modern domestic dog, <it>Canis lupus familiaris</it>, although compared to other organisms, catalogs of canine copy number variants (CNVs) are poorly defined. To this end, we developed a customized high-density tiling array across the canine genome and used it to discover CNVs in nine genetically diverse dogs and a gray wolf.</p> <p>Results</p> <p>In total, we identified 403 CNVs that overlap 401 genes, which are enriched for defense/immunity, oxidoreductase, protease, receptor, signaling molecule and transporter genes. Furthermore, we performed detailed comparisons between CNVs located within versus outside of segmental duplications (SDs) and find that CNVs in SDs are enriched for gene content and complexity. Finally, we compiled all known dog CNV regions and genotyped them with a custom aCGH chip in 61 dogs from 12 diverse breeds. These data allowed us to perform the first population genetics analysis of canine structural variation and identify CNVs that potentially contribute to breed specific traits.</p> <p>Conclusions</p> <p>Our comprehensive analysis of canine CNVs will be an important resource in genetically dissecting canine phenotypic and behavioral variation.</p

Determining Frequent Patterns of Copy Number Alterations in Cancer

Cancer progression is often driven by an accumulation of genetic changes but also accompanied by increasing genomic instability. These processes lead to a complicated landscape of copy number alterations (CNAs) within individual tumors and great diversity across tumor samples. High resolution array-based comparative genomic hybridization (aCGH) is being used to profile CNAs of ever larger tumor collections, and better computational methods for processing these data sets and identifying potential driver CNAs are needed. Typical studies of aCGH data sets take a pipeline approach, starting with segmentation of profiles, calls of gains and losses, and finally determination of frequent CNAs across samples. A drawback of pipelines is that choices at each step may produce different results, and biases are propagated forward. We present a mathematically robust new method that exploits probe-level correlations in aCGH data to discover subsets of samples that display common CNAs. Our algorithm is related to recent work on maximum-margin clustering. It does not require pre-segmentation of the data and also provides grouping of recurrent CNAs into clusters. We tested our approach on a large cohort of glioblastoma aCGH samples from The Cancer Genome Atlas and recovered almost all CNAs reported in the initial study. We also found additional significant CNAs missed by the original analysis but supported by earlier studies, and we identified significant correlations between CNAs