Reconstructing DNA copy number by joint segmentation of multiple sequences

Breast tumours maintain a reservoir of subclonal diversity during expansion

Our knowledge of copy number evolution during the expansion of primary breast tumours is limited^1,2. Here, to investigate this process, we developed a single-cell, single-molecule DNA-sequencing method and performed copy number analysis of 16,178 single cells from 8 human triple-negative breast cancers and 4 cell lines. The results show that breast tumours and cell lines comprise a large milieu of subclones (7-22) that are organized into a few (3-5) major superclones. Evolutionary analysis suggests that after clonal TP53 mutations, multiple loss-of-heterozygosity events and genome doubling, there was a period of transient genomic instability followed by ongoing copy number evolution during the primary tumour expansion. By subcloning single daughter cells in culture, we show that tumour cells rediversify their genomes and do not retain isogenic properties. These data show that triple-negative breast cancers continue to evolve chromosome aberrations and maintain a reservoir of subclonal diversity during primary tumour growth.

EnsembleCNV: an ensemble machine learning algorithm to identify and genotype copy number variation using SNP array data

The associations between diseases/traits and copy number variants (CNVs) have not been systematically investigated in genome-wide association studies (GWASs), primarily due to a lack of robust and accurate tools for CNV genotyping. Herein, we propose a novel ensemble learning framework, ensembleCNV, to detect and genotype CNVs using single nucleotide polymorphism (SNP) array data. EnsembleCNV (a) identifies and eliminates batch effects at raw data level; (b) assembles individual CNV calls into CNV regions (CNVRs) from multiple existing callers with complementary strengths by a heuristic algorithm; (c) re-genotypes each CNVR with local likelihood model adjusted by global information across multiple CNVRs; (d) refines CNVR boundaries by local correlation structure in copy number intensities; (e) provides direct CNV genotyping accompanied with confidence score, directly accessible for downstream quality control and association analysis. Benchmarked on two large datasets, ensembleCNV outperformed competing methods and achieved a high call rate (93.3%) and reproducibility (98.6%), while concurrently achieving high sensitivity by capturing 85% of common CNVs documented in the 1000 Genomes Project. Given this CNV call rate and accuracy, which are comparable to SNP genotyping, we suggest ensembleCNV holds significant promise for performing genome-wide CNV association studies and investigating how CNVs predispose to human diseases.

WaveDec: A Wavelet Approach to Identify Both Shared and Individual Patterns of Copy-Number Variations

Copy-number variations (CNVs) are associated with complex diseases and particular tumor types. Array-based comparative genomic hybridization (aCGH) is a common approach for the detection of CNVs. Traditional CNV detection methods for multiple aCGH samples mainly use batch samples to find common variations, not accounting for the individual characteristics of each sample. Accurately differentiating both the commonly shared and the individual CNV patterns is pivotal to identify cell populations, or to distinguish cell growth (as in cancer) from invasion of new cells. Our preliminary results have now demonstrated that both the shared and individual CNV patterns have distinctive characteristics after wavelet transform.

METHODS

To exploit these characteristics, we propose to formulate a quadratic data-separation problem within the wavelet space to discriminate the shared and individual CNVs from raw data. We have elaborated a numerical solution and shown that the solution can be obtained by solving decoupled subproblems. By this approach, computational costs can be limited, enabling efficient application in the analysis of large sequencing datasets.

RESULTS

The advantages of our proposed method, called WaveDec, have been demonstrated by comparison with popular CNV-detection methods using synthetic and empirical aCGH data. The performance of WaveDec was further validated by experiments with single-cell-sequencing data.

CONCLUSION

WaveDec can successfully differentiate shared and individual patterns, and performs well even in data contaminated with high levels of noise.

SIGNIFICANCE

Both the shared and individual patterns can be uniquely characterized as well as effectively decomposed within the wavelet space.

ALLELE-SPECIFIC COPY NUMBER ESTIMATION BY WHOLE EXOME SEQUENCING

Whole exome sequencing is currently a technology of choice in large-scale cancer genomics studies, where the priority is to identify cancer-associated variants in coding regions. We describe a method for estimating allele-specific copy number using whole exome sequencing data from tumor and matched normal.

Detection Copy Number Variants from NGS with Sparse and Smooth Constraints

It is known that copy number variations (CNVs) are associated with complex diseases and particular tumor types, thus reliable identification of CNVs is of great potential value. Recent advances in next generation sequencing (NGS) data analysis have helped manifest the richness of CNV information. However, the performances of these methods are not consistent. Reliably finding CNVs in NGS data in an efficient way remains a challenging topic, worthy of further investigation. Accordingly, we tackle the problem by formulating CNVs identification into a quadratic optimization problem involving two constraints. By imposing the constraints of sparsity and smoothness, the reconstructed read depth signal from NGS is anticipated to fit the CNVs patterns more accurately. An efficient numerical solution tailored from alternating direction minimization (ADM) framework is elaborated. We demonstrate the advantages of the proposed method, namely ADM-CNV, by comparing it with six popular CNV detection methods using synthetic, simulated, and empirical sequencing data. It is shown that the proposed approach can successfully reconstruct CNV patterns from raw data, and achieve superior or comparable performance in detection of the CNVs compared to the existing counterparts.

nbCNV: a multi-constrained optimization model for discovering copy number variants in single-cell sequencing data

Background

Variations in DNA copy number have an important contribution to the development of several diseases, including autism, schizophrenia and cancer. Single-cell sequencing technology allows the dissection of genomic heterogeneity at the single-cell level, thereby providing important evolutionary information about cancer cells. In contrast to traditional bulk sequencing, single-cell sequencing requires the amplification of the whole genome of a single cell to accumulate enough samples for sequencing. However, the amplification process inevitably introduces amplification bias, resulting in an over-dispersing portion of the sequencing data. Recent study has manifested that the over-dispersed portion of the single-cell sequencing data could be well modelled by negative binomial distributions.

Results

We developed a read-depth based method, nbCNV to detect the copy number variants (CNVs). The nbCNV method uses two constraints-sparsity and smoothness to fit the CNV patterns under the assumption that the read signals are negatively binomially distributed. The problem of CNV detection was formulated as a quadratic optimization problem, and was solved by an efficient numerical solution based on the classical alternating direction minimization method.

Conclusions

Extensive experiments to compare nbCNV with existing benchmark models were conducted on both simulated data and empirical single-cell sequencing data. The results of those experiments demonstrate that nbCNV achieves superior performance and high robustness for the detection of CNVs in single-cell sequencing data.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-016-1239-7) contains supplementary material, which is available to authorized users.

A semiparametric Bayesian model for comparing DNA copy numbers

We propose a two-step method for the analysis of copy number data. We first define the partitions of genome aberrations and conditional on the partitions we introduce a semiparametric Bayesian model for the analysis of multiple samples from patients with different subtypes of a disease. While the biological interest is to identify regions of differential copy numbers across disease subtypes, our model also includes sample-specific random effects that account for copy number alterations between different samples in the same disease subtype. We model the subtype and sample-specific effects using a random effects mixture model. The subtype's main effects are characterized by a mixture distribution whose components are assigned Dirichlet process priors. The performance of the proposed model is examined using simulated data as well as a breast cancer genomic data set.

VTET: a variable threshold exact test for identifying disease-associated copy number variations enriched in short genomic regions

Copy number variations (CNVs) constitute a major source of genetic variations in human populations and have been reported to be associated with complex diseases. Methods have been developed for detecting CNVs and testing CNV associations in genome-wide association studies (GWAS) based on SNP arrays. Commonly used two-step testing procedures work well only for long CNVs while direct CNV association testing methods work only for recurrent CNVs. Assuming that short CNVs disrupting any part of a given genomic region increase disease risk, we developed a variable threshold exact test (VTET) for testing disease associations of CNVs randomly distributed in the genome using intensity data from SNP arrays. By extensive simulations, we found that VTET outperformed two-step testing procedures based on existing CNV calling algorithms for short CNVs and that the performance of VTET was robust to the length of the genomic region. In addition, VTET had a comparable performance with CNVtools for testing the association of recurrent CNVs. Thus, we expect VTET to be useful for testing disease associations of both recurrent and randomly distributed CNVs using existing GWAS data. We applied VTET to a lung cancer GWAS and identified a genome-wide significant region on chromosome 18q22.3 for lung squamous cell carcinoma.

Segmentor3IsBack: an R package for the fast and exact segmentation of Seq-data

Background

Change point problems arise in many genomic analyses such as the detection of copy number variations or the detection of transcribed regions. The expanding Next Generation Sequencing technologies now allow to locate change points at the nucleotide resolution.

Results

Because of its complexity which is almost linear in the sequence length when the maximal number of segments is constant, and as its performance had been acknowledged for microarrays, we propose to use the Pruned Dynamic Programming algorithm for Seq-experiment outputs. This requires the adaptation of the algorithm to the negative binomial distribution with which we model the data. We show that if the dispersion in the signal is known, the PDP algorithm can be used, and we provide an estimator for this dispersion. We describe a compression framework which reduces the time complexity without modifying the accuracy of the segmentation. We propose to estimate the number of segments via a penalized likelihood criterion. We illustrate the performance of the proposed methodology on RNA-Seq data.

Conclusions

We illustrate the results of our approach on a real dataset and show its good performance. Our algorithm is available as an R package on the CRAN repository.

Next Generation Statistical Genetics: Modeling, Penalization, and Optimization in High-Dimensional Data

Statistical genetics is undergoing the same transition to big data that all branches of applied statistics are experiencing. With the advent of inexpensive DNA sequencing, the transition is only accelerating. This brief review highlights some modern techniques with recent successes in statistical genetics. These include: (a) lasso penalized regression and association mapping, (b) ethnic admixture estimation, (c) matrix completion for genotype and sequence data, (d) the fused lasso and copy number variation, (e) haplotyping, (f) estimation of relatedness, (g) variance components models, and (h) rare variant testing. For more than a century, genetics has been both a driver and beneficiary of statistical theory and practice. This symbiotic relationship will persist for the foreseeable future.