Phylogenetic analysis of multiprobe fluorescence in situ hybridization data from tumor cell populations

A zero-agnostic model for copy number evolution in cancer

MOTIVATION

New low-coverage single-cell DNA sequencing technologies enable the measurement of copy number profiles from thousands of individual cells within tumors. From this data, one can infer the evolutionary history of the tumor by modeling transformations of the genome via copy number aberrations. Copy number aberrations alter multiple adjacent genomic loci, violating the standard phylogenetic assumption that loci evolve independently. Thus, specialized models to infer copy number phylogenies have been introduced. A widely used model is the copy number transformation (CNT) model in which a genome is represented by an integer vector and a copy number aberration is an event that either increases or decreases the number of copies of a contiguous segment of the genome. The CNT distance between a pair of copy number profiles is the minimum number of events required to transform one profile to another. While this distance can be computed efficiently, no efficient algorithm has been developed to find the most parsimonious phylogeny under the CNT model.

RESULTS

We introduce the zero-agnostic copy number transformation (ZCNT) model, a simplification of the CNT model that allows the amplification or deletion of regions with zero copies. We derive a closed form expression for the ZCNT distance between two copy number profiles and show that, unlike the CNT distance, the ZCNT distance forms a metric. We leverage the closed-form expression for the ZCNT distance and an alternative characterization of copy number profiles to derive polynomial time algorithms for two natural relaxations of the small parsimony problem on copy number profiles. While the alteration of zero copy number regions allowed under the ZCNT model is not biologically realistic, we show on both simulated and real datasets that the ZCNT distance is a close approximation to the CNT distance. Extending our polynomial time algorithm for the ZCNT small parsimony problem, we develop an algorithm, Lazac, for solving the large parsimony problem on copy number profiles. We demonstrate that Lazac outperforms existing methods for inferring copy number phylogenies on both simulated and real data.

A zero-agnostic model for copy number evolution in cancer

Motivation

New low-coverage single-cell DNA sequencing technologies enable the measurement of copy number profiles from thousands of individual cells within tumors. From this data, one can infer the evolutionary history of the tumor by modeling transformations of the genome via copy number aberrations. A widely used model to infer such copy number phylogenies is the copy number transformation (CNT) model in which a genome is represented by an integer vector and a copy number aberration is an event that either increases or decreases the number of copies of a contiguous segment of the genome. The CNT distance between a pair of copy number profiles is the minimum number of events required to transform one profile to another. While this distance can be computed efficiently, no efficient algorithm has been developed to find the most parsimonious phylogeny under the CNT model.

Results

We introduce the zero-agnostic copy number transformation (ZCNT) model, a simplification of the CNT model that allows the amplification or deletion of regions with zero copies. We derive a closed form expression for the ZCNT distance between two copy number profiles and show that, unlike the CNT distance, the ZCNT distance forms a metric. We leverage the closed-form expression for the ZCNT distance and an alternative characterization of copy number profiles to derive polynomial time algorithms for two natural relaxations of the small parsimony problem on copy number profiles. While the alteration of zero copy number regions allowed under the ZCNT model is not biologically realistic, we show on both simulated and real datasets that the ZCNT distance is a close approximation to the CNT distance. Extending our polynomial time algorithm for the ZCNT small parsimony problem, we develop an algorithm, Lazac, for solving the large parsimony problem on copy number profiles. We demonstrate that Lazac outperforms existing methods for inferring copy number phylogenies on both simulated and real data.

Joint Clustering of Single-Cell Sequencing and Fluorescence In Situ Hybridization Data for Reconstructing Clonal Heterogeneity in Cancers

Aneuploidy and whole genome duplication (WGD) events are common features of cancers associated with poor outcomes, but the ways they influence trajectories of clonal evolution are poorly understood. Phylogenetic methods for reconstructing clonal evolution from genomic data have proven a powerful tool for understanding how clonal evolution occurs in the process of cancer progression, but extant methods so far have limited the ability to resolve tumor evolution via ploidy changes. This limitation exists in part because single-cell DNA-sequencing (scSeq), which has been crucial to developing detailed profiles of clonal evolution, has difficulty in resolving ploidy changes and WGD. Multiplex interphase fluorescence in situ hybridization (miFISH) provides a more unambiguous signal of single-cell ploidy changes but it is limited to profiling small numbers of single markers. Here, we develop a joint clustering method to combine these two data sources with the goal of better resolving ploidy changes in tumor evolution. We develop a probabilistic framework to maximize the probability of latent variables given the pre-clustered datasets, which we optimize via Markov chain Monte Carlo sampling combined with linear regression. We validate the method by using simulated data derived from a glioblastoma (GBM) case profiled by both scSeq and miFISH. We further apply the method to two GBM cases with scSeq and miFISH data by reconstructing a phylogenetic tree from the joint clustering results, demonstrating their synergistic value in understanding how focal copy number changes and WGD events can collectively contribute to tumor progression.

Tumor heterogeneity assessed by sequencing and fluorescence in situ hybridization (FISH) data

MOTIVATION

Computational reconstruction of clonal evolution in cancers has become a crucial tool for understanding how tumors initiate and progress and how this process varies across patients. The field still struggles, however, with special challenges of applying phylogenetic methods to cancers, such as the prevalence and importance of copy number alteration (CNA) and structural variation (SV) events in tumor evolution, which are difficult to profile accurately by prevailing sequencing methods in such a way that subsequent reconstruction by phylogenetic inference algorithms is accurate.

RESULTS

In the present work, we develop computational methods to combine sequencing with multiplex interphase fluorescence in situ hybridization (miFISH) to exploit the complementary advantages of each technology in inferring accurate models of clonal CNA evolution accounting for both focal changes and aneuploidy at whole-genome scales. By integrating such information in an integer linear programming (ILP) framework, we demonstrate on simulated data that incorporation of FISH data substantially improves accurate inference of focal CNA and ploidy changes in clonal evolution from deconvolving bulk sequence data. Analysis of real glioblastoma data for which FISH, bulk sequence, and single cell sequence are all available confirms the power of FISH to enhance accurate reconstruction of clonal copy number evolution in conjunction with bulk and optionally single-cell sequence data.

AVAILABILITY

Source code is available on Github at https://github.com/CMUSchwartzLab/FISH_deconvolution.

Assessing the contribution of tumor mutational phenotypes to cancer progression risk

Cancer occurs via an accumulation of somatic genomic alterations in a process of clonal evolution. There has been intensive study of potential causal mutations driving cancer development and progression. However, much recent evidence suggests that tumor evolution is normally driven by a variety of mechanisms of somatic hypermutability, which act in different combinations or degrees in different cancers. These variations in mutability phenotypes are predictive of progression outcomes independent of the specific mutations they have produced to date. Here we explore the question of how and to what degree these differences in mutational phenotypes act in a cancer to predict its future progression. We develop a computational paradigm using evolutionary tree inference (tumor phylogeny) algorithms to derive features quantifying single-tumor mutational phenotypes, followed by a machine learning framework to identify key features predictive of progression. Analyses of breast invasive carcinoma and lung carcinoma demonstrate that a large fraction of the risk of future clinical outcomes of cancer progression-overall survival and disease-free survival-can be explained solely from mutational phenotype features derived from the phylogenetic analysis. We further show that mutational phenotypes have additional predictive power even after accounting for traditional clinical and driver gene-centric genomic predictors of progression. These results confirm the importance of mutational phenotypes in contributing to cancer progression risk and suggest strategies for enhancing the predictive power of conventional clinical data or driver-centric biomarkers.

The evolution of single cell-derived colorectal cancer cell lines is dominated by the continued selection of tumor-specific genomic imbalances, despite random chromosomal instability

Intratumor heterogeneity is a major challenge in cancer treatment. To decipher patterns of chromosomal heterogeneity, we analyzed six colorectal cancer cell lines by multiplex interphase FISH (miFISH). The mismatch-repair-deficient cell lines DLD-1 and HCT116 had the most stable copy numbers, whereas aneuploid cell lines (HT-29, SW480, SW620 and H508) displayed a higher degree of instability. We subsequently assessed the clonal evolution of single cells in two colorectal carcinoma cell lines, SW480 and HT-29, which both have aneuploid karyotypes but different degrees of chromosomal instability. The clonal compositions of the single cell-derived daughter lines, as assessed by miFISH, differed for HT-29 and SW480. Daughters of HT-29 were stable, clonal, with little heterogeneity. Daughters of SW480 were more heterogeneous, with the single cell-derived daughter lines separating into two distinct populations with different ploidy (hyper-diploid and near-triploid), morphology, gene expression and tumorigenicity. To better understand the evolutionary trajectory for the two SW480 populations, we constructed phylogenetic trees which showed ongoing instability in the daughter lines. When analyzing the evolutionary development over time, most single cell-derived daughter lines maintained their major clonal pattern, with the exception of one daughter line that showed a switch involving a loss of APC. Our meticulous analysis of the clonal evolution and composition of these colorectal cancer models shows that all chromosomes are subject to segregation errors, however, specific net genomic imbalances are maintained. Karyotype evolution is driven by the necessity to arrive at and maintain a specific plateau of chromosomal copy numbers as the drivers of carcinogenesis.

Deconvolution and phylogeny inference of structural variations in tumor genomic samples

Motivation

Phylogenetic reconstruction of tumor evolution has emerged as a crucial tool for making sense of the complexity of emerging cancer genomic datasets. Despite the growing use of phylogenetics in cancer studies, though, the field has only slowly adapted to many ways that tumor evolution differs from classic species evolution. One crucial question in that regard is how to handle inference of structural variations (SVs), which are a major mechanism of evolution in cancers but have been largely neglected in tumor phylogenetics to date, in part due to the challenges of reliably detecting and typing SVs and interpreting them phylogenetically.

Results

We present a novel method for reconstructing evolutionary trajectories of SVs from bulk whole-genome sequence data via joint deconvolution and phylogenetics, to infer clonal sub-populations and reconstruct their ancestry. We establish a novel likelihood model for joint deconvolution and phylogenetic inference on bulk SV data and formulate an associated optimization algorithm. We demonstrate the approach to be efficient and accurate for realistic scenarios of SV mutation on simulated data. Application to breast cancer genomic data from The Cancer Genome Atlas shows it to be practical and effective at reconstructing features of SV-driven evolution in single tumors.

Availability and implementation

Python source code and associated documentation are available at https://github.com/jaebird123/tusv.

Phylogenetic Reconstruction for Copy-Number Evolution Problems

Cancer is known for its heterogeneity and is regarded as an evolutionary process driven by somatic mutations and clonal expansions. This evolutionary process can be modeled by a phylogenetic tree and phylogenetic analysis of multiple subclones of cancer cells can facilitate the study of the tumor variants progression. Copy-number aberration occurs frequently in many types of tumors in terms of segmental amplifications and deletions. In this paper, we developed a distance-based method for reconstructing phylogenies from copy-number profiles of cancer cells. We demonstrate the importance of distance correction from the edit (minimum) distance to the estimated actual number of events. Experimental results show that our approaches provide accurate and scalable results in estimating the actual number of evolutionary events between copy number profiles and in reconstructing phylogenies.

Single-cell genetic analysis of clonal dynamics in colorectal adenomas indicates CDX2 gain as a predictor of recurrence

Colorectal adenomas are common precancerous lesions with the potential for malignant transformation to colorectal adenocarcinoma. Endoscopic polypectomy provides an opportunity for cancer prevention; however, recurrence rates are high. We collected formalin-fixed paraffin-embedded tissue of 15 primary adenomas with recurrence, 15 adenomas without recurrence, and 14 matched pair samples (primary adenoma and the corresponding recurrent adenoma). The samples were analysed by array-comparative genomic hybridisation (aCGH) and single-cell multiplex interphase fluorescence in situ hybridisation (miFISH) to understand clonal evolution, to examine the dynamics of copy number alterations (CNAs) and to identify molecular markers for recurrence prediction. The miFISH probe panel consisted of 14 colorectal carcinogenesis-relevant genes (COX2, PIK3CA, APC, CLIC1, EGFR, MYC, CCND1, CDX2, CDH1, TP53, HER2, SMAD7, SMAD4 and ZNF217), and a centromere probe (CEP10). The aCGH analysis confirmed the genetic landscape typical for colorectal tumorigenesis, that is, CNAs of chromosomes 7, 13q, 18 and 20q. Focal aberrations (≤10 Mbp) were mapped to chromosome bands 6p22.1-p21.33 (33.3%), 7q22.1 (31.4%) and 16q21 (29.4%). MiFISH detected gains of EGFR (23.6%), CDX2 (21.8%) and ZNF217 (18.2%). Most adenomas exhibited a major clone population which was accompanied by multiple smaller clone populations. Gains of CDX2 were exclusively seen in primary adenomas with recurrence (25%) compared to primary adenomas without recurrence (0%). Generation of phylogenetic trees for matched pair samples revealed four distinct patterns of clonal dynamics. In conclusion, adenoma development and recurrence are complex genetic processes driven by multiple CNAs whose evaluations by miFISH, with emphasis on CDX2, might serve as a predictor of recurrence.

An Improved Binary Differential Evolution Algorithm to Infer Tumor Phylogenetic Trees

Tumourigenesis is a mutation accumulation process, which is likely to start with a mutated founder cell. The evolutionary nature of tumor development makes phylogenetic models suitable for inferring tumor evolution through genetic variation data. Copy number variation (CNV) is the major genetic marker of the genome with more genes, disease loci, and functional elements involved. Fluorescence in situ hybridization (FISH) accurately measures multiple gene copy number of hundreds of single cells. We propose an improved binary differential evolution algorithm, BDEP, to infer tumor phylogenetic tree based on FISH platform. The topology analysis of tumor progression tree shows that the pathway of tumor subcell expansion varies greatly during different stages of tumor formation. And the classification experiment shows that tree-based features are better than data-based features in distinguishing tumor. The constructed phylogenetic trees have great performance in characterizing tumor development process, which outperforms other similar algorithms.

A Linear-Time Algorithm for the Copy Number Transformation Problem

Problems of genome rearrangement are central in both evolution and cancer. Most evolutionary scenarios have been studied under the assumption that the genome contains a single copy of each gene. In contrast, tumor genomes undergo deletions and duplications, and thus, the number of copies of genes varies. The number of copies of each segment along a chromosome is called its copy number profile (CNP). Understanding CNP changes can assist in predicting disease progression and treatment. To date, questions related to distances between CNPs gained little scientific attention. Here we focus on the following fundamental problem, introduced by Schwarz et al.: given two CNPs, u and v, compute the minimum number of operations transforming u into v, where the edit operations are segmental deletions and amplifications. We establish the computational complexity of this problem, showing that it is solvable in linear time and constant space.

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.

The Cellular Origin and Evolution of Breast Cancer

In this review, we will discuss how the cell of origin may modulate breast cancer intratumoral heterogeneity (ITH) as well as the role of ITH in the evolution of cancer. The clonal evolution and the cancer stem cell (CSC) models, as well as a model that integrates clonal evolution with a CSC hierarchy, have all been proposed to explain the development of ITH. The extent of ITH correlates with clinical outcome and reflects the cellular complexity and dynamics within a tumor. A unique subtype of breast cancer, the claudin-low subtype that is highly resistant to chemotherapy and most closely resembles mammary epithelial stem cells, will be discussed. Furthermore, we will review how the interactions among various tumor cells, some with distinct mutations, may impact breast cancer treatment. Finally, novel technologies that may help advance our understanding of ITH and lead to improvements in the design of new treatments also will be discussed.

Big data need big theory too

The current interest in big data, machine learning and data analytics has generated the widespread impression that such methods are capable of solving most problems without the need for conventional scientific methods of inquiry. Interest in these methods is intensifying, accelerated by the ease with which digitized data can be acquired in virtually all fields of endeavour, from science, healthcare and cybersecurity to economics, social sciences and the humanities. In multiscale modelling, machine learning appears to provide a shortcut to reveal correlations of arbitrary complexity between processes at the atomic, molecular, meso- and macroscales. Here, we point out the weaknesses of pure big data approaches with particular focus on biology and medicine, which fail to provide conceptual accounts for the processes to which they are applied. No matter their 'depth' and the sophistication of data-driven methods, such as artificial neural nets, in the end they merely fit curves to existing data. Not only do these methods invariably require far larger quantities of data than anticipated by big data aficionados in order to produce statistically reliable results, but they can also fail in circumstances beyond the range of the data used to train them because they are not designed to model the structural characteristics of the underlying system. We argue that it is vital to use theory as a guide to experimental design for maximal efficiency of data collection and to produce reliable predictive models and conceptual knowledge. Rather than continuing to fund, pursue and promote 'blind' big data projects with massive budgets, we call for more funding to be allocated to the elucidation of the multiscale and stochastic processes controlling the behaviour of complex systems, including those of life, medicine and healthcare.This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.

Analysis of gene copy number changes in tumor phylogenetics

BACKGOUND

Evolution of cancer cells is characterized by large scale and rapid changes in the chromosomal  landscape. The fluorescence in situ hybridization (FISH) technique provides a way to measure the copy numbers of preselected genes in a group of cells and has been found to be a reliable source of data to model the evolution of tumor cells. Chowdhury et al. (Bioinformatics 29(13):189-98, 23; PLoS Comput Biol 10(7):1003740, 24) recently develop a computational model for tumor progression driven by gains and losses in cell count patterns obtained by FISH probes. Their model aims to find the rectilinear Steiner minimum tree (RSMT) (Chowdhury et al. in Bioinformatics 29(13):189-98, 23) and the duplication Steiner minimum tree (DSMT) (Chowdhury et al. in PLoS Comput Biol 10(7):1003740, 24) that describe the progression of FISH cell count patterns over its branches in a parsimonious manner. Both the RSMT and DSMT problems are NP-hard and heuristics are required to solve the problems efficiently.

METHODS

In this paper we propose two approaches to solve the RSMT problem, one inspired by iterative methods to address the "small phylogeny" problem (Sankoff et al. in J Mol Evol 7(2):133-49, 27; Blanchette et al. in Genome Inform 8:25-34, 28), and the other based on maximum parsimony phylogeny inference. We further show how to extend these heuristics to obtain solutions to the DSMT problem, that models large scale duplication events.

RESULTS

Experimental results from both simulated and real tumor data show that our methods outperform previous heuristics (Chowdhury et al. in Bioinformatics 29(13):189-98, 23; Chowdhury et al. in PLoS Comput Biol 10(7):1003740, 24) in obtaining solutions to both RSMT and DSMT problems.

CONCLUSION

The methods introduced here are able to provide more parsimony phylogenies compared to earlier ones which are consider better choices.

Classifying the Progression of Ductal Carcinoma from Single-Cell Sampled Data via Integer Linear Programming: A Case Study

Ductal Carcinoma In Situ (DCIS) is a precursor lesion of Invasive Ductal Carcinoma (IDC) of the breast. Investigating its temporal progression could provide fundamental new insights for the development of better diagnostic tools to predict which cases of DCIS will progress to IDC. We investigate the problem of reconstructing a plausible progression from single-cell sampled data of an individual with synchronous DCIS and IDC. Specifically, by using a number of assumptions derived from the observation of cellular atypia occurring in IDC, we design a possible predictive model using integer linear programming (ILP). Computational experiments carried out on a preexisting data set of 13 patients with simultaneous DCIS and IDC show that the corresponding predicted progression models are classifiable into categories having specific evolutionary characteristics. The approach provides new insights into mechanisms of clonal progression in breast cancers and helps illustrate the power of the ILP approach for similar problems in reconstructing tumor evolution scenarios under complex sets of constraints.

FISHtrees 3.0: Tumor Phylogenetics Using a Ploidy Probe

Advances in fluorescence in situ hybridization (FISH) make it feasible to detect multiple copy-number changes in hundreds of cells of solid tumors. Studies using FISH, sequencing, and other technologies have revealed substantial intra-tumor heterogeneity. The evolution of subclones in tumors may be modeled by phylogenies. Tumors often harbor aneuploid or polyploid cell populations. Using a FISH probe to estimate changes in ploidy can guide the creation of trees that model changes in ploidy and individual gene copy-number variations. We present FISHtrees 3.0, which implements a ploidy-based tree building method based on mixed integer linear programming (MILP). The ploidy-based modeling in FISHtrees includes a new formulation of the problem of merging trees for changes of a single gene into trees modeling changes in multiple genes and the ploidy. When multiple samples are collected from each patient, varying over time or tumor regions, it is useful to evaluate similarities in tumor progression among the samples. Therefore, we further implemented in FISHtrees 3.0 a new method to build consensus graphs for multiple samples. We validate FISHtrees 3.0 on a simulated data and on FISH data from paired cases of cervical primary and metastatic tumors and on paired breast ductal carcinoma in situ (DCIS) and invasive ductal carcinoma (IDC). Tests on simulated data show improved accuracy of the ploidy-based approach relative to prior ploidyless methods. Tests on real data further demonstrate novel insights these methods offer into tumor progression processes. Trees for DCIS samples are significantly less complex than trees for paired IDC samples. Consensus graphs show substantial divergence among most paired samples from both sets. Low consensus between DCIS and IDC trees may help explain the difficulty in finding biomarkers that predict which DCIS cases are at most risk to progress to IDC. The FISHtrees software is available at ftp://ftp.ncbi.nih.gov/pub/FISHtrees.

OncoNEM: inferring tumor evolution from single-cell sequencing data

Single-cell sequencing promises a high-resolution view of genetic heterogeneity and clonal evolution in cancer. However, methods to infer tumor evolution from single-cell sequencing data lag behind methods developed for bulk-sequencing data. Here, we present OncoNEM, a probabilistic method for inferring intra-tumor evolutionary lineage trees from somatic single nucleotide variants of single cells. OncoNEM identifies homogeneous cellular subpopulations and infers their genotypes as well as a tree describing their evolutionary relationships. In simulation studies, we assess OncoNEM's robustness and benchmark its performance against competing methods. Finally, we show its applicability in case studies of muscle-invasive bladder cancer and essential thrombocythemia.

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.

Reference-free inference of tumor phylogenies from single-cell sequencing data

BACKGROUND

Effective management and treatment of cancer continues to be complicated by the rapid evolution and resulting heterogeneity of tumors. Phylogenetic study of cell populations in single tumors provides a way to delineate intra-tumoral heterogeneity and identify robust features of evolutionary processes. The introduction of single-cell sequencing has shown great promise for advancing single-tumor phylogenetics; however, the volume and high noise in these data present challenges for inference, especially with regard to chromosome abnormalities that typically dominate tumor evolution. Here, we investigate a strategy to use such data to track differences in tumor cell genomic content during progression.

RESULTS

We propose a reference-free approach to mining single-cell genome sequence reads to allow predictive classification of tumors into heterogeneous cell types and reconstruct models of their evolution. The approach extracts k-mer counts from single-cell tumor genomic DNA sequences, and uses differences in normalized k-mer frequencies as a proxy for overall evolutionary distance between distinct cells. The approach computationally simplifies deriving phylogenetic markers, which normally relies on first aligning sequence reads to a reference genome and then processing the data to extract meaningful progression markers for constructing phylogenetic trees. The approach also provides a way to bypass some of the challenges that massive genome rearrangement typical of tumor genomes presents for reference-based methods. We illustrate the method on a publicly available breast tumor single-cell sequencing dataset.

CONCLUSIONS

We have demonstrated a computational approach for learning tumor progression from single cell sequencing data using k-mer counts. k-mer features classify tumor cells by stage of progression with high accuracy. Phylogenies built from these k-mer spectrum distance matrices yield splits that are statistically significant when tested for their ability to partition cells at different stages of cancer.

Phylogenetic analysis of multiple FISH markers in oral tongue squamous cell carcinoma suggests that a diverse distribution of copy number changes is associated with poor prognosis

Oral tongue squamous cell carcinoma (OTSCC) is associated with poor prognosis. To improve prognostication, we analyzed four gene probes (TERC, CCND1, EGFR and TP53) and the centromere probe CEP4 as a marker of chromosomal instability, using fluorescence in situ hybridization (FISH) in single cells from the tumors of sixty-five OTSCC patients (Stage I, n = 15; Stage II, n = 30; Stage III, n = 7; Stage IV, n = 13). Unsupervised hierarchical clustering of the FISH data distinguished three clusters related to smoking status. Copy number increases of all five markers were found to be correlated to non-smoking habits, while smokers in this cohort had low-level copy number gains. Using the phylogenetic modeling software FISHtrees, we constructed models of tumor progression for each patient based on the four gene probes. Then, we derived test statistics on the models that are significant predictors of disease-free and overall survival, independent of tumor stage and smoking status in multivariate analysis. The patients whose tumors were modeled as progressing by a more diverse distribution of copy number changes across the four genes have poorer prognosis. This is consistent with the view that multiple genetic pathways need to become deregulated in order for cancer to progress.

A simplicial complex-based approach to unmixing tumor progression data

BACKGROUND

Tumorigenesis is an evolutionary process by which tumor cells acquire mutations through successive diversification and differentiation. There is much interest in reconstructing this process of evolution due to its relevance to identifying drivers of mutation and predicting future prognosis and drug response. Efforts are challenged by high tumor heterogeneity, though, both within and among patients. In prior work, we showed that this heterogeneity could be turned into an advantage by computationally reconstructing models of cell populations mixed to different degrees in distinct tumors. Such mixed membership model approaches, however, are still limited in their ability to dissect more than a few well-conserved cell populations across a tumor data set.

RESULTS

We present a method to improve on current mixed membership model approaches by better accounting for conserved progression pathways between subsets of cancers, which imply a structure to the data that has not previously been exploited. We extend our prior methods, which use an interpretation of the mixture problem as that of reconstructing simple geometric objects called simplices, to instead search for structured unions of simplices called simplicial complexes that one would expect to emerge from mixture processes describing branches along an evolutionary tree. We further improve on the prior work with a novel objective function to better identify mixtures corresponding to parsimonious evolutionary tree models. We demonstrate that this approach improves on our ability to accurately resolve mixtures on simulated data sets and demonstrate its practical applicability on a large RNASeq tumor data set.

CONCLUSIONS

Better exploiting the expected geometric structure for mixed membership models produced from common evolutionary trees allows us to quickly and accurately reconstruct models of cell populations sampled from those trees. In the process, we hope to develop a better understanding of tumor evolution as well as other biological problems that involve interpreting genomic data gathered from heterogeneous populations of cells.

BitPhylogeny: a probabilistic framework for reconstructing intra-tumor phylogenies

Cancer has long been understood as a somatic evolutionary process, but many details of tumor progression remain elusive. Here, we present BitPhylogenyBitPhylogeny, a probabilistic framework to reconstruct intra-tumor evolutionary pathways. Using a full Bayesian approach, we jointly estimate the number and composition of clones in the sample as well as the most likely tree connecting them. We validate our approach in the controlled setting of a simulation study and compare it against several competing methods. In two case studies, we demonstrate how BitPhylogeny BitPhylogeny reconstructs tumor phylogenies from methylation patterns in colon cancer and from single-cell exomes in myeloproliferative neoplasm.

Cancer evolution: mathematical models and computational inference

Cancer is a somatic evolutionary process characterized by the accumulation of mutations, which contribute to tumor growth, clinical progression, immune escape, and drug resistance development. Evolutionary theory can be used to analyze the dynamics of tumor cell populations and to make inference about the evolutionary history of a tumor from molecular data. We review recent approaches to modeling the evolution of cancer, including population dynamics models of tumor initiation and progression, phylogenetic methods to model the evolutionary relationship between tumor subclones, and probabilistic graphical models to describe dependencies among mutations. Evolutionary modeling helps to understand how tumors arise and will also play an increasingly important prognostic role in predicting disease progression and the outcome of medical interventions, such as targeted therapy.

Single-cell genetic analysis reveals insights into clonal development of prostate cancers and indicates loss of PTEN as a marker of poor prognosis

Gauging the risk of developing progressive disease is a major challenge in prostate cancer patient management. We used genetic markers to understand genomic alteration dynamics during disease progression. By using a novel, advanced, multicolor fluorescence in situ hybridization approach, we enumerated copy numbers of six genes previously identified by array comparative genomic hybridization to be involved in aggressive prostate cancer [TBL1XR1, CTTNBP2, MYC (alias c-myc), PTEN, MEN1, and PDGFB] in six nonrecurrent and seven recurrent radical prostatectomy cases. An ERG break-apart probe to detect TMPRSS2-ERG fusions was included. Subsequent hybridization of probe panels and cell relocation resulted in signal counts for all probes in each individual cell analyzed. Differences in the degree of chromosomal and genomic instability (ie, tumor heterogeneity) or the percentage of cells with TMPRSS2-ERG fusion between samples with or without progression were not observed. Tumors from patients that progressed had more chromosomal gains and losses, and showed a higher degree of selection for a predominant clonal pattern. PTEN loss was the most frequent aberration in progressers (57%), followed by TBL1XR1 gain (29%). MYC gain was observed in one progresser, which was the only lesion with an ERG gain, but no TMPRSS2-ERG fusion. According to our results, a probe set consisting of PTEN, MYC, and TBL1XR1 would detect progressers with 86% sensitivity and 100% specificity. This will be evaluated further in larger studies.

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.

Intravital biobank and personalized cancer therapy: the correlation with omics

Biobanks have played a decisive role in all aspects of the field of cancer, including pathogenesis, diagnosis, prognosis and treatment. The significance of cancer biobanks is epitomized through the appropriate application of various "-omic" techniques (omics). The mutually motivated relationship between biobanks and omics has intensified the development of cancer research. Human cancer tissues that are maintained in intravital biobanks (or living tissue banks) retain native tumor microenvironment, tissue architecture, hormone responsiveness and cell-to-cell signalling properties. Intravital biobanks replicate the structural complexity and heterogeneity of human cancers, making them an ideal platform for preclinical studies. The application of omics with intravital biobanks renders them more active, which makes it possible for the cancer-related evaluations to be dynamically monitored on a real-time basis. Integrating intravital biobank and modern omics will provide a useful tool for the discovery and development of new drugs or novel therapeutic strategies. More importantly, intravital biobanks may play an essential role in the creation of meaningful patient-tailored therapies as for personalized medicine.