Inferring progression models for CGH data

Comparing copy-number profiles under multi-copy amplifications and deletions

BACKGROUND

During cancer progression, malignant cells accumulate somatic mutations that can lead to genetic aberrations. In particular, evolutionary events akin to segmental duplications or deletions can alter the copy-number profile (CNP) of a set of genes in a genome. Our aim is to compute the evolutionary distance between two cells for which only CNPs are known. This asks for the minimum number of segmental amplifications and deletions to turn one CNP into another. This was recently formalized into a model where each event is assumed to alter a copy-number by 1 or -1, even though these events can affect large portions of a chromosome.

RESULTS

We propose a general cost framework where an event can modify the copy-number of a gene by larger amounts. We show that any cost scheme that allows segmental deletions of arbitrary length makes computing the distance strongly NP-hard. We then devise a factor 2 approximation algorithm for the problem when copy-numbers are non-zero and provide an implementation called cnp2cnp. We evaluate our approach experimentally by reconstructing simulated cancer phylogenies from the pairwise distances inferred by cnp2cnp and compare it against two other alternatives, namely the MEDICC distance and the Euclidean distance.

CONCLUSIONS

The experimental results show that our distance yields more accurate phylogenies on average than these alternatives if the given CNPs are error-free, but that the MEDICC distance is slightly more robust against error in the data. In all cases, our experiments show that either our approach or the MEDICC approach should preferred over the Euclidean distance.

The evolution of tumour phylogenetics: principles and practice

Rapid advances in high-throughput sequencing and a growing realization of the importance of evolutionary theory to cancer genomics have led to a proliferation of phylogenetic studies of tumour progression. These studies have yielded not only new insights but also a plethora of experimental approaches, sometimes reaching conflicting or poorly supported conclusions. Here, we consider this body of work in light of the key computational principles underpinning phylogenetic inference, with the goal of providing practical guidance on the design and analysis of scientifically rigorous tumour phylogeny studies. We survey the range of methods and tools available to the researcher, their key applications, and the various unsolved problems, closing with a perspective on the prospects and broader implications of this field.

Inferring models of multiscale copy number evolution for single-tumor phylogenetics

Motivation: Phylogenetic algorithms have begun to see widespread use in cancer research to reconstruct processes of evolution in tumor progression. Developing reliable phylogenies for tumor data requires quantitative models of cancer evolution that include the unusual genetic mechanisms by which tumors evolve, such as chromosome abnormalities, and allow for heterogeneity between tumor types and individual patients. Previous work on inferring phylogenies of single tumors by copy number evolution assumed models of uniform rates of genomic gain and loss across different genomic sites and scales, a substantial oversimplification necessitated by a lack of algorithms and quantitative parameters for fitting to more realistic tumor evolution models.

Results: We propose a framework for inferring models of tumor progression from single-cell gene copy number data, including variable rates for different gain and loss events. We propose a new algorithm for identification of most parsimonious combinations of single gene and single chromosome events. We extend it via dynamic programming to include genome duplications. We implement an expectation maximization (EM)-like method to estimate mutation-specific and tumor-specific event rates concurrently with tree reconstruction. Application of our algorithms to real cervical cancer data identifies key genomic events in disease progression consistent with prior literature. Classification experiments on cervical and tongue cancer datasets lead to improved prediction accuracy for the metastasis of primary cervical cancers and for tongue cancer survival.

Availability and implementation: Our software (FISHtrees) and two datasets are available at ftp://ftp.ncbi.nlm.nih.gov/pub/FISHtrees.

Contact:russells@andrew.cmu.edu

Supplementary information:Supplementary data are available at Bioinformatics online.

Algorithms to model single gene, single chromosome, and whole genome copy number changes jointly in tumor phylogenetics

We present methods to construct phylogenetic models of tumor progression at the cellular level that include copy number changes at the scale of single genes, entire chromosomes, and the whole genome. The methods are designed for data collected by fluorescence in situ hybridization (FISH), an experimental technique especially well suited to characterizing intratumor heterogeneity using counts of probes to genetic regions frequently gained or lost in tumor development. Here, we develop new provably optimal methods for computing an edit distance between the copy number states of two cells given evolution by copy number changes of single probes, all probes on a chromosome, or all probes in the genome. We then apply this theory to develop a practical heuristic algorithm, implemented in publicly available software, for inferring tumor phylogenies on data from potentially hundreds of single cells by this evolutionary model. We demonstrate and validate the methods on simulated data and published FISH data from cervical cancers and breast cancers. Our computational experiments show that the new model and algorithm lead to more parsimonious trees than prior methods for single-tumor phylogenetics and to improved performance on various classification tasks, such as distinguishing primary tumors from metastases obtained from the same patient population.

Cancer is an evolutionary system whose growth and development is attributed to aberrations in well-known genes and to cancer-type specific genomic imbalances. Here, we present methods for reconstructing the evolution of individual tumors based on cell-to-cell variations between copy numbers of targeted regions of the genome. The methods are designed to work with fluorescence in situ hybridization (FISH), a technique that allows one to profile copy number changes in potentially thousands of single cells per study. Our work advances the prior art by developing theory and practical algorithms for building evolutionary trees of single tumors that can model gain or loss of genetic regions at the scale of single genes, whole chromosomes, or the entire genome, all common events in tumor evolution. We apply these methods on simulated and real tumor data to demonstrate substantial improvements in tree-building accuracy and in our ability to accurately classify tumors from their inferred evolutionary models. The newly developed algorithms have been released through our publicly available software, FISHtrees.

Methods and challenges in timing chromosomal abnormalities within cancer samples

Motivation: Tumors acquire many chromosomal amplifications, and those acquired early in the lifespan of the tumor may be not only important for tumor growth but also can be used for diagnostic purposes. Many methods infer the order of the accumulation of abnormalities based on their occurrence in a large cohort of patients. Recently, Durinck et al. (2011) and Greenman et al. (2012) developed methods to order a single tumor’s chromosomal amplifications based on the patterns of mutations accumulated within those regions. This method offers an unprecedented opportunity to assess the etiology of a single tumor sample, but has not been widely evaluated.

Results: We show that the model for timing chromosomal amplifications is limited in scope, particularly for regions with high levels of amplification. We also show that the estimation of the order of events can be sensitive for events that occur early in the progression of the tumor and that the partial maximum likelihood method of Greenman et al. (2012) can give biased estimates, particularly for moderate read coverage or normal contamination. We propose a maximum-likelihood estimation procedure that fully accounts for sequencing variability and show that it outperforms the partial maximum-likelihood estimation method. We also propose a Bayesian estimation procedure that stabilizes the estimates in certain settings. We implement these methods on a small number of ovarian tumors, and the results suggest possible differences in how the tumors acquired amplifications.

Availability and implementation: We provide implementation of these methods in an R package cancerTiming, which is available from the Comprehensive R Archive Network (CRAN) at http://CRAN.R-project.org/.

Contact:epurdom@stat.Berkeley.edu

Supplementary information:Supplementary data are available at Bioinformatics online.

Specific genomic regions are differentially affected by copy number alterations across distinct cancer types, in aggregated cytogenetic data

Background

Regional genomic copy number alterations (CNA) are observed in the vast majority of cancers. Besides specifically targeting well-known, canonical oncogenes, CNAs may also play more subtle roles in terms of modulating genetic potential and broad gene expression patterns of developing tumors. Any significant differences in the overall CNA patterns between different cancer types may thus point towards specific biological mechanisms acting in those cancers. In addition, differences among CNA profiles may prove valuable for cancer classifications beyond existing annotation systems.

Principal Findings

We have analyzed molecular-cytogenetic data from 25579 tumors samples, which were classified into 160 cancer types according to the International Classification of Disease (ICD) coding system. When correcting for differences in the overall CNA frequencies between cancer types, related cancers were often found to cluster together according to similarities in their CNA profiles. Based on a randomization approach, distance measures from the cluster dendrograms were used to identify those specific genomic regions that contributed significantly to this signal. This approach identified 43 non-neutral genomic regions whose propensity for the occurrence of copy number alterations varied with the type of cancer at hand. Only a subset of these identified loci overlapped with previously implied, highly recurrent (hot-spot) cytogenetic imbalance regions.

Conclusions

Thus, for many genomic regions, a simple null-hypothesis of independence between cancer type and relative copy number alteration frequency can be rejected. Since a subset of these regions display relatively low overall CNA frequencies, they may point towards second-tier genomic targets that are adaptively relevant but not necessarily essential for cancer development.

Testing clonality of three and more tumors using their loss of heterozygosity profiles

Cancer patients often develop multiple malignancies that may be either metastatic spread of a previous cancer (clonal tumors) or new primary cancers (independent tumors). If diagnosis cannot be easily made on the basis of the pathology review, the patterns of somatic mutations in the tumors can be compared. Previously we have developed statistical methods for testing clonality of two tumors using their loss of heterozygosity (LOH) profiles at several candidate markers. These methods can be applied to all possible pairs of tumors when multiple tumors are analyzed, but this strategy can lead to inconsistent results and loss of statistical power. In this work we will extend clonality tests to three and more malignancies from the same patient. A non-parametric test can be performed using any possible subset of tumors, with the subsequent adjustment for multiple testing. A parametric likelihood model is developed for 3 or 4 tumors, and it can be used to estimate the phylogenetic tree of tumors. The proposed tests are more powerful than combination of all possible pairwise tests.

Accurate reconstruction of the temporal order of mutations in neoplastic progression

The canonical route from normal tissue to cancer occurs through sequential acquisition of somatic mutations. Many studies have constructed a linear genetic model for tumorigenesis using the genetic alterations associated with samples at different stages of neoplastic progression from cross-sectional data. The common interpretation of these models is that they reflect the temporal order within any given tumor. Linear genetic methods implicitly neglect genetic heterogeneity within a neoplasm; each neoplasm is assumed to consist of one dominant clone. We modeled neoplastic progression of colorectal cancer using an agent-based model of a colon crypt and found clonal heterogeneity within our simulated neoplasms, as observed in vivo. Just 7.3% of cells within neoplasms acquired mutations in the same order as the linear model. In 41% of the simulated neoplasms, no cells acquired mutations in the same order as the linear model. We obtained similarly poor results when comparing the temporal order with oncogenetic tree models inferred from cross-sectional data. However, when we reconstructed the cell lineage of mutations within a neoplasm using several biopsies, we found that 99.7% cells within neoplasms acquired their mutations in an order consistent with the cell lineage mutational order. Thus, we find that using cross-sectional data to infer mutational order is misleading, whereas phylogenetic methods based on sampling intratumor heterogeneity accurately reconstructs the evolutionary history of tumors. In addition, we find evidence that disruption of differentiation is likely the first lesion in progression for most cancers and should be one of the few regularities of neoplastic progression across cancers.

Tracing the tumor lineage

Defining the pathways through which tumors progress is critical to our understanding and treatment of cancer. We do not routinely sample patients at multiple time points during the progression of their disease, and thus our research is limited to inferring progression a posteriori from the examination of a single tumor sample. Despite this limitation, inferring progression is possible because the tumor genome contains a natural history of the mutations that occur during the formation of the tumor mass. There are two approaches to reconstructing a lineage of progression: (1) inter-tumor comparisons, and (2) intra-tumor comparisons. The inter-tumor approach consists of taking single samples from large collections of tumors and comparing the complexity of the genomes to identify early and late mutations. The intra-tumor approach involves taking multiple samples from individual heterogeneous tumors to compare divergent clones and reconstruct a phylogenetic lineage. Here we discuss how these approaches can be used to interpret the current models for tumor progression. We also compare data from primary and metastatic copy number profiles to shed light on the final steps of breast cancer progression. Finally, we discuss how recent technical advances in single cell genomics will herald a new era in understanding the fundamental basis of tumor heterogeneity and progression.