Cancer development is characterized by chromosomal instability, manifesting in frequent occurrences of different genomic alteration mechanisms ranging in extent and impact. Mathematical modeling can help evaluate the role of each mutational process during tumor progression, however existing frameworks can only capture certain aspects of chromosomal instability (CIN). We present CINner, a mathematical framework for modeling genomic diversity and selection during tumor evolution. The main advantage of CINner is its flexibility to incorporate many genomic events that directly impact cellular fitness, from driver gene mutations to copy number alterations (CNAs), including focal amplifications and deletions, missegregations and whole-genome duplication (WGD). We apply CINner to find chromosome-arm selection parameters that drive tumorigenesis in the absence of WGD in chromosomally stable cancer types from the Pan-Cancer Analysis of Whole Genomes (PCAWG, [Formula: see text]). We found that the selection parameters predict WGD prevalence among different chromosomally unstable tumors, hinting that the selective advantage of WGD cells hinges on their tolerance for aneuploidy and escape from nullisomy. Analysis of inference results using CINner across cancer types in The Cancer Genome Atlas ([Formula: see text]) further reveals that the inferred selection parameters reflect the bias between tumor suppressor genes and oncogenes on specific genomic regions. Direct application of CINner to model the WGD proportion and fraction of genome altered (FGA) in PCAWG uncovers the increase in CNA probabilities associated with WGD in each cancer type. CINner can also be utilized to study chromosomally stable cancer types, by applying a selection model based on driver gene mutations and focal amplifications or deletions (chronic lymphocytic leukemia in PCAWG, [Formula: see text]). Finally, we used CINner to analyze the impact of CNA probabilities, chromosome selection parameters, tumor growth dynamics and population size on cancer fitness and heterogeneity. We expect that CINner will provide a powerful modeling tool for the oncology community to quantify the impact of newly uncovered genomic alteration mechanisms on shaping tumor progression and adaptation.

Gradient estimation is often necessary for fitting generative models with discrete latent variables, in contexts such as reinforcement learning and variational autoencoder (VAE) training. The DisARM estimator achieves state of the art gradient variance for Bernoulli latent variable models in many contexts. However, DisARM and other estimators have potentially exploding variance near the boundary of the parameter space, where solutions tend to lie. To ameliorate this issue, we propose a new gradient estimator bitflip-1 that is lower variance at the boundaries of the parameter space. As bitflip-1 has complementary properties to existing estimators, we introduce an aggregated estimator, unbiased gradient variance clipping (UGC) that uses either a bitflip-1 or a DisARM gradient update for each coordinate. We theoretically prove that UGC has uniformly lower variance than DisARM. Empirically, we observe that UGC achieves the optimal value of the optimization objectives in toy experiments, discrete VAE training, and in a best subset selection problem.

MOTIVATION: By collecting multiple samples per subject, researchers can characterize intra-subject variation using physiologically relevant measurements such as gene expression profiling. This can yield important insights into fundamental biological questions ranging from cell type identity to tumour development. For each subject, the data measurements can be written as a matrix with the different subsamples (e.g. multiple tissues) indexing the columns and the genes indexing the rows. In this context, neither the genes nor the tissues are expected to be independent and straightforward application of traditional statistical methods that ignore this two-way dependence might lead to erroneous conclusions. Herein, we present a suite of tools embedded within the R/Bioconductor package HDTD for robustly estimating and performing hypothesis tests about the mean relationship and the covariance structure within the rows and columns. We illustrate the utility of HDTD by applying it to analyze data generated by the Genotype-Tissue Expression consortium. AVAILABILITY AND IMPLEMENTATION: The R package HDTD is part of Bioconductor. The source code and a comprehensive user's guide are available at http://bioconductor.org/packages/release/bioc/html/HDTD.html CONTACT: : [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: In metabolomics, the goal is to identify and measure the concentrations of different metabolites (small molecules) in a cell or a biological system. The metabolites form an important layer in the complex metabolic network, and the interactions between different metabolites are often of interest. It is crucial to perform proper normalization of metabolomics data, but current methods may not be applicable when estimating interactions in the form of correlations between metabolites. We propose a normalization approach based on a mixed model, with simultaneous estimation of a correlation matrix. We also investigate how the common use of a calibration standard in nuclear magnetic resonance (NMR) experiments affects the estimation of correlations. RESULTS: We show with both real and simulated data that our proposed normalization method is robust and has good performance when discovering true correlations between metabolites. The standardization of NMR data is shown in simulation studies to affect our ability to discover true correlations to a small extent. However, comparing standardized and non-standardized real data does not result in any large differences in correlation estimates. AVAILABILITY AND IMPLEMENTATION: Source code is freely available at https://sourceforge.net/projects/metabnorm/ CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Most methods for estimating differential expression from RNA-seq are based on statistics that compare normalized read counts between treatment classes. Unfortunately, reads are in general too short to be mapped unambiguously to features of interest, such as genes, isoforms or haplotype-specific isoforms. There are methods for estimating expression levels that account for this source of ambiguity. However, the uncertainty is not generally accounted for in downstream analysis of gene expression experiments. Moreover, at the individual transcript level, it can sometimes be too large to allow useful comparisons between treatment groups. RESULTS: In this article we make two proposals that improve the power, specificity and versatility of expression analysis using RNA-seq data. First, we present a Bayesian method for model selection that accounts for read mapping ambiguities using random effects. This polytomous model selection approach can be used to identify many interesting patterns of gene expression and is not confined to detecting differential expression between two groups. For illustration, we use our method to detect imprinting, different types of regulatory divergence in cis and in trans and differential isoform usage, but many other applications are possible. Second, we present a novel collapsing algorithm for grouping transcripts into inferential units that exploits the posterior correlation between transcript expression levels. The aggregate expression levels of these units can be estimated with useful levels of uncertainty. Our algorithm can improve the precision of expression estimates when uncertainty is large with only a small reduction in biological resolution. AVAILABILITY AND IMPLEMENTATION: We have implemented our software in the mmdiff and mmcollapse multithreaded C++ programs as part of the open-source MMSEQ package, available on https://github.com/eturro/mmseq.

MOTIVATION: Identification of genomic regions of interest in ChIP-seq data, commonly referred to as peak-calling, aims to find the locations of transcription factor binding sites, modified histones or nucleosomes. The BayesPeak algorithm was developed to model the data structure using Bayesian statistical techniques and was shown to be a reliable method, but did not have a full-genome implementation. RESULTS: In this note we present BayesPeak, an R package for genome-wide peak-calling that provides a flexible implementation of the BayesPeak algorithm and is compatible with downstream BioConductor packages. The BayesPeak package introduces a new method for summarizing posterior probability output, along with methods for handling overfitting and support for parallel processing. We briefly compare the package with other common peak-callers. AVAILABILITY: Available as part of BioConductor version 2.6. URL: http://bioconductor.org/packages/release/bioc/html/BayesPeak.html.

The cancer stem cell (CSC) concept is a highly debated topic in cancer research. While experimental evidence in favor of the cancer stem cell theory is apparently abundant, the results are often criticized as being difficult to interpret. An important reason for this is that most experimental data that support this model rely on transplantation studies. In this study we use a novel cellular Potts model to elucidate the dynamics of established malignancies that are driven by a small subset of CSCs. Our results demonstrate that epigenetic mutations that occur during mitosis display highly altered dynamics in CSC-driven malignancies compared to a classical, non-hierarchical model of growth. In particular, the heterogeneity observed in CSC-driven tumors is considerably higher. We speculate that this feature could be used in combination with epigenetic (methylation) sequencing studies of human malignancies to prove or refute the CSC hypothesis in established tumors without the need for transplantation. Moreover our tumor growth simulations indicate that CSC-driven tumors display evolutionary features that can be considered beneficial during tumor progression. Besides an increased heterogeneity they also exhibit properties that allow the escape of clones from local fitness peaks. This leads to more aggressive phenotypes in the long run and makes the neoplasm more adaptable to stringent selective forces such as cancer treatment. Indeed when therapy is applied the clone landscape of the regrown tumor is more aggressive with respect to the primary tumor, whereas the classical model demonstrated similar patterns before and after therapy. Understanding these often counter-intuitive fundamental properties of (non-)hierarchically organized malignancies is a crucial step in validating the CSC concept as well as providing insight into the therapeutical consequences of this model.

MOTIVATION: Copy number abnormalities (CNAs) represent an important type of genetic mutation that can lead to abnormal cell growth and proliferation. New high-throughput sequencing technologies promise comprehensive characterization of CNAs. In contrast to microarrays, where probe design follows a carefully developed protocol, reads represent a random sample from a library and may be prone to representation biases due to GC content and other factors. The discrimination between true and false positive CNAs becomes an important issue. RESULTS: We present a novel approach, called CNAseg, to identify CNAs from second-generation sequencing data. It uses depth of coverage to estimate copy number states and flowcell-to-flowcell variability in cancer and normal samples to control the false positive rate. We tested the method using the COLO-829 melanoma cell line sequenced to 40-fold coverage. An extensive simulation scheme was developed to recreate different scenarios of copy number changes and depth of coverage by altering a real dataset with spiked-in CNAs. Comparison to alternative approaches using both real and simulated datasets showed that CNAseg achieves superior precision and improved sensitivity estimates. AVAILABILITY: The CNAseg package and test data are available at http://www.compbio.group.cam.ac.uk/software.html.

MOTIVATION: The current generation of single nucleotide polymorphism (SNP) arrays allows measurement of copy number aberrations (CNAs) in cancer at more than one million locations in the genome in hundreds of tumour samples. Most research has focused on single-sample CNA discovery, the so-called segmentation problem. The availability of high-density, large sample-size SNP array datasets makes the identification of recurrent copy number changes in cancer, an important issue that can be addressed using the cross-sample information. RESULTS: We present a novel approach for finding regions of recurrent copy number aberrations, called CNAnova, from Affymetrix SNP 6.0 array data. The method derives its statistical properties from a control dataset composed of normal samples and, in contrast to previous methods, does not require segmentation and permutation steps. For rigorous testing of the algorithm and comparison to existing methods, we developed a simulation scheme that uses the noise distribution present in Affymetrix arrays. Application of the method to 128 acute lymphoblastic leukaemia samples shows that CNAnova achieves lower error rate than a popular alternative approach. We also describe an extension of the CNAnova framework to identify recurrent CNA regions with intra-tumour heterogeneity, present in either primary or relapsed samples from the same patients. AVAILABILITY: The CNAnova package and synthetic datasets are available at http://www.compbio.group.cam.ac.uk/software.html.

BACKGROUND: High-throughput measurement of allele-specific expression (ASE) is a relatively new and exciting application area for array-based technologies. In this paper, we explore several data sets which make use of Illumina's GoldenGate BeadArray technology to measure ASE. This platform exploits coding SNPs to obtain relative expression measurements for alleles at approximately 1500 positions in the genome. RESULTS: We analyze data from a mixture experiment where genomic DNA samples from pairs of individuals of known genotypes are pooled to create allelic imbalances at varying levels for the majority of SNPs on the array. We observe that GoldenGate has less sensitivity at detecting subtle allelic imbalances (around 1.3 fold) compared to extreme imbalances, and note the benefit of applying local background correction to the data. Analysis of data from a dye-swap control experiment allowed us to quantify dye-bias, which can be reduced considerably by careful normalization. The need to filter the data before carrying out further downstream analysis to remove non-responding probes, which show either weak, or non-specific signal for each allele, was also demonstrated. Throughout this paper, we find that a linear model analysis of the data from each SNP is a flexible modelling strategy that allows for testing of allelic imbalances in each sample when replicate hybridizations are available. CONCLUSIONS: Our analysis shows that local background correction carried out by Illumina's software, together with quantile normalization of the red and green channels within each array, provides optimal performance in terms of false positive rates. In addition, we strongly encourage intensity-based filtering to remove SNPs which only measure non-specific signal. We anticipate that a similar analysis strategy will prove useful when quantifying ASE on Illumina's higher density Infinium BeadChips.

BACKGROUND: A key stage for all microarray analyses is the extraction of feature-intensities from an image. If this step goes wrong, then subsequent preprocessing and processing stages will stand little chance of rectifying the matter. Illumina employ random construction of their BeadArrays, making feature-intensity extraction even more important for the Illumina platform than for other technologies. In this paper we show that using raw Illumina data it is possible to identify, control, and perhaps correct for a range of spatial-related phenomena that affect feature-intensity extraction. RESULTS: We note that feature intensities can be unnaturally high when in the proximity of a number of phenomena relating either to the images themselves or to the layout of the beads on an array. Additionally we note that beads neighbour beads of the same type more often than one might expect, which may cause concern in some models of hybridization. We highlight issues in the identification of a bead's location, and in particular how this both affects and is affected by its intensity. Finally we show that beads can be wrongly identified in the image on either a local or array-wide scale, with obvious implications for data quality. CONCLUSIONS: The image processing issues identified will often pass unnoticed by an analysis of the standard data returned from an experiment. We detail some simple diagnostics that can be implemented to identify problems of this nature, and outline approaches to correcting for such problems. These approaches require access to the raw data from the arrays, not just the summarized data usually returned, making the acquisition of such raw data highly desirable.

UNLABELLED: Illumina produces a number of microarray-based technologies for human genotyping. An Infinium BeadChip is a two-color platform that types between 10(5) and 10(6) single nucleotide polymorphisms (SNPs) per sample. Despite being widely used, there is a shortage of open source software to process the raw intensities from this platform into genotype calls. To this end, we have developed the R/Bioconductor package crlmm for analyzing BeadChip data. After careful preprocessing, our software applies the CRLMM algorithm to produce genotype calls, confidence scores and other quality metrics at both the SNP and sample levels. We provide access to the raw summary-level intensity data, allowing users to develop their own methods for genotype calling or copy number analysis if they wish. AVAILABILITY AND IMPLEMENTATION: The crlmm Bioconductor package is available from http://www.bioconductor.org. Data packages and documentation are available from http://rafalab.jhsph.edu/software.html.

BACKGROUND: Chromatin immunoprecipitation on tiling arrays (ChIP-chip) has been employed to examine features such as protein binding and histone modifications on a genome-wide scale in a variety of cell types. Array data from the latter studies typically have a high proportion of enriched probes whose signals vary considerably (due to heterogeneity in the cell population), and this makes their normalization and downstream analysis difficult. RESULTS: Here we present strategies for analyzing such experiments, focusing our discussion on the analysis of Bromodeoxyruridine (BrdU) immunoprecipitation on tiling array (BrdU-IP-chip) datasets. BrdU-IP-chip experiments map large, recently replicated genomic regions and have similar characteristics to histone modification/location data. To prepare such data for downstream analysis we employ a dynamic programming algorithm that identifies a set of putative unenriched probes, which we use for both within-array and between-array normalization. We also introduce a second dynamic programming algorithm that incorporates a priori knowledge to identify and quantify positive signals in these datasets. CONCLUSION: Highly enriched IP-chip datasets are often difficult to analyze with traditional array normalization and analysis strategies. Here we present and test a set of analytical tools for their normalization and quantification that allows for accurate identification and analysis of enriched regions.

BACKGROUND: High-throughput sequencing technology has become popular and widely used to study protein and DNA interactions. Chromatin immunoprecipitation, followed by sequencing of the resulting samples, produces large amounts of data that can be used to map genomic features such as transcription factor binding sites and histone modifications. METHODS: Our proposed statistical algorithm, BayesPeak, uses a fully Bayesian hidden Markov model to detect enriched locations in the genome. The structure accommodates the natural features of the Solexa/Illumina sequencing data and allows for overdispersion in the abundance of reads in different regions. Moreover, a control sample can be incorporated in the analysis to account for experimental and sequence biases. Markov chain Monte Carlo algorithms are applied to estimate the posterior distributions of the model parameters, and posterior probabilities are used to detect the sites of interest. CONCLUSION: We have presented a flexible approach for identifying peaks from ChIP-seq reads, suitable for use on both transcription factor binding and histone modification data. Our method estimates probabilities of enrichment that can be used in downstream analysis. The method is assessed using experimentally verified data and is shown to provide high-confidence calls with low false positive rates.

BACKGROUND: Illumina bead-based arrays are becoming increasingly popular due to their high degree of replication and reported high data quality. However, little attention has been paid to the pre-processing of Illumina data. In this paper, we present our experience of analysing the raw data from an Illumina spike-in experiment and offer guidelines for those wishing to analyse expression data or develop new methodologies for this technology. RESULTS: We find that the local background estimated by Illumina is consistently low, and subtracting this background is beneficial for detecting differential expression (DE). Illumina's summary method performs well at removing outliers, producing estimates which are less biased and are less variable than other robust summary methods. However, quality assessment on summarised data may miss spatial artefacts present in the raw data. Also, we find that the background normalisation method used in Illumina's proprietary software (BeadStudio) can cause problems with a standard DE analysis. We demonstrate that variances calculated from the raw data can be used as inverse weights in the DE analysis to improve power. Finally, variability in both expression levels and DE statistics can be attributed to differences in probe composition. These differences are not accounted for by current analysis methods and require further investigation. CONCLUSION: Analysing Illumina expression data using BeadStudio is reasonable because of the conservative estimates of summary values produced by the software. Improvements can however be made by not using background normalisation. Access to the raw data allows for a more detailed quality assessment and flexible analyses. In the case of a gene expression study, data can be analysed on an appropriate scale using established tools. Similar improvements can be expected for other Illumina assays.

UNLABELLED: The R/Bioconductor package beadarray allows raw data from Illumina experiments to be read and stored in convenient R classes. Users are free to choose between various methods of image processing, background correction and normalization in their analysis rather than using the defaults in Illumina's; proprietary software. The package also allows quality assessment to be carried out on the raw data. The data can then be summarized and stored in a format which can be used by other R/Bioconductor packages to perform downstream analyses. Summarized data processed by Illumina's; BeadStudio software can also be read and analysed in the same manner. AVAILABILITY: The beadarray package is available from the Bioconductor web page at www.bioconductor.org. A user's guide and example data sets are provided with the package.

BACKGROUND: The sequencing of many genomes and tiling arrays consisting of millions of DNA segments spanning entire genomes have made high-resolution copy number analysis possible. Microarray-based comparative genomic hybridization (array CGH) has enabled the high-resolution detection of DNA copy number aberrations. While many of the methods and algorithms developed for the analysis microarrays have focused on expression analysis, the same technology can be used to detect genetic alterations, using for example standard commercial Affymetrix arrays. Due to the nature of the resultant data, standard techniques for processing GeneChip expression experiments are inapplicable. RESULTS: We have developed a robust and flexible methodology for high-resolution analysis of DNA copy number of whole genomes, using Affymetrix high-density expression oligonucleotide microarrays. Copy number is obtained from fluorescence signals after processing with novel normalization, spatial artifact correction, data transformation and deletion/duplication detection. We applied our approach to identify deleted and amplified regions in E. coli mutants obtained after prolonged starvation. CONCLUSION: The availability of Affymetrix expression chips for a wide variety of organisms makes the proposed array CGH methodology useful more generally.

The analysis of methylation patterns is a promising approach to investigate the genealogy of cell populations in an organism. In a stem cell-niche scenario, sampled methylation patterns are the stochastic outcome of a complex interplay between niche structural features such as the number of stem cells within a niche and the niche succession time, the methylation/demethylation process, and the randomness due to sampling. As a consequence, methylation pattern studies can reveal niche characteristics but also require appropriate statistical methods. The analysis of methylation patterns sampled from colon crypts is a prototype of such a study. Previous analyses were based on forward simulation of the cell content of the whole crypt and subsequent comparisons between simulated and experimental data using a few statistics as a proxy to summarize the data. In this paper we develop a more powerful method to analyze these data based on coalescent modelling and Bayesian inference. Results support a scenario where the colon crypt is maintained by a high number of stem cells; the posterior indicates a number greater than eight and the posterior mode is between 15 and 20. The results also provide further evidence for synergistic effects in the methylation/demethylation process that could for the first time be quantitatively assessed through their long-term consequences such as the coexistence of hypermethylated and hypomethylated patterns in the same colon crypt.

Abstract Summary: We have developed a new method (BioHMM) for segmenting array comparative genomic hybridization data into states with the same underlying copy number. By utilizing a heterogeneous hidden Markov model, BioHMM incorporates relevant biological factors (e.g. the distance between adjacent clones) in the segmentation process. Availability: BioHMM is available as part of the R library snapCGH which can be downloaded from Contact: [email protected] Supplementary information: Supplementary information is available at