A mathematical methodology for determining the temporal order of pathway alterations arising during gliomagenesis

Current status of precision oncology in adult glioblastoma

The concept of precision oncology, the application of targeted drugs based on comprehensive molecular profiling, has revolutionized treatment strategies in oncology. This review summarizes the current status of precision oncology in glioblastoma (GBM), the most common and aggressive primary brain tumor in adults with a median survival below 2 years. Targeted treatments without prior target verification have consistently failed. Patients with BRAF V600E-mutated GBM benefit from BRAF/MEK-inhibition, whereas targeting EGFR alterations was unsuccessful due to poor tumor penetration, tumor cell heterogeneity, and pathway redundancies. Systematic screening for actionable molecular alterations resulted in low rates (< 10%) of targeted treatments. Efficacy was observed in one-third and currently appears to be limited to BRAF-, VEGFR-, and mTOR-directed treatments. Advancing precision oncology for GBM requires consideration of pathways instead of single alterations, new trial concepts enabling rapid and adaptive drug evaluation, a focus on drugs with sufficient bioavailability in the CNS, and the extension of target discovery and validation to the tumor microenvironment, tumor cell networks, and their interaction with immune cells and neurons.

Computational Methods Summarizing Mutational Patterns in Cancer: Promise and Limitations for Clinical Applications

Since the rise of next-generation sequencing technologies, the catalogue of mutations in cancer has been continuously expanding. To address the complexity of the cancer-genomic landscape and extract meaningful insights, numerous computational approaches have been developed over the last two decades. In this review, we survey the current leading computational methods to derive intricate mutational patterns in the context of clinical relevance. We begin with mutation signatures, explaining first how mutation signatures were developed and then examining the utility of studies using mutation signatures to correlate environmental effects on the cancer genome. Next, we examine current clinical research that employs mutation signatures and discuss the potential use cases and challenges of mutation signatures in clinical decision-making. We then examine computational studies developing tools to investigate complex patterns of mutations beyond the context of mutational signatures. We survey methods to identify cancer-driver genes, from single-driver studies to pathway and network analyses. In addition, we review methods inferring complex combinations of mutations for clinical tasks and using mutations integrated with multi-omics data to better predict cancer phenotypes. We examine the use of these tools for either discovery or prediction, including prediction of tumor origin, treatment outcomes, prognosis, and cancer typing. We further discuss the main limitations preventing widespread clinical integration of computational tools for the diagnosis and treatment of cancer. We end by proposing solutions to address these challenges using recent advances in machine learning.

Non-coding RNAs and glioma: Focus on cancer stem cells

Glioblastoma and gliomas can have a wide range of histopathologic subtypes. These heterogeneous histologic phenotypes originate from tumor cells with the distinct functions of tumorigenesis and self-renewal, called glioma stem cells (GSCs). GSCs are characterized based on multi-layered epigenetic mechanisms, which control the expression of many genes. This epigenetic regulatory mechanism is often based on functional non-coding RNAs (ncRNAs). ncRNAs have become increasingly important in the pathogenesis of human cancer and work as oncogenes or tumor suppressors to regulate carcinogenesis and progression. These RNAs by being involved in chromatin remodeling and modification, transcriptional regulation, and alternative splicing of pre-mRNA, as well as mRNA stability and protein translation, play a key role in tumor development and progression. Numerous studies have been performed to try to understand the dysregulation pattern of these ncRNAs in tumors and cancer stem cells (CSCs), which show robust differentiation and self-regeneration capacity. This review provides recent findings on the role of ncRNAs in glioma development and progression, particularly their effects on CSCs, thus accelerating the clinical implementation of ncRNAs as promising tumor biomarkers and therapeutic targets.

EGFR, the Lazarus target for precision oncology in glioblastoma

The Lazarus effect is a rare condition that happens when someone seemingly dead shows signs of life. The epidermal growth factor receptor (EGFR) represents a target in the fatal neoplasm glioblastoma (GBM) that through a series of negative clinical trials has prompted a vocal subset of the neuro-oncology community to declare this target dead. However, an argument can be made that the core tenets of precision oncology were overlooked in the initial clinical enthusiasm over EGFR as a therapeutic target in GBM. Namely, the wrong drugs were tested on the wrong patients at the wrong time. Furthermore, new insights into the biology of EGFR in GBM vis-à-vis other EGFR-driven neoplasms, such as non-small cell lung cancer, and development of novel GBM-specific EGFR therapeutics resurrects this target for future studies. Here, we will examine the distinct EGFR biology in GBM, how it exacerbates the challenge of treating a CNS neoplasm, how these unique challenges have influenced past and present EGFR-targeted therapeutic design and clinical trials, and what adjustments are needed to therapeutically exploit EGFR in this devastating disease.

Single-Cell Transcriptomics Revealed Subtype-Specific Tumor Immune Microenvironments in Human Glioblastomas

Human glioblastoma (GBM), the most aggressive brain tumor, comprises six major subtypes of malignant cells, giving rise to both inter-patient and intra-tumor heterogeneity. The interaction between different tumor subtypes and non-malignant cells to collectively shape a tumor microenvironment has not been systematically characterized. Herein, we sampled the cellular milieu of surgically resected primary tumors from 7 GBM patients using single-cell transcriptome sequencing. A lineage relationship analysis revealed that a neural-progenitor-2-like (NPC2-like) state with high metabolic activity was associated with the tumor cells of origin. Mesenchymal-1-like (MES1-like) and mesenchymal-2-like (MES2-like) tumor cells correlated strongly with immune infiltration and chronic hypoxia niche responses. We identified four subsets of tumor-associated macrophages/microglia (TAMs), among which TAM-1 co-opted both acute and chronic hypoxia-response signatures, implicated in tumor angiogenesis, invasion, and poor prognosis. MES-like GBM cells expressed the highest number of M2-promoting ligands compared to other cellular states while all six states were associated with TAM M2-type polarization and immunosuppression via a set of 10 ligand–receptor signaling pathways. Our results provide new insights into the differential roles of GBM cell subtypes in the tumor immune microenvironment that may be deployed for patient stratification and personalized treatment.

Conditional prediction of consecutive tumor evolution using cancer progression models: What genotype comes next?

Accurate prediction of tumor progression is key for adaptive therapy and precision medicine. Cancer progression models (CPMs) can be used to infer dependencies in mutation accumulation from cross-sectional data and provide predictions of tumor progression paths. However, their performance when predicting complete evolutionary trajectories is limited by violations of assumptions and the size of available data sets. Instead of predicting full tumor progression paths, here we focus on short-term predictions, more relevant for diagnostic and therapeutic purposes. We examine whether five distinct CPMs can be used to answer the question "Given that a genotype with n mutations has been observed, what genotype with n + 1 mutations is next in the path of tumor progression?" or, shortly, "What genotype comes next?". Using simulated data we find that under specific combinations of genotype and fitness landscape characteristics CPMs can provide predictions of short-term evolution that closely match the true probabilities, and that some genotype characteristics can be much more relevant than global features. Application of these methods to 25 cancer data sets shows that their use is hampered by a lack of information needed to make principled decisions about method choice. Fruitful use of these methods for short-term predictions requires adapting method's use to local genotype characteristics and obtaining reliable indicators of performance; it will also be necessary to clarify the interpretation of the method's results when key assumptions do not hold.

A probabilistic method for leveraging functional annotations to enhance estimation of the temporal order of pathway mutations during carcinogenesis

BACKGROUND

Cancer arises through accumulation of somatically acquired genetic mutations. An important question is to delineate the temporal order of somatic mutations during carcinogenesis, which contributes to better understanding of cancer biology and facilitates identification of new therapeutic targets. Although a number of statistical and computational methods have been proposed to estimate the temporal order of mutations, they do not account for the differences in the functional impacts of mutations and thus are likely to be obscured by the presence of passenger mutations that do not contribute to cancer progression. In addition, many methods infer the order of mutations at the gene level, which have limited power due to the low mutation rate in most genes.

RESULTS

In this paper, we develop a Probabilistic Approach for estimating the Temporal Order of Pathway mutations by leveraging functional Annotations of mutations (PATOPA). PATOPA infers the order of mutations at the pathway level, wherein it uses a probabilistic method to characterize the likelihood of mutational events from different pathways occurring in a certain order. The functional impact of each mutation is incorporated to weigh more on a mutation that is more integral to tumor development. A maximum likelihood method is used to estimate parameters and infer the probability of one pathway being mutated prior to another. Simulation studies and analysis of whole exome sequencing data from The Cancer Genome Atlas (TCGA) demonstrate that PATOPA is able to accurately estimate the temporal order of pathway mutations and provides new biological insights on carcinogenesis of colorectal and lung cancers.

CONCLUSIONS

PATOPA provides a useful tool to estimate temporal order of mutations at the pathway level while leveraging functional annotations of mutations.

Uncovering the subtype-specific temporal order of cancer pathway dysregulation

Cancer is driven by genetic mutations that dysregulate pathways important for proper cell function. Therefore, discovering these cancer pathways and their dysregulation order is key to understanding and treating cancer. However, the heterogeneity of mutations between different individuals makes this challenging and requires that cancer progression is studied in a subtype-specific way. To address this challenge, we provide a mathematical model, called Subtype-specific Pathway Linear Progression Model (SPM), that simultaneously captures cancer subtypes and pathways and order of dysregulation of the pathways within each subtype. Experiments with synthetic data indicate the robustness of SPM to problem specifics including noise compared to an existing method. Moreover, experimental results on glioblastoma multiforme and colorectal adenocarcinoma show the consistency of SPM's results with the existing knowledge and its superiority to an existing method in certain cases. The implementation of our method is available at https://github.com/Dalton386/SPM.

Motion, fixation probability and the choice of an evolutionary process

Seemingly minor details of mathematical and computational models of evolution are known to change the effect of population structure on the outcome of evolutionary processes. For example, birth-death dynamics often result in amplification of selection, while death-birth processes have been associated with suppression. In many biological populations the interaction structure is not static. Instead, members of the population are in motion and can interact with different individuals at different times. In this work we study populations embedded in a flowing medium; the interaction network is then time dependent. We use computer simulations to investigate how this dynamic structure affects the success of invading mutants, and compare these effects for different coupled birth and death processes. Specifically, we show how the speed of the motion impacts the fixation probability of an invading mutant. Flows of different speeds interpolate between evolutionary dynamics on fixed heterogeneous graphs and well-stirred populations; this allows us to systematically compare against known results for static structured populations. We find that motion has an active role in amplifying or suppressing selection by fragmenting and reconnecting the interaction graph. While increasing flow speeds suppress selection for most evolutionary models, we identify characteristic responses to flow for the different update rules we test. In particular we find that selection can be maximally enhanced or suppressed at intermediate flow speeds.

Whether a mutation spreads in a population or not is one of the most important questions in biology. The evolution of cancer and antibiotic resistance, for example, are mediated by invading mutants. Recent work has shown that population structure can have important consequences for the outcome of evolution. For instance, a mutant can have a higher or a lower chance of invasion than in unstructured populations. These effects can depend on seemingly minor details of the evolutionary model, such as the order of birth and death events. Many biological populations are in motion, for example due to external stirring. Experimentally this is known to be important; the performance of mutants in E. coli populations, for example, depends on the rate of mixing. Here, we focus on simulations of populations in a flowing medium, and compare the success of a mutant for different flow speeds. We contrast different evolutionary models, and identify what features of the evolutionary model affect mutant success for different speeds of the flow. We find that the chance of mutant invasion can be at its highest (or lowest) at intermediate flow speeds, depending on the order in which birth and death events occur in the evolutionary process.

Every which way? On predicting tumor evolution using cancer progression models

Successful prediction of the likely paths of tumor progression is valuable for diagnostic, prognostic, and treatment purposes. Cancer progression models (CPMs) use cross-sectional samples to identify restrictions in the order of accumulation of driver mutations and thus CPMs encode the paths of tumor progression. Here we analyze the performance of four CPMs to examine whether they can be used to predict the true distribution of paths of tumor progression and to estimate evolutionary unpredictability. Employing simulations we show that if fitness landscapes are single peaked (have a single fitness maximum) there is good agreement between true and predicted distributions of paths of tumor progression when sample sizes are large, but performance is poor with the currently common much smaller sample sizes. Under multi-peaked fitness landscapes (i.e., those with multiple fitness maxima), performance is poor and improves only slightly with sample size. In all cases, detection regime (when tumors are sampled) is a key determinant of performance. Estimates of evolutionary unpredictability from the best performing CPM, among the four examined, tend to overestimate the true unpredictability and the bias is affected by detection regime; CPMs could be useful for estimating upper bounds to the true evolutionary unpredictability. Analysis of twenty-two cancer data sets shows low evolutionary unpredictability for several of the data sets. But most of the predictions of paths of tumor progression are very unreliable, and unreliability increases with the number of features analyzed. Our results indicate that CPMs could be valuable tools for predicting cancer progression but that, currently, obtaining useful predictions of paths of tumor progression from CPMs is dubious, and emphasize the need for methodological work that can account for the probably multi-peaked fitness landscapes in cancer.

In silico learning of tumor evolution through mutational time series

Cancer is caused by the effects of somatic mutations known as drivers. Although a number of major cancer drivers have been identified, it is suspected that many more comparatively rare and conditional drivers exist, and the interactions between different cancer-associated mutations that might be relevant for tumor progression are not well understood. We applied an advanced neural network approach to learn the sequence of mutations and the mutational burden in colon and lung cancers and to identify mutations that are associated with individual drivers. A significant ordering of driver mutations is demonstrated, and numerous, previously undetected conditional drivers are identified. These findings broaden the existing understanding of the mechanisms of tumor progression and have implications for therapeutic strategies.

Cancer arises through the accumulation of somatic mutations over time. Understanding the sequence of mutation occurrence during cancer progression can assist early and accurate diagnosis and improve clinical decision-making. Here we employ long short-term memory (LSTM) networks, a class of recurrent neural network, to learn the evolution of a tumor through an ordered sequence of mutations. We demonstrate the capacity of LSTMs to learn complex dynamics of the mutational time series governing tumor progression, allowing accurate prediction of the mutational burden and the occurrence of mutations in the sequence. Using the probabilities learned by the LSTM, we simulate mutational data and show that the simulation results are statistically indistinguishable from the empirical data. We identify passenger mutations that are significantly associated with established cancer drivers in the sequence and demonstrate that the genes carrying these mutations are substantially enriched in interactions with the corresponding driver genes. Breaking the network into modules consisting of driver genes and their interactors, we show that these interactions are associated with poor patient prognosis, thus likely conferring growth advantage for tumor progression. Thus, application of LSTM provides for prediction of numerous additional conditional drivers and reveals hitherto unknown aspects of cancer evolution.

An Integrated Framework for Identifying Mutated Driver Pathway and Cancer Progression

Next-generation sequencing (NGS) technologies provide amount of somatic mutation data in a large number of patients. The identification of mutated driver pathway and cancer progression from these data is a challenging task because of the heterogeneity of interpatient. In addition, cancer progression at the pathway level has been proved to be more reasonable than at the gene level. In this paper, we introduce an integrated framework to identify mutated driver pathways and cancer progression (iMDPCP) at the pathway level from somatic mutation data. First, we use uncertainty coefficient to quantify mutual exclusivity on gene driver pathways and develop a computational framework to identify mutated driver pathways based on the adaptive discrete differential evolution algorithm. Then, we construct cancer progression model for driver pathways based on the Bayesian Network. Finally, we evaluate the performance of iMDPCP on real cancer somatic mutation datasets. The experimental results indicate that iMDPCP is more accurate than state-of-the-art methods according to the enrichment of KEGG pathways, and it also provides new insights on identifying cancer progression at the pathway level.

Dissecting human gliomas by single-cell RNA sequencing

Diffuse gliomas are the most common human primary brain tumors and remain incurable. They are complex entities in which diverse genetic and nongenetic effects determine tumor biology and clinical course. Our current understanding of gliomas in patients is primarily based on genomic and transcriptomic methods that have profiled them as bulk, providing critical information yet masking the diversity of cells within each tumor. Recent advances in single-cell DNA and RNA profiling have paved the way to studying tumors at cellular resolution. Here, we review initial studies deploying single-cell analysis in clinical glioma samples, with a focus on RNA expression profiling. We highlight how these studies provide new insights into glioma biology, tumor heterogeneity, cancer cell lineages, cancer stem cell programs, the tumor microenvironment, and glioma classification.

Single-Cell RNA-Sequencing in Glioma

PURPOSE OF REVIEW

In this review, we seek to summarize the literature concerning the use of single-cell RNA-sequencing for CNS gliomas.

RECENT FINDINGS

Single-cell analysis has revealed complex tumor heterogeneity, subpopulations of proliferating stem-like cells and expanded our view of tumor microenvironment influence in the disease process. Although bulk RNA-sequencing has guided our initial understanding of glioma genetics, this method does not accurately define the heterogeneous subpopulations found within these tumors. Single-cell techniques have appealing applications in cancer research, as diverse cell types and the tumor microenvironment have important implications in therapy. High cost and difficult protocols prevent widespread use of single-cell RNA-sequencing; however, continued innovation will improve accessibility and expand our of knowledge gliomas.

Looking beyond drivers and passengers in cancer genome sequencing data

Cancer arises as a result of acquired changes in the DNA sequence of the genome of somatic cells. A subset of the genetic changes, dubbed driver mutations, propels tumor growth, and the remaining changes are passengers, apparently inconsequential for neoplastic transformation. Massive genome sequencing of thousands of tumors from all major cancer types has enabled cataloging of the so-called driver and passenger mutations, and facilitated molecular classification of cancer, guiding precision medicine approach for the patients. Nonetheless, innovative analyses of cancer genomics data has led to novel, sometimes serendipitous findings that have aided to our understanding of other aspects of the biology of the disease and opened up new frontiers. For instance, emerging findings show that mutational patterns in cancer genomes can help detect signatures of known and novel DNA damage and repair processes, provide a likely chronological account of genomic changes in cancer genomes, and allow revisiting the models of cancer evolution. These findings have stimulated original approaches to identify disease etiology, stratify patients, target the disease, and monitor patient responses, complementing driver-mutation centric approaches. In this review, we discuss these emerging approaches and unexpected breakthroughs, and their implications for basic cancer research and clinical practices.

Variable selection for disease progression models: methods for oncogenetic trees and application to cancer and HIV

Background

Disease progression models are important for understanding the critical steps during the development of diseases. The models are imbedded in a statistical framework to deal with random variations due to biology and the sampling process when observing only a finite population. Conditional probabilities are used to describe dependencies between events that characterise the critical steps in the disease process.

Many different model classes have been proposed in the literature, from simple path models to complex Bayesian networks. A popular and easy to understand but yet flexible model class are oncogenetic trees. These have been applied to describe the accumulation of genetic aberrations in cancer and HIV data. However, the number of potentially relevant aberrations is often by far larger than the maximal number of events that can be used for reliably estimating the progression models. Still, there are only a few approaches to variable selection, which have not yet been investigated in detail.

Results

We fill this gap and propose specifically for oncogenetic trees ten variable selection methods, some of these being completely new. We compare them in an extensive simulation study and on real data from cancer and HIV. It turns out that the preselection of events by clique identification algorithms performs best. Here, events are selected if they belong to the largest or the maximum weight subgraph in which all pairs of vertices are connected.

Conclusions

The variable selection method of identifying cliques finds both the important frequent events and those related to disease pathways.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-017-1762-1) contains supplementary material, which is available to authorized users.

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.

Computational approaches for the identification of cancer genes and pathways

High‐throughput DNA sequencing techniques enable large‐scale measurement of somatic mutations in tumors. Cancer genomics research aims at identifying all cancer‐related genes and solid interpretation of their contribution to cancer initiation and development. However, this venture is characterized by various challenges, such as the high number of neutral passenger mutations and the complexity of the biological networks affected by driver mutations. Based on biological pathway and network information, sophisticated computational methods have been developed to facilitate the detection of cancer driver mutations and pathways. They can be categorized into (1) methods using known pathways from public databases, (2) network‐based methods, and (3) methods learning cancer pathways de novo. Methods in the first two categories use and integrate different types of data, such as biological pathways, protein interaction networks, and gene expression measurements. The third category consists of de novo methods that detect combinatorial patterns of somatic mutations across tumor samples, such as mutual exclusivity and co‐occurrence. In this review, we discuss recent advances, current limitations, and future challenges of these approaches for detecting cancer genes and pathways. We also discuss the most important current resources of cancer‐related genes. WIREs Syst Biol Med 2017, 9:e1364. doi: 10.1002/wsbm.1364

For further resources related to this article, please visit the WIREs website.

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.

The mathematics of cancer: integrating quantitative models

Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments. In turn, mathematical modelling contributes to cancer research by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research in cancer biology.

Defining order and timing of mutations during cancer progression: the TO-DAG probabilistic graphical model

Somatic mutations arise and accumulate both during tumor genesis and progression. However, the order in which mutations occur is an open question and the inference of the temporal ordering at the gene level could potentially impact on patient treatment. Thus, exploiting recent observations suggesting that the occurrence of mutations is a non-memoryless process, we developed a computational approach to infer timed oncogenetic directed acyclic graphs (TO-DAGs) from human tumor mutation data. Such graphs represent the path and the waiting times of alterations during tumor evolution. The probability of occurrence of each alteration in a path is the probability that the alteration occurs when all alterations prior to it have occurred. The waiting time between an alteration and the subsequent is modeled as a stochastic function of the conditional probability of the event given the occurrence of the previous one. TO-DAG performances have been evaluated both on synthetic data and on somatic non-silent mutations from prostate cancer and melanoma patients and then compared with those of current well-established approaches. TO-DAG shows high performance scores on synthetic data and recognizes mutations in gatekeeper tumor suppressor genes as trigger for several downstream mutational events in the human tumor data.

Cancer stem cells in glioblastoma

Glioblastoma is the most prevalent and malignant primary brain tumor, containing self-renewing, tumorigenic cancer stem cells (CSCs) that contribute to tumor initiation and therapeutic resistance. In this review, Lathia et al. discuss how the integration of genetics, epigenetics, and metabolism has shaped our understanding of how CSCs function to drive GBM growth.

Tissues with defined cellular hierarchies in development and homeostasis give rise to tumors with cellular hierarchies, suggesting that tumors recapitulate specific tissues and mimic their origins. Glioblastoma (GBM) is the most prevalent and malignant primary brain tumor and contains self-renewing, tumorigenic cancer stem cells (CSCs) that contribute to tumor initiation and therapeutic resistance. As normal stem and progenitor cells participate in tissue development and repair, these developmental programs re-emerge in CSCs to support the development and progressive growth of tumors. Elucidation of the molecular mechanisms that govern CSCs has informed the development of novel targeted therapeutics for GBM and other brain cancers. CSCs are not self-autonomous units; rather, they function within an ecological system, both actively remodeling the microenvironment and receiving critical maintenance cues from their niches. To fulfill the future goal of developing novel therapies to collapse CSC dynamics, drawing parallels to other normal and pathological states that are highly interactive with their microenvironments and that use developmental signaling pathways will be beneficial.

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.

Heterogeneity of epidermal growth factor receptor signalling networks in glioblastoma

As tumours evolve, the daughter cells of the initiating cell often become molecularly heterogeneous and develop different functional properties and therapeutic vulnerabilities. In glioblastoma (GBM), a lethal form of brain cancer, the heterogeneous expression of the epidermal growth factor receptor (EGFR) poses a substantial challenge for the effective use of EGFR-targeted therapies. Understanding the mechanisms that cause EGFR heterogeneity in GBM should provide better insights into how they, and possibly other amplified receptor tyrosine kinases, affect cellular signalling, metabolism and drug resistance.

Inferring mutational timing and reconstructing tumour evolutionary histories

Cancer evolution can be considered within a Darwinian framework. Both micro and macro-evolutionary theories can be applied to understand tumour progression and treatment failure. Owing to cancers' complexity and heterogeneity the rules of tumour evolution, such as the role of selection, remain incompletely understood. The timing of mutational events during tumour evolution presents diagnostic, prognostic and therapeutic opportunities. Here we review the current sampling and computational approaches for inferring mutational timing and the evidence from next generation sequencing-informed data on mutational timing across all tumour types. We discuss how this knowledge can be used to illuminate the genes and pathways that drive cancer initiation and relapse; and to support drug development and clinical trial design.

Simultaneous inference of cancer pathways and tumor progression from cross-sectional mutation data

Recent cancer sequencing studies provide a wealth of somatic mutation data from a large number of patients. One of the most intriguing and challenging questions arising from this data is to determine whether the temporal order of somatic mutations in a cancer follows any common progression. Since we usually obtain only one sample from a patient, such inferences are commonly made from cross-sectional data from different patients. This analysis is complicated by the extensive variation in the somatic mutations across different patients, variation that is reduced by examining combinations of mutations in various pathways. Thus far, methods to reconstruct tumor progression at the pathway level have restricted attention to known, a priori defined pathways. In this work we show how to simultaneously infer pathways and the temporal order of their mutations from cross-sectional data, leveraging on the exclusivity property of driver mutations within a pathway. We define the pathway linear progression model, and derive a combinatorial formulation for the problem of finding the optimal model from mutation data. We show that with enough samples the optimal solution to this problem uniquely identifies the correct model with high probability even when errors are present in the mutation data. We then formulate the problem as an integer linear program (ILP), which allows the analysis of datasets from recent studies with large numbers of samples. We use our algorithm to analyze somatic mutation data from three cancer studies, including two studies from The Cancer Genome Atlas (TCGA) on large number of samples on colorectal cancer and glioblastoma. The models reconstructed with our method capture most of the current knowledge of the progression of somatic mutations in these cancer types, while also providing new insights on the tumor progression at the pathway level.

Identifying restrictions in the order of accumulation of mutations during tumor progression: effects of passengers, evolutionary models, and sampling

BACKGROUND

Cancer progression is caused by the sequential accumulation of mutations, but not all orders of accumulation are equally likely. When the fixation of some mutations depends on the presence of previous ones, identifying restrictions in the order of accumulation of mutations can lead to the discovery of therapeutic targets and diagnostic markers. The purpose of this study is to conduct a comprehensive comparison of the performance of all available methods to identify these restrictions from cross-sectional data. I used simulated data sets (where the true restrictions are known) but, in contrast to previous work, I embedded restrictions within evolutionary models of tumor progression that included passengers (mutations not responsible for the development of cancer, known to be very common). This allowed me to assess, for the first time, the effects of having to filter out passengers, of sampling schemes (when, how, and how many samples), and of deviations from order restrictions.

RESULTS

Poor choices of method, filtering, and sampling lead to large errors in all performance measures. Having to filter passengers lead to decreased performance, especially because true restrictions were missed. Overall, the best method for identifying order restrictions were Oncogenetic Trees, a fast and easy to use method that, although unable to recover dependencies of mutations on more than one mutation, showed good performance in most scenarios, superior to Conjunctive Bayesian Networks and Progression Networks. Single cell sampling provided no advantage, but sampling in the final stages of the disease vs. sampling at different stages had severe effects. Evolutionary model and deviations from order restrictions had major, and sometimes counterintuitive, interactions with other factors that affected performance.

CONCLUSIONS

This paper provides practical recommendations for using these methods with experimental data. It also identifies key areas of future methodological work and, in particular, it shows that it is both possible and necessary to embed assumptions about order restrictions and the nature of driver status within evolutionary models of cancer progression to evaluate the performance of inferential approaches.

Identification of constrained cancer driver genes based on mutation timing

Cancer drivers are genomic alterations that provide cells containing them with a selective advantage over their local competitors, whereas neutral passengers do not change the somatic fitness of cells. Cancer-driving mutations are usually discriminated from passenger mutations by their higher degree of recurrence in tumor samples. However, there is increasing evidence that many additional driver mutations may exist that occur at very low frequencies among tumors. This observation has prompted alternative methods for driver detection, including finding groups of mutually exclusive mutations and incorporating prior biological knowledge about gene function or network structure. Dependencies among drivers due to epistatic interactions can also result in low mutation frequencies, but this effect has been ignored in driver detection so far. Here, we present a new computational approach for identifying genomic alterations that occur at low frequencies because they depend on other events. Unlike passengers, these constrained mutations display punctuated patterns of occurrence in time. We test this driver-passenger discrimination approach based on mutation timing in extensive simulation studies, and we apply it to cross-sectional copy number alteration (CNA) data from ovarian cancer, CNA and single-nucleotide variant (SNV) data from breast tumors and SNV data from colorectal cancer. Among the top ranked predicted drivers, we find low-frequency genes that have already been shown to be involved in carcinogenesis, as well as many new candidate drivers. The mutation timing approach is orthogonal and complementary to existing driver prediction methods. It will help identifying from cancer genome data the alterations that drive tumor progression.

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.

Most human non-GCIMP glioblastoma subtypes evolve from a common proneural-like precursor glioma

To understand the relationships between the non-GCIMP glioblastoma (GBM) subgroups, we performed mathematical modeling to predict the temporal sequence of driver events during tumorigenesis. The most common order of evolutionary events is 1) chromosome (chr) 7 gain and chr10 loss, followed by 2) CDKN2A loss and/or TP53 mutation, and 3) alterations canonical for specific subtypes. We then developed a computational methodology to identify drivers of broad copy number changes, identifying PDGFA (chr7) and PTEN (chr10) as driving initial nondisjunction events. These predictions were validated using mouse modeling, showing that PDGFA is sufficient to induce proneural-like gliomas and that additional NF1 loss converts proneural to the mesenchymal subtype. Our findings suggest that most non-GCIMP mesenchymal GBMs arise as, and evolve from, a proneural-like precursor.

RESICstance is futile-but not in glioblastoma

Genomic alterations that occur early in tumorigenesis represent fundamental diver lesions and are perhaps of highest priority as a means to intervene therapeutically. In this issue of Cancer Cell, Ozawa and colleagues apply an algorithm to identify early events in glioblastoma and validate their findings in a rigorous manner.

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

Motivation: Development and progression of solid tumors can be attributed to a process of mutations, which typically includes changes in the number of copies of genes or genomic regions. Although comparisons of cells within single tumors show extensive heterogeneity, recurring features of their evolutionary process may be discerned by comparing multiple regions or cells of a tumor. A useful source of data for studying likely progression of individual tumors is fluorescence in situ hybridization (FISH), which allows one to count copy numbers of several genes in hundreds of single cells. Novel algorithms for interpreting such data phylogenetically are needed, however, to reconstruct likely evolutionary trajectories from states of single cells and facilitate analysis of tumor evolution.

Results: In this article, we develop phylogenetic methods to infer likely models of tumor progression using FISH copy number data and apply them to a study of FISH data from two cancer types. Statistical analyses of topological characteristics of the tree-based model provide insights into likely tumor progression pathways consistent with the prior literature. Furthermore, tree statistics from the resulting phylogenies can be used as features for prediction methods. This results in improved accuracy, relative to unstructured gene copy number data, at predicting tumor state and future metastasis.

Availability: Source code for software that does FISH tree building (FISHtrees) and the data on cervical and breast cancer examined here are available at ftp://ftp.ncbi.nlm.nih.gov/pub/FISHtrees.

Contact:sachowdh@andrew.cmu.edu

Supplementary information:Supplementary data are available at Bioinformatics online.

Learning oncogenetic networks by reducing to mixed integer linear programming

Cancer can be a result of accumulation of different types of genetic mutations such as copy number aberrations. The data from tumors are cross-sectional and do not contain the temporal order of the genetic events. Finding the order in which the genetic events have occurred and progression pathways are of vital importance in understanding the disease. In order to model cancer progression, we propose Progression Networks, a special case of Bayesian networks, that are tailored to model disease progression. Progression networks have similarities with Conjunctive Bayesian Networks (CBNs) [1],a variation of Bayesian networks also proposed for modeling disease progression. We also describe a learning algorithm for learning Bayesian networks in general and progression networks in particular. We reduce the hard problem of learning the Bayesian and progression networks to Mixed Integer Linear Programming (MILP). MILP is a Non-deterministic Polynomial-time complete (NP-complete) problem for which very good heuristics exists. We tested our algorithm on synthetic and real cytogenetic data from renal cell carcinoma. We also compared our learned progression networks with the networks proposed in earlier publications. The software is available on the website https://bitbucket.org/farahani/diprog.

Computational medicine: translating models to clinical care

Because of the inherent complexity of coupled nonlinear biological systems, the development of computational models is necessary for achieving a quantitative understanding of their structure and function in health and disease. Statistical learning is applied to high-dimensional biomolecular data to create models that describe relationships between molecules and networks. Multiscale modeling links networks to cells, organs, and organ systems. Computational approaches are used to characterize anatomic shape and its variations in health and disease. In each case, the purposes of modeling are to capture all that we know about disease and to develop improved therapies tailored to the needs of individuals. We discuss advances in computational medicine, with specific examples in the fields of cancer, diabetes, cardiology, and neurology. Advances in translating these computational methods to the clinic are described, as well as challenges in applying models for improving patient health.

Temporal ordering of cancer microarray data through a reinforcement learning based approach

Temporal modeling and analysis and more specifically, temporal ordering are very important problems within the fields of bioinformatics and computational biology, as the temporal analysis of the events characterizing a certain biological process could provide significant insights into its development and progression. Particularly, in the case of cancer, understanding the dynamics and the evolution of this disease could lead to better methods for prediction and treatment. In this paper we tackle, from a computational perspective, the temporal ordering problem, which refers to constructing a sorted collection of multi-dimensional biological data, collection that reflects an accurate temporal evolution of biological systems. We introduce a novel approach, based on reinforcement learning, more precisely, on Q-learning, for the biological temporal ordering problem. The experimental evaluation is performed using several DNA microarray data sets, two of which contain cancer gene expression data. The obtained solutions are correlated either to the given correct ordering (in the cases where this is provided for validation), or to the overall survival time of the patients (in the case of the cancer data sets), thus confirming a good performance of the proposed model and indicating the potential of our proposal.

Network analysis of genomic alteration profiles reveals co-altered functional modules and driver genes for glioblastoma

The heterogeneity of genetic alterations in human cancer genomes presents a major challenge to advancing our understanding of cancer mechanisms and identifying cancer driver genes. To tackle this heterogeneity problem, many approaches have been proposed to investigate genetic alterations and predict driver genes at the individual pathway level. However, most of these approaches ignore the correlation of alteration events between pathways and miss many genes with rare alterations collectively contributing to carcinogenesis. Here, we devise a network-based approach to capture the cooperative functional modules hidden in genome-wide somatic mutation and copy number alteration profiles of glioblastoma (GBM) from The Cancer Genome Atlas (TCGA), where a module is a set of altered genes with dense interactions in the protein interaction network. We identify 7 pairs of significantly co-altered modules that involve the main pathways known to be altered in GBM (TP53, RB and RTK signaling pathways) and highlight the striking co-occurring alterations among these GBM pathways. By taking into account the non-random correlation of gene alterations, the property of co-alteration could distinguish oncogenic modules that contain driver genes involved in the progression of GBM. The collaboration among cancer pathways suggests that the redundant models and aggravating models could shed new light on the potential mechanisms during carcinogenesis and provide new indications for the design of cancer therapeutic strategies.