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Yuan X, Gao M, Bai J, Duan J. SVSR: A Program to Simulate Structural Variations and Generate Sequencing Reads for Multiple Platforms. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2020; 17:1082-1091. [PMID: 30334804 DOI: 10.1109/tcbb.2018.2876527] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Structural variation accounts for a major fraction of mutations in the human genome and confers susceptibility to complex diseases. Next generation sequencing along with the rapid development of computational methods provides a cost-effective procedure to detect such variations. Simulation of structural variations and sequencing reads with real characteristics is essential for benchmarking the computational methods. Here, we develop a new program, SVSR, to simulate five types of structural variations (indels, tandem duplication, CNVs, inversions, and translocations) and SNPs for the human genome and to generate sequencing reads with features from popular platforms (Illumina, SOLiD, 454, and Ion Torrent). We adopt a selection model trained from real data to predict copy number states, starting from the first site of a particular genome to the end. Furthermore, we utilize references of microbial genomes to produce insertion fragments and design probabilistic models to imitate inversions and translocations. Moreover, we create platform-specific errors and base quality profiles to generate normal, tumor, or normal-tumor mixture reads. Experimental results show that SVSR could capture more features that are realistic and generate datasets with satisfactory quality scores. SVSR is able to evaluate the performance of structural variation detection methods and guide the development of new computational methods.
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Xi J, Li A, Wang M. HetRCNA: A Novel Method to Identify Recurrent Copy Number Alternations from Heterogeneous Tumor Samples Based on Matrix Decomposition Framework. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2020; 17:422-434. [PMID: 29994262 DOI: 10.1109/tcbb.2018.2846599] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
A common strategy to discovering cancer associated copy number aberrations (CNAs) from a cohort of cancer samples is to detect recurrent CNAs (RCNAs). Although the previous methods can successfully identify communal RCNAs shared by nearly all tumor samples, detecting subgroup-specific RCNAs and their related subgroup samples from cancer samples with heterogeneity is still invalid for these existing approaches. In this paper, we introduce a novel integrated method called HetRCNA, which can identify statistically significant subgroup-specific RCNAs and their related subgroup samples. Based on matrix decomposition framework with weight constraint, HetRCNA can successfully measure the subgroup samples by coefficients of left vectors with weight constraint and subgroup-specific RCNAs by coefficients of the right vectors and significance test. When we evaluate HetRCNA on simulated dataset, the results show that HetRCNA gives the best performances among the competing methods and is robust to the noise factors of the simulated data. When HetRCNA is applied on a real breast cancer dataset, our approach successfully identifies a bunch of RCNA regions and the result is highly correlated with the results of the other two investigated approaches. Notably, the genomic regions identified by HetRCNA harbor many breast cancer related genes reported by previous researches.
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Alonso MH, Aussó S, Lopez-Doriga A, Cordero D, Guinó E, Solé X, Barenys M, de Oca J, Capella G, Salazar R, Sanz-Pamplona R, Moreno V. Comprehensive analysis of copy number aberrations in microsatellite stable colon cancer in view of stromal component. Br J Cancer 2017; 117:421-431. [PMID: 28683472 PMCID: PMC5537504 DOI: 10.1038/bjc.2017.208] [Citation(s) in RCA: 91] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2017] [Revised: 05/11/2017] [Accepted: 06/09/2017] [Indexed: 01/07/2023] Open
Abstract
BACKGROUND Somatic copy number aberrations (CNAs) are common acquired changes in cancer cells having an important role in the progression of colon cancer (colorectal cancer, CRC). This study aimed to perform a characterisation of CNA and their impact in gene expression. METHODS Copy number aberrations were inferred from SNP array data in a series of 99 CRC. Copy number aberration events were calculated and used to assess the association between copy number dosage, clinical and molecular characteristics of the tumours, and gene expression changes. All analyses were adjusted for the quantity of stroma in each sample, which was inferred from gene expression data. RESULTS High heterogeneity among samples was observed; the proportion of altered genome ranged between 0.04 and 26.6%. Recurrent CNA regions with gains were frequent in chromosomes 7p, 8q, 13q, and 20, whereas 8p, 17p, and 18 cumulated losses. A significant positive correlation was observed between the number of somatic mutations and total CNA (Spearman's r=0.42, P=0.006). Approximately 37% of genes located in CNA regions changed their level of expression and the average partial correlation (adjusted for stromal content) with copy number was 0.54 (interquartile range 0.20 to 0.81). Altered genes showed enrichment in pathways relevant for CRC. Tumours classified as CMS2 and CMS4 by the consensus molecular subtyping showed higher frequency of CNA. Losses of one small region in 1p36.33, with gene CDK11B, were associated with poor prognosis. More than 66% of the recurrent CNA were validated in the The Cancer Genome Atlas (TCGA) data when analysed with the same procedure. Furthermore, 79% of the genes with altered expression in our data were validated in the TCGA. CONCLUSIONS Although CNA are frequent events in microsatellite stable CRC, few focal recurrent regions were found. These aberrations have strong effects on gene expression and contribute to deregulate relevant cancer pathways. Owing to the diploid nature of stromal cells, it is important to consider the purity of tumour samples to accurately calculate CNA events in CRC.
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Affiliation(s)
- M Henar Alonso
- Unit of Biomarkers and Susceptibility, Cancer Prevention and Control Program, Catalan Institute of Oncology (ICO), CIBERESP, Gran Via 199, Hospitalet Llobregat, 08908 Barcelona, Spain.,Molecular Mechanisms and Experimental Therapy Cancer Program, Bellvitge Biomedical Research Institute (IDIBELL), Barcelona, Spain
| | - Susanna Aussó
- Unit of Biomarkers and Susceptibility, Cancer Prevention and Control Program, Catalan Institute of Oncology (ICO), CIBERESP, Gran Via 199, Hospitalet Llobregat, 08908 Barcelona, Spain.,Molecular Mechanisms and Experimental Therapy Cancer Program, Bellvitge Biomedical Research Institute (IDIBELL), Barcelona, Spain
| | - Adriana Lopez-Doriga
- Unit of Biomarkers and Susceptibility, Cancer Prevention and Control Program, Catalan Institute of Oncology (ICO), CIBERESP, Gran Via 199, Hospitalet Llobregat, 08908 Barcelona, Spain.,Molecular Mechanisms and Experimental Therapy Cancer Program, Bellvitge Biomedical Research Institute (IDIBELL), Barcelona, Spain
| | - David Cordero
- Unit of Biomarkers and Susceptibility, Cancer Prevention and Control Program, Catalan Institute of Oncology (ICO), CIBERESP, Gran Via 199, Hospitalet Llobregat, 08908 Barcelona, Spain.,Molecular Mechanisms and Experimental Therapy Cancer Program, Bellvitge Biomedical Research Institute (IDIBELL), Barcelona, Spain
| | - Elisabet Guinó
- Unit of Biomarkers and Susceptibility, Cancer Prevention and Control Program, Catalan Institute of Oncology (ICO), CIBERESP, Gran Via 199, Hospitalet Llobregat, 08908 Barcelona, Spain.,Molecular Mechanisms and Experimental Therapy Cancer Program, Bellvitge Biomedical Research Institute (IDIBELL), Barcelona, Spain
| | - Xavier Solé
- Unit of Biomarkers and Susceptibility, Cancer Prevention and Control Program, Catalan Institute of Oncology (ICO), CIBERESP, Gran Via 199, Hospitalet Llobregat, 08908 Barcelona, Spain.,Molecular Mechanisms and Experimental Therapy Cancer Program, Bellvitge Biomedical Research Institute (IDIBELL), Barcelona, Spain
| | - Mercè Barenys
- Molecular Mechanisms and Experimental Therapy Cancer Program, Bellvitge Biomedical Research Institute (IDIBELL), Barcelona, Spain.,Gastroenterology Service, Hospital de Viladecans, Barcelona, Spain.,Faculty of Medicine, Department of Clinical Sciences, University of Barcelona (UB), Barcelona, Spain
| | - Javier de Oca
- Molecular Mechanisms and Experimental Therapy Cancer Program, Bellvitge Biomedical Research Institute (IDIBELL), Barcelona, Spain.,Faculty of Medicine, Department of Clinical Sciences, University of Barcelona (UB), Barcelona, Spain.,Department of General and Digestive Surgery, Bellvitge University Hospital, Barcelona, Spain
| | - Gabriel Capella
- Molecular Mechanisms and Experimental Therapy Cancer Program, Bellvitge Biomedical Research Institute (IDIBELL), Barcelona, Spain.,Faculty of Medicine, Department of Clinical Sciences, University of Barcelona (UB), Barcelona, Spain.,Hereditary Cancer Program, Catalan Institute of Oncology (ICO) and CIBERONC, Barcelona, Spain
| | - Ramón Salazar
- Molecular Mechanisms and Experimental Therapy Cancer Program, Bellvitge Biomedical Research Institute (IDIBELL), Barcelona, Spain.,Faculty of Medicine, Department of Clinical Sciences, University of Barcelona (UB), Barcelona, Spain.,Oncology Department, Catalan Institute of Oncology (ICO) and CIBERONC, Barcelona, Spain
| | - Rebeca Sanz-Pamplona
- Unit of Biomarkers and Susceptibility, Cancer Prevention and Control Program, Catalan Institute of Oncology (ICO), CIBERESP, Gran Via 199, Hospitalet Llobregat, 08908 Barcelona, Spain.,Molecular Mechanisms and Experimental Therapy Cancer Program, Bellvitge Biomedical Research Institute (IDIBELL), Barcelona, Spain
| | - Victor Moreno
- Unit of Biomarkers and Susceptibility, Cancer Prevention and Control Program, Catalan Institute of Oncology (ICO), CIBERESP, Gran Via 199, Hospitalet Llobregat, 08908 Barcelona, Spain.,Molecular Mechanisms and Experimental Therapy Cancer Program, Bellvitge Biomedical Research Institute (IDIBELL), Barcelona, Spain.,Faculty of Medicine, Department of Clinical Sciences, University of Barcelona (UB), Barcelona, Spain
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A novel network regularized matrix decomposition method to detect mutated cancer genes in tumour samples with inter-patient heterogeneity. Sci Rep 2017; 7:2855. [PMID: 28588243 PMCID: PMC5460199 DOI: 10.1038/s41598-017-03141-w] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2017] [Accepted: 04/20/2017] [Indexed: 01/01/2023] Open
Abstract
Inter-patient heterogeneity is a major challenge for mutated cancer genes detection which is crucial to advance cancer diagnostics and therapeutics. To detect mutated cancer genes in heterogeneous tumour samples, a prominent strategy is to determine whether the genes are recurrently mutated in their interaction network context. However, recent studies show that some cancer genes in different perturbed pathways are mutated in different subsets of samples. Subsequently, these genes may not display significant mutational recurrence and thus remain undiscovered even in consideration of network information. We develop a novel method called mCGfinder to efficiently detect mutated cancer genes in tumour samples with inter-patient heterogeneity. Based on matrix decomposition framework incorporated with gene interaction network information, mCGfinder can successfully measure the significance of mutational recurrence of genes in a subset of samples. When applying mCGfinder on TCGA somatic mutation datasets of five types of cancers, we find that the genes detected by mCGfinder are significantly enriched for known cancer genes, and yield substantially smaller p-values than other existing methods. All the results demonstrate that mCGfinder is an efficient method in detecting mutated cancer genes.
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Xi J, Li A. Discovering Recurrent Copy Number Aberrations in Complex Patterns via Non-Negative Sparse Singular Value Decomposition. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2016; 13:656-668. [PMID: 26372614 DOI: 10.1109/tcbb.2015.2474404] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Recurrent copy number aberrations (RCNAs) in multiple cancer samples are strongly associated with tumorigenesis, and RCNA discovery is helpful to cancer research and treatment. Despite the emergence of numerous RCNA discovering methods, most of them are unable to detect RCNAs in complex patterns that are influenced by complicating factors including aberration in partial samples, co-existing of gains and losses and normal-like tumor samples. Here, we propose a novel computational method, called non-negative sparse singular value decomposition (NN-SSVD), to address the RCNA discovering problem in complex patterns. In NN-SSVD, the measurement of RCNA is based on the aberration frequency in a part of samples rather than all samples, which can circumvent the complexity of different RCNA patterns. We evaluate NN-SSVD on synthetic dataset by comparison on detection scores and Receiver Operating Characteristics curves, and the results show that NN-SSVD outperforms existing methods in RCNA discovery and demonstrate more robustness to RCNA complicating factors. Applying our approach on a breast cancer dataset, we successfully identify a number of genomic regions that are strongly correlated with previous studies, which harbor a bunch of known breast cancer associated genes.
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Commo F, Guinney J, Ferté C, Bot B, Lefebvre C, Soria JC, André F. rCGH: a comprehensive array-based genomic profile platform for precision medicine. Bioinformatics 2015; 32:1402-4. [PMID: 26708336 PMCID: PMC4848396 DOI: 10.1093/bioinformatics/btv718] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2015] [Accepted: 12/03/2015] [Indexed: 12/19/2022] Open
Abstract
Summary: We present rCGH, a comprehensive array-based comparative genomic hybridization analysis workflow, integrating computational improvements and functionalities specifically designed for precision medicine. rCGH supports the major microarray platforms, ensures a full traceability and facilitates profiles interpretation and decision-making through sharable interactive visualizations. Availability and implementation: The rCGH R package is available on bioconductor (under Artistic-2.0). The aCGH-viewer is available at https://fredcommo.shinyapps.io/aCGH_viewer, and the application implementation is freely available for installation at https://github.com/fredcommo/aCGH_viewer. Contact:frederic.commo@gustaveroussy.fr Supplementary information:Supplementary data are available at Bioinformatics online.
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Affiliation(s)
- Frederic Commo
- INSERM U981, Gustave Roussy, University Paris-Sud, Villejuif 94805, France, Sage Bionetworks, Seattle, WA 98109, USA and
| | | | - Charles Ferté
- INSERM U981, Gustave Roussy, University Paris-Sud, Villejuif 94805, France, Sage Bionetworks, Seattle, WA 98109, USA and
| | - Brian Bot
- Sage Bionetworks, Seattle, WA 98109, USA and
| | - Celine Lefebvre
- INSERM U981, Gustave Roussy, University Paris-Sud, Villejuif 94805, France
| | - Jean-Charles Soria
- INSERM U981, Gustave Roussy, University Paris-Sud, Villejuif 94805, France, Department of Medical Oncology, Gustave Roussy, Villejuif 94805, France
| | - Fabrice André
- INSERM U981, Gustave Roussy, University Paris-Sud, Villejuif 94805, France, Department of Medical Oncology, Gustave Roussy, Villejuif 94805, France
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Walter V, Wright FA, Nobel AB. Consistent testing for recurrent genomic aberrations. Biometrika 2015; 102:783-796. [PMID: 30799871 DOI: 10.1093/biomet/asv046] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We consider the detection and identification of recurrent departures from stationary behaviour in genomic or similarly arranged data containing measurements at an ordered set of variables. Our primary focus is on departures that occur only at a single variable, or within a small window of contiguous variables, but involve more than one sample. This encompasses the identification of aberrant markers in genome-wide measurements of DNA copy number and DNA methylation, as well as meta-analyses of genome-wide association studies. We propose and analyse a cyclic shift-based procedure for testing recurrent departures from stationarity. Our analysis establishes the consistency of cyclic shift [Formula: see text]-values for datasets with a fixed set of samples as the number of observed variables tends to infinity, under the assumption that each sample is an independent realization of a stationary Markov chain. Our results apply to any test statistic satisfying a simple invariance condition.
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Affiliation(s)
- V Walter
- Department of Biochemistry and Molecular Biology, Pennyslvania State University College of Medicine, Milton S. Hershey Medical Center, 500 University Drive, P.O. Box 850, Hershey, Pennsylvania 17033 U.S.A
| | - F A Wright
- Department of Statistics, North Carolina State University Bioinformatics Research Center, Campus Box 7566, 2601 Stinson Drive, Raleigh, North Carolina 27695 U.S.A.,
| | - A B Nobel
- Department of Statistics and Operations Research, CB 3260, University of North Carolina, Chapel Hill, North Carolina, 27599 U.S.A.,
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Wang X, Li X, Cheng Y, Sun X, Sun X, Self S, Kooperberg C, Dai JY. Copy number alterations detected by whole-exome and whole-genome sequencing of esophageal adenocarcinoma. Hum Genomics 2015; 9:22. [PMID: 26374103 PMCID: PMC4570720 DOI: 10.1186/s40246-015-0044-0] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2015] [Accepted: 08/25/2015] [Indexed: 02/08/2023] Open
Abstract
Background Esophageal adenocarcinoma (EA) is among the leading causes of cancer mortality, especially in developed countries. A high level of somatic copy number alterations (CNAs) accumulates over the decades in the progression from Barrett’s esophagus, the precursor lesion, to EA. Accurate identification of somatic CNAs is essential to understand cancer development. Many studies have been conducted for the detection of CNA in EA using microarrays. Next-generation sequencing (NGS) technologies are believed to have advantages in sensitivity and accuracy to detect CNA, yet no NGS-based CNA detection in EA has been reported. Results In this study, we analyzed whole-exome (WES) and whole-genome sequencing (WGS) data for detecting CNA from a published large-scale genomic study of EA. Two specific comparisons were conducted. First, the recurrent CNAs based on WGS and WES data from 145 EA samples were compared to those found in five previous microarray-based studies. We found that the majority of the previously identified regions were also detected in this study. Interestingly, some novel amplifications and deletions were discovered using the NGS data. In particular, SKI and PRKCZ detected in a deletion region are involved in transforming growth factor-β pathway, suggesting the potential utility of novel biomarkers for EA. Second, we compared CNAs detected in WGS and WES data from the same 15 EA samples. No large-scale CNA was identified statistically more frequently by WES or WGS, while more focal-scale CNAs were detected by WGS than by WES. Conclusions Our results suggest that NGS can replace microarrays to detect CNA in EA. WGS is superior to WES in that it can offer finer resolution for the detection, though if the interest is on recurrent CNAs, WES can be preferable to WGS for its cost-effectiveness. Electronic supplementary material The online version of this article (doi:10.1186/s40246-015-0044-0) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Xiaoyu Wang
- Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Research Center, Seattle, WA, USA.
| | - Xiaohong Li
- Human Biology, Fred Hutchinson Cancer Research Center, Seattle, WA, USA. .,Public Health Science Division, Fred Hutchinson Cancer Research Center, Seattle, WA, USA.
| | - Yichen Cheng
- Public Health Science Division, Fred Hutchinson Cancer Research Center, Seattle, WA, USA.
| | - Xin Sun
- Institute of Occupational Health and Poison Control, Chinese Center for Disease Control and Prevention, Beijing, China.
| | - Xibin Sun
- Henan Office for Cancer Research and Control, Henan Cancer Hospital, Zhengzhou, Henan, China.
| | - Steve Self
- Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Research Center, Seattle, WA, USA.
| | - Charles Kooperberg
- Public Health Science Division, Fred Hutchinson Cancer Research Center, Seattle, WA, USA.
| | - James Y Dai
- Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Research Center, Seattle, WA, USA. .,Public Health Science Division, Fred Hutchinson Cancer Research Center, Seattle, WA, USA.
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Integration of genomic data enables selective discovery of breast cancer drivers. Cell 2014; 159:1461-75. [PMID: 25433701 DOI: 10.1016/j.cell.2014.10.048] [Citation(s) in RCA: 70] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2014] [Revised: 08/01/2014] [Accepted: 10/03/2014] [Indexed: 01/03/2023]
Abstract
Identifying driver genes in cancer remains a crucial bottleneck in therapeutic development and basic understanding of the disease. We developed Helios, an algorithm that integrates genomic data from primary tumors with data from functional RNAi screens to pinpoint driver genes within large recurrently amplified regions of DNA. Applying Helios to breast cancer data identified a set of candidate drivers highly enriched with known drivers (p < 10(-14)). Nine of ten top-scoring Helios genes are known drivers of breast cancer, and in vitro validation of 12 candidates predicted by Helios found ten conferred enhanced anchorage-independent growth, demonstrating Helios's exquisite sensitivity and specificity. We extensively characterized RSF-1, a driver identified by Helios whose amplification correlates with poor prognosis, and found increased tumorigenesis and metastasis in mouse models. We have demonstrated a powerful approach for identifying driver genes and how it can yield important insights into cancer.
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Wu HT, Hajirasouliha I, Raphael BJ. Detecting independent and recurrent copy number aberrations using interval graphs. ACTA ACUST UNITED AC 2014; 30:i195-203. [PMID: 24931984 PMCID: PMC4058951 DOI: 10.1093/bioinformatics/btu276] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Abstract
Motivation: Somatic copy number aberrations (SCNAs) are frequent in cancer genomes, but many of these are random, passenger events. A common strategy to distinguish functional aberrations from passengers is to identify those aberrations that are recurrent across multiple samples. However, the extensive variability in the length and position of SCNAs makes the problem of identifying recurrent aberrations notoriously difficult. Results: We introduce a combinatorial approach to the problem of identifying independent and recurrent SCNAs, focusing on the key challenging of separating the overlaps in aberrations across individuals into independent events. We derive independent and recurrent SCNAs as maximal cliques in an interval graph constructed from overlaps between aberrations. We efficiently enumerate all such cliques, and derive a dynamic programming algorithm to find an optimal selection of non-overlapping cliques, resulting in a very fast algorithm, which we call RAIG (Recurrent Aberrations from Interval Graphs). We show that RAIG outperforms other methods on simulated data and also performs well on data from three cancer types from The Cancer Genome Atlas (TCGA). In contrast to existing approaches that employ various heuristics to select independent aberrations, RAIG optimizes a well-defined objective function. We show that this allows RAIG to identify rare aberrations that are likely functional, but are obscured by overlaps with larger passenger aberrations. Availability:http://compbio.cs.brown.edu/software. Contact:braphael@brown.edu Supplementary information:Supplementary data are available at Bioinformatics online.
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Affiliation(s)
- Hsin-Ta Wu
- Department of Computer Science and Center for Computational Molecular Biology, Brown University, Providence, RI 02906, USA
| | - Iman Hajirasouliha
- Department of Computer Science and Center for Computational Molecular Biology, Brown University, Providence, RI 02906, USA
| | - Benjamin J Raphael
- Department of Computer Science and Center for Computational Molecular Biology, Brown University, Providence, RI 02906, USA
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