Inferring growth and genetic evolution of tumors from genome sequences

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Inferring growth and genetic evolution of tumors from genome sequences Verena Körber1,2 and Thomas Höfer1,2 Abstract

Cancer has long been viewed as an evolutionary process. Deep genome sequencing is now providing extensive catalogues of somatic mutations and their frequencies in tumors. These data have stimulated the development of mathematical inference methods for elucidating how genetic evolution and clonal growth of cancers are intertwined. Here, we review recent progress in this field that has shed light on early mutational events linked to tumor origins and subsequent paths of selective or neutral evolution of tumors. These techniques also enable quantification of the selective advantage of oncogenic driver mutations. Collectively, the modeling approaches now allow us to infer key dynamic processes of tumor development from somatic mutation patterns. Addresses 1 Division of Theoretical Systems Biology, German Cancer Research Centre (DKFZ), Im Neuenheimer Feld 280, D-69120, Heidelberg, Germany 2 Bioquant Center, Heidelberg University, Im Neuenheimer Feld 267, D69120, Heidelberg, Germany Corresponding author: Höfer, Thomas ([email protected])

In the past decade, cancer mutations have been catalogued on an unprecedented scale, owing to progress in DNA sequencing technology and associated computational approaches (e.g. Refs. [5e7]). This progress in identifying mutations and quantifying their allele frequencies has paved the way for the development of mathematical inference methods that address the evolutionary pathways and dynamics of cancer growth, treatment resistance and recurrence. Recent work in this field has raised fundamental questions on the modes of evolution seen at different stages of tumor development and during response to treatment. In particular, several studies have challenged the hitherto prevailing paradigm of continuous Darwinian evolution of tumors [8e10]. The interpretation of cancer genomes and associated phylogenetic inferences are now increasingly placed in the context of the clonal growth dynamics of cancers. While mathematical models of cancer growth have traditionally not considered genetic evolution [11], these new developments offer a promising route to understanding genetic cancer evolution within the ecology of tissues and organisms.

Current Opinion in Systems Biology 2019, 16:1–9 This reviews comes from a themed issue on Mathematical modelling Edited by Joerg Stelling and Mustafa Khammash For a complete overview see the Issue and the Editorial Available online 26 November 2019 https://doi.org/10.1016/j.coisb.2019.10.015 2452-3100/© 2019 Elsevier Ltd. All rights reserved.

Keywords Tumor growth, Cancer evolution, Dynamics systems, Agent-based modeling, Clonal dynamics, Selective advantage.

Introduction The progression of a normal cell in a multicellular organism to a growing tumor cell population has been described as an evolutionary process driven by random acquisition of mutations and selection of oncogenic drivers [1,2]. The research program resulting from this view entails identifying the mutations harbored by cancer cells, defining their selective advantage and thus understanding the evolutionary paths taken by individual tumors prior, and in response, to treatment. Elucidating the dynamics of cancer evolution may help improve both therapy modalities [3] and scheduling [4]. www.sciencedirect.com

Subclonal phylogenies and temporal sequences of driver mutations Mathematical methods for phylogenetic reconstruction generally have two, partially overlapping, aims: to identify the branching pattern of genetic subclones in a tumor and the temporal order in which cancer driver mutations have become fixed. Mathematical inference methods have been tailored to the specific qualities of bulk versus single-cell sequencing data [12,13]. Deep, shot-gun genome sequencing of bulk cell populations yields reliable frequencies of mutations (variant allele frequencies, VAFs) but is not conclusive on which of the lower-frequency mutations co-occur in the same cells. Nevertheless, subclonal inference greatly benefits from the analysis of all somatic mutations that become amplified as a subclone grows, not just cancer drivers. Phylogenetic inference from these data is based on sorting somatic mutations with the same VAF into a subclone. This has been done by clustering mutations without assumptions on the underlying evolutionary process, or by more sophisticated Bayesian inference or maximum-likelihood approaches employing for example, multinomial distributions on evolutionary Current Opinion in Systems Biology 2019, 16:1–9

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trees (e.g. Refs. [10,14,15]). With the usual sequencing coverage for whole-genome sequencing (w30x), early (clonal) mutations can be distinguished from later occurring (subclonal) ones, thus providing a coarsegrained temporal order of mutations. Higher coverage (e.g., 90e150x) greatly aids reliable discrimination between clonal and subclonal events and allows resolution of w2e5 subclones with different frequencies (Figure 1a). However, there are principal limitations in distinguishing small subclones, and, beyond the distinction between the clonal tumor stem and subclonal branches, the reconstruction of phylogenetic trees may not be unique (see Figure 2). In addition to deeper sequencing, drawing multiple samples of a tumor has been found to aid phylogenetic reconstruction (Figure 1b). Such approaches have used longitudinal sampling (often of primary and recurrent tumors of the same patient) [10,16,17], sampling primary tumor and metastases [18,19], or sampling multiple regions of a tumor [20e22]. Nevertheless, the inherent limitations of phylogenetic inference from bulk sequencing data should be kept in mind. A case in point is the recent debate on the migration patterns of metastasizing tumors [18,19,23] where data were often compatible with multiple seeding patterns [23,24]. Converting mutation count into real time via mutation rates, several studies encompassing multiple cancer entities have concluded that human cancers typically originate years to decades prior to initial diagnosis [25e 27], which, interestingly, has included even extremely fast-growing glioblastomas [10]. In contrast to bulk sequencing, single-cell genome sequencing allows identifying co-occurring mutation in individual cells. In principle, better subclonal resolution than for bulk data, down to the level of single cells, could be achieved. However, the current experimental protocols suffer from high rates of allelic dropouts, and the considerable cost limits available data sets usually to <1000 cells, resulting in appreciable subsampling of tumors. The analysis of these data usually focuses on cancer driver mutations (rather than all somatic mutations as in the analysis of bulk data). Using sophisticated mathematical inference tools, detailed sequences of the acquisition of driver mutations have been reconstructed [13,28,29]. A recent study on normal human hematopoiesis has leveraged a much broader array of somatic mutations in individual cells by first growing clones and subjecting them to whole-genome sequencing; coalescent theory has then been used for phylogenetic reconstruction and estimating the number of hematopoietic stem cells [30]. Another promising approach consists in combining deep whole genome sequencing of tumor cell populations with targeted sequencing of single cells [18,31]. Current Opinion in Systems Biology 2019, 16:1–9

Modeling clonal growth and genetic evolution Reconstruction of subclones and phylogenetic trees from genome sequences is often viewed as a kind of classification problem (e.g., which mutations belong to which subclone). However, to rationalize the observed patterns, several groups have turned to studying the underlying processes of mutation and cell proliferation that shape the observable VAF distributions and patterns. On the one hand, developing expectations on the shape of clone size distributions aids inference of subclones; on the other, such data can also be used to infer quantitative properties of the evolutionary process (rates of mutation, proliferation etc.) from the experimental data. This has been done by developing dynamical systems (stochastic and/or approximative deterministic) that consider the effect of mutations on the rates of cell proliferation, cell death or cell differentiation into non-dividing tumor cells [9,10,17,32e34]. Many approaches do not consider regional variation of mutation patterns, as usually only one sample per tumor is available. By contrast, the Curtis group have regularly employed regional sampling and fit three-dimensional, spatially heterogeneous models of tumor growth and evolution to these data, making use of Approximate Bayesian Computing [8,35,36]. In the following, we discuss recent results of non-spatial and spatially resolved modeling approaches.

Selective versus neutral evolution of cancer Given the enormous number of tumor-specific somatic mutations found by whole-genome sequencing (usually between 103 and 104 per tumor sample), a critical e and incompletely understood e question is which of these mutations confer selective advantage to cells. From a computational angle, this problem has been addressed using the ratio of non-synonymous to synonymous single-nucleotide substitutions (dN/dS ratio) [37]. More recent work takes a different viewpoint and explicitly considers the underlying evolutionary dynamics. The basic tenet of the latter approaches is that selection and neutral evolution cause distinct patterns of allele frequencies of mutations in cell populations. Are oncogenic mutations in normal tissues selected?

A provocative new perspective on the origin of cancer has been afforded by genome or transcriptome sequencing of normal tissue in adults, which uncovers numerous cancer mutations [38e41]. Lung, skin and esophagus exhibit the most mutations, suggesting strong mutagenic impact of the environment [41]. Statistical analyses of the dN/dS ratio suggest that many of these mutations have been under positive selection and may have caused local clonal expansions in tissues, albeit without evident pathology. However, a contrasting view of these phenomena has been put forward [42]. It is based on previous work on clone size distributions in www.sciencedirect.com

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Phylogenetic reconstruction from bulk sequencing data. (a) Subclonal resolution improves with higher sequencing depth. (b) Inference of phylogenetic structure is improved by analyzing multiple samples of the same tumor. The absence of shared mutations at small variant allele frequencies (VAFs) suggests early branching between the two analyzed regions. Mutations colored in orange and light green are clonally present in the respective sample but subclonal in the overall tumor. These mutations could have been erroneously classified as clonal if analyzing a single sample only. (c) Inference of phylogenetic structure is improved by analyzing multiple samples of the same tumor. The presence of shared mutations at small variant allele frequencies suggests a shared phylogenetic structure between both samples. Subclonal mutations on the purple branch would have been erroneously classified as clonal if analyzing a single sample only.

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Clonal growth dynamics within tumors shape the variant allele frequency distribution measured with deep bulk sequencing. (a) In a neutrally evolving tumor, heterozygous mutations already present in the founder cell will be measured at variant allele frequencies around 0.5 (corresponding to the right peak in the variant allele frequency histogram); intratumoral heterogeneity is shaped by neutral drift and is reflected by a subclonal tail at low variant allele frequencies. (b) With ongoing selection, clones with acquired oncogenic driver mutations will be selected. Mutations present in the founder cell of large clones can be identified as subclonal peaks in the variant allele frequency distribution (red peak).

normal stem cell systems, showing that clonal expansions arise naturally with time through neutral drift [43]. Indeed, the clone size distributions found for oncogenic mutations in human epidermis [38] are compatible with neutral drift [42]. Moreover, clonal hematopoiesis in the elderly can occur without evident oncogenic mutations [40], and large hematopoietic stem cell clones have been detected in otherwise normal mice [44]. Collectively, these findings raise the question on how one can infer from experimental data whether clonal expansions were due to neutral drift or selection.

mechanisms is limited, the Hippo signaling pathway that controls organ size [45], is a key tumor suppressor pathway [46]. Also, chemokine signaling and macrophages have been shown to regulate stem cell responses to skin injury [47]. Moreover, we do not know how large the selective advantages of oncogenic lesions found in normal cells are, and small advantages may result in limited clonal growth. In any event, the new data showing abundant oncogenic mutations in apparently normal tissues [38e41] highlight our lack of understanding of how pre-neoplasia develops into cancer.

For understanding the origin of cancer, a critical question is: If clones in normal tissues with oncogenic drivers expand selectively, why do they not proceed to fullblown neoplasia? One hypothesis to reconcile dN/dS ratios indicating positive selection with limited clonal expansion is that the local spread of pre-neoplastic clones is curbed by homeostatic mechanisms regulating tissue size. While our understanding of such

Do tumors evolve continuously?

Current Opinion in Systems Biology 2019, 16:1–9

The traditional view of tumor evolution posits ongoing addition of driver mutations that drive sequential clonal replacements (often referred to as linear tumor evolution) [48]. Recent phylogenetic studies across several cancer entities have elucidated a characteristic pattern of early acquisition of pro-proliferative genetic lesions (often involving copy number alterations), followed by www.sciencedirect.com

Modeling tumor growth and evolution Körber and Höfer

subsequent stabilization of tumor cell survival through activating telomere lengthening mechanisms [10,27,49]. Branched evolution has also been invoked, corresponding to the co-occurrence of multiple subclonal alterations that compete or cooperate during tumor growth. Recent inferences of tumor evolution from genome sequencing data have challenged this view and postulated Big Bang or Punctuated Evolution models for several entities [48,50]. A key feature of these models is that the driver mutations that cause tumor growth are acquired early during tumorigenesis, while subsequently there is little selection and hence late-arising driver mutations will be hardly detectable. A “big bang” may actually consist of the stepwise acquisition of mutations in a short space of time, possibly leading to intermingled subclones establishing intratumoral genetic heterogeneity early on. Phylogenetic reconstruction from multiregion sequencing data and stochastic simulations of the expanding tumor mass have supported this model for colorectal cancer [8,36]. Other entities for which bigbang evolution has been described include uveal melanoma [51] and triple negative breast cancer [50,52]. Of note, spatial sampling bias may result in similar patterns as clonal selection, so that selection may erroneously be inferred due to limited sampling [53]. Alternatively, the multiple oncogenic drivers may be generated by a single catastrophic event such as chromothripsis [54,55]. Thus it now appears that different kinds of tumors can arise via different evolutionary scenarios. Follow-up studies have attempted to define general signatures of selective versus neutral tumor evolution in VAF distributions of somatic mutations obtained by bulk sequencing of single samples [9] or multiple regions within a tumor [35]. In one study [9], which has recently been extended to account for the stochasticity of clonal expansions [56], genome sequence data of 14 entities have been compared to the theoretical expectation of neutral mutation accumulation in exponentially growing tumors. The authors conclude that a neutral model of tumor evolution cannot be rejected for a variety of human cancers. However, agreement (within error bounds) between experimental data and a neutral model does not necessarily imply absence of selection, as selective sweeps can give rise to similar VAF distributions as neutrally evolving tumors [57e59]. Moreover, cell death shapes these distributions [33,56] but e due to incomplete knowledge of cell death rates e this effect has been hard to account for. Thus, the inference of the mode of tumor evolution from VAF distributions requires careful consideration of additional parameters. Does cancer treatment exert selective pressure?

Whether selective or neutral, somatic mutations are continuously acquired over the course of tumorigenesis. www.sciencedirect.com

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Even mutations that are neutral during growth may confer a selective advantage under treatment. Indeed, resistance mutations have been observed in response to targeted treatment with tyrosine kinase inhibitors (e.g. Refs. [60,61]). A critical question is whether resistance mutations existed at low frequency already prior to treatment or evolved during treatment, which can readily be addressed by phylogenetic inference approaches. For example, studies of different breast cancer subtypes [52,53,62] suggest that treatment resistance is already acquired early during tumorigenesis. While these studies are primarily informative on treatment resistance in breast cancer, they also highlight caveats in analyzing clonal replacements using sequencing data. Treatment resistance to chemotherapy or radiotherapy is also of paramount importance and is often linked to the acquisition of resistance mutations. However, phylogenetic reconstruction of ultra-deep sequenced genomes of matched pairs of primary and recurrent primary glioblastomas showed little evidence of selective pressure exerted by standard treatment [10]. An earlier study reported slight enrichment in recurrent tumors of a gene mutation affecting a TGF-beta binding protein, but its role for treatment resistance is not clear [63]. The lack of resistance mutations in glioblastoma has now also been found in a larger study, suggesting that treatment failure is due to transcriptional reprogramming rather than genetic adaptation [64]. Nongenetic sources for therapy resistance have also been reported for other entities, involving cell-cycle state [65], hierarchical tissue organization, and transcriptional or epigenetic heterogeneity [49,52]. Taken together, these reports emphasize that sources of treatment resistance are manifold and not limited to genetic heterogeneity.

Somatic mutations contain information on clonal tumor growth High fraction of cell death consistent with cancer originating in stem cells

Somatic mutations accumulate with time in cells, with replication-dependent and independent mutational signatures [66]. For normal, dividing human and murine cells, the average mutation rate across the genome has been reported to lie between 2  10 9 and 8  10 9 mutations per base and division [67]. Using mutation rate estimates, the mutational burden of a cell can roughly be converted into the total number of divisions it has undergone. This number can be contrasted with the number of effective cell divisions (self-renewing division minus cell death events) that can be estimated from the total number of cells in the tumor. An ultra-deep whole-genome sequencing study of primary glioblastoma has found that tumor cells had accumulated about ten times as many somatic mutations during tumor development as would be expected Current Opinion in Systems Biology 2019, 16:1–9

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from the number of effective cell divisions, even when factoring in the possibility of an increased somatic mutation rate in the tumor [10]. Hence, the authors concluded that the vast majority of tumor cell divisions (70e90%) did not contribute to tumor growth but were followed by cell death. A very similar conclusion was obtained previously by estimating the selective advantage of driver mutations in several human tumors (including glioblastoma) in terms of the excess of cell division over cell loss; a driver mutation typically shifted this balance by less than 1% [32]. These findings may seem surprising at first but are well compatible with a hierarchical model of cancer growth, where selfrenewing cancer stem cells give rise to more differentiated cancer cells undergoing a limited number of divisions and, in many instances, eventually dying [33]. Initial driver mutations may just cause a slight excess of self-renewing cancer (stem) cell divisions over death of derived cancer cells; this balance would then need to be shifted further by additional drivers to achieve the rapid growth seen in many cancer entities. These findings are also in line with the wide-spread activation of telomer maintenance mechanisms during cancer evolution [10,27,49]. Driver mutations may confer large selective advantage

The selective advantage of oncogenic drivers ultimately determines the speed of tumor growth. Attempts to estimate the selective advantage of a driver in various cancers have been based on the number of driver versus neutral (“passenger”) mutations across patients [32], the growth of tumor clones within patients [17,34] and the VAF distribution a particular driver across patients [10]. All these are based, in various forms, on mathematical models that link tumor growth and acquisition of mutations. An intuitive way to look at selection in a growing tumor cell population is to compare the growth rate of a clone with a newly acquired driver with the growth rate of the remainder of the tumor that does not (yet) harbor this driver. The growth rate is equal to the difference of proliferation rate and the rate at which self-renewing tumor cells are removed (by death or differentiation into cells with limited life span). At the beginning of oncogenesis, these rates may remain nearly balanced, such that tumors initially grow very slowly. Hence small absolute changes to the rate of cell proliferation, death or differentiation by introduction of a new driver mutation can substantially accelerate effective growth rate [10,32]. Subclonal growth rates have been inferred to increase by: 10% (for lung adenocarcinoma), up to about 200% (for AML) [34], by about 100% for TP53 and ATM mutations and 35% for a KRAS mutation in chronic lymphocytic leukemia [17], and by up to 300% for activating TERT promoter mutations in glioblastoma [10]. How the selective advantage conferred by individual driver mutations depends on the cell type Current Opinion in Systems Biology 2019, 16:1–9

and its differentiation state is largely unknown and subject to ongoing research.

Mathematical and computational challenges The mathematical methods to model and infer the genetic evolution of tumors derive largely from classical population genetics. When attempting to bring together theory with the now highly resolved data on somatic mutations, new mathematical, statistical and computational challenges are arising. One question of central importance concerns the inference of subclonal structure from VAF distributions. While traditional methods are based on statistical ideas on the distribution of read counts, a recent study also factors in dynamic features of neutral evolution to distinguish more accurately the signatures of neutral and selective evolution in VAF distributions [71]. This approach relies on an analytical description for the site frequency spectrum of neutral mutations that is expected for large populations. Indeed, analytical theory on cancer evolution has had a long history. The most common approach derives from a concept originally introduced by Luria and Delbru ¨ck in their quantification of bacterial mutation rates, namely considering the stochastic emergence and evolution of mutant clones in a deterministically behaving bulk population [72]. Various types of simplifying assumptions have usually to be made to make the problem at hand analytically tractable (e.g. Refs. [8e10,17,25,32e 34,56]). Basic mathematical advances are still being made, such as the recent derivation of neutral clone size distributions in non-exponentially growing populations [73]. However, including many realistic factors, such as selective expansions and further evolution of multiple clones at distinct spatial sites and developmental hierarchies emerging from tumor stem cells [34,74], makes models analytically intractable. Stochastic simulations of tumor growth and mutation acquisition are increasingly used, and advanced tools allow spatially-resolved agentbased simulations at realistic tumor sizes of the order of 109 cells [35] Such approaches are becoming applicable for parameter inference from experimental data via Approximate Bayesian Computing [53].

Conclusions The recent work reviewed here is beginning to show that the vast amount of tumor genome sequences now available contains rich information on the dynamics of tumor development, going beyond catalogues of driver mutations and their phylogenies. In particular, the early stages of oncogenesis are coming into focus, due to the development of increasingly sophisticated modeling and inference approaches. In the future, it will also be important to test the inferences made from developed tumors in models of natural oncogenesis (i.e., without the introduction of oncogenes [68e70]), to understand how widespread oncogenic mutations in www.sciencedirect.com

Modeling tumor growth and evolution Körber and Höfer

normal tissues eventually become drivers in growing tumors. Mechanistic insights into tumor development provided by genome sequencing and mathematical modeling may ultimately provide new opportunities for early diagnosis.

Conflict of interest statement Nothing declared.

Acknowledgements We thank Peter Lichter, Bernhard Radlwimmer, Guido Reifenberger, and ¨fer group for Hans-Reimer Rodewald, as well as all members of the Ho stimulating discussions. We acknowledge funding through BMBF grants SYSMED-NB (grant no. 01ZX1307B) and SYS-GLIO (grant no. 031A425) as well as DKFZ core funding.

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Current Opinion in Systems Biology 2019, 16:1–9

By analyzing the ratio of non-synonymous to synonymous substitutions (dN/dS) in cancer, the authors conclude that negative selection is rare in tumorigenesis and that tumors on average carry four driver mutations under positive selection. 38. Martincorena I, Roshan A, Gerstung M, Ellis P, Van Loo P, McLaren S, Wedge DC, Fullam A, Alexandrov LB, Tubio JM, et al.: High burden and pervasive positive selection of somatic mutations in normal human skin. Science 2015, 348: 880–886. 39. Martincorena I, Fowler JC, Wabik A, Lawson ARJ, Abascal F, * * Hall MWJ, Cagan A, Murai K, Mahbubani K, Stratton MR, et al.: Somatic mutant clones colonize the human esophagus with age. Science 2018, 362:911–917. By targeted genome sequencing of normal tissue samples, this study and Ref. 38 found high prevalence of known cancer driver mutations and evidence for positive selection. 40. Zink F, Stacey SN, Norddahl GL, Frigge ML, Magnusson OT, * * Jonsdottir I, Thorgeirsson TE, Sigurdsson A, Gudjonsson SA, Gudmundsson J, et al.: Clonal hematopoiesis, with and without candidate driver mutations, is commonly in the elderly. Blood 2017, 130:742–752. By sequencing the blood of more than 10,000 individuals the authors show that large expansions of hematopoietic stem cell clones are frequent in the elderly and not necessarily linked to known driver mutations. 41. Yizhak K, Aguet F, Kim J, Hess JM, Kübler K, Grimsby J, * * Frazer R, Zhang H, Haradhvala NJ, Rosebrock D, et al.: RNA sequence analysis reveals macroscopic somatic clonal expansion across normal tissues. Science 2019, 364, eaaw0726. Continuing the analysis of cancer driver mutations in normal tissues (Refs 38–40), this study uses RNA samples from a wide range of tissues and again finds numerous driver mutations. The highest frequencies are observed in skin, lung and esophagus. 42. Simons BD: Deep sequencing as a probe of normal stem cell * fate and preneoplasia in human epidermis. Proc Natl Acad Sci 2016, 113:128–133. This study argues that the data presented in Ref. 38 mainly conform to the clone size distribution expected under random drift, although the ratio between nonsynonymous and synonymous mutations is indicative of positive selection. The short paper as well as the reply by Martincorena et al. discuss the problems in distinguishing between selection and neutral drift. 43. Klein AM, Simons BD: Universal patterns of stem cell fate in cycling adult tissues. Development 2011, 138:3103–3111. 44. Pei W, Feyerabend TB, Rössler J, Wang X, Postrach D, Busch K, Rode I, Klapproth K, Dietlein N, Quedenau C, et al.: Polylox barcoding reveals haematopoietic stem cell fates realized in vivo. Nature 2017, 548:456–460. 45. Fu V, Plouffe SW, Guan KL: The Hippo pathway in organ development, homeostasis, and regeneration. Curr Opin Cell Biol 2017, 49:99–107. 46. Wang Y, Xu X, Maglic D, Dill MT, Mojumdar K, Ng PK, Jeong KJ, Tsang YH, Moreno D, Bhavana VH, et al.: Comprehensive molecular characterization of the Hippo signaling pathway in cancer. Cell Rep 2018, 25:1304–1317. 47. Chen CC, Wang L, Plikus MV, Jiang TX, Murray PJ, Ramos R, Guerrero-Juarez CF, Hughes MW, Lee OK, Shi S, et al.: Organlevel quorum sensing directs regeneration in hair stem cell populations. Cell 2015, 161:277–290. 48. Hu Z, Sun R, Curtis C: A population genetics perspective on * * the determinants of intra-tumor heterogeneity. Biochim Biophys Acta Rev Canc 2017, 1867:109–126. Succinct review of the different modes of genetic evolution that can underlie intratumoral heterogeneity and modeling approaches to infer cancer evolution from deep sequencing data. 49. Ackermann S, Cartolano M, Hero B, Welte A, Kahlert Y, * Roderwieser A, Bartenhagen C, Walter E, Gecht J, Kerschke L, et al.: A mechanistic classification of clinical phenotypes in neuroblastoma. Science 2018, 362:1165–1170. This study links survival of neuroblastoma patients to the presence or absence of telomere stabilizing mechanisms.

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Modeling tumor growth and evolution Körber and Höfer

9

Clonal evolution in patients with chronic lymphocytic leukaemia developing resistance to BTK. Nat Commun 2016, 7:11589.

50. Gao R, Davis A, McDonald TO, Sei E, Shi X, Wang Y, Tsai P-C, * * Casasent A, Waters J, Zhang H, et al.: Punctuated copy number evolution and clonal stasis in triple-negative breast cancer. Nat Genet 2016, 48:119–1130. Single cell sequencing study on the evolutionary history in triplenegative breast cancer. Using mathematical modeling and phylogenetic inference the authors show that breast cancer likely arises from punctuated rather than gradual evolution.

62. Brady SW, McQuerry JA, Qiao Y, Piccolo SR, Shrestha G, Jenkins DF, Layer RM, Pedersen BS, Miller RH, Esch A, et al.: Combating subclonal evolution of resistant cancer phenotypes. Nat Commun 2017, 8:1231.

51. Field MG, Durante MA, Anbunathan H, Cai LZ, Decatur CL, Bowcock AM, Kurtenbach S, Harbour JW: Punctuated evolution of canonical genomic aberrations in uveal melanoma. Nat Commun 2018, 9:116.

63. Wang J, Cazzato E, Ladewig E, Frattini V, Rosenbloom DIS, Zairis S, Abate F, Liu Z, Elliott O, Shin Y-J, et al.: Clonal evolution of glioblastoma under therapy. Nat Genet 2016, 48: 768–776.

52. Kim C, Gao R, Sei E, Brandt R, Hartman J, Hatschek T, Crosetto N, Foukakis T, Navin NE: Chemoresistance evolution in triple-negative breast cancer delineated by single-cell sequencing. Cell 2018, 173:879–893.

64. Rippaus N, F-Bruns A, Tanner G, Taylor C, Droop A, Care MA, * * Wilkinson J, Jenkinson MD, Brodbelt A, Chakrabarty A, et al.: JARID2 facilitates transcriptional reprogramming in glioblastoma in response to standard treatment. bioRxiv 2019: 649400. By comparing RNA sequencing data of primary (treatment-naïve) and recurrent glioblastomas, the authors suggest that treatment-resistance arises from transcriptional dysregulation of a specific set of genes in response to treatment rather than selection.

53. Caswell-Jin JL, McNamara K, Reiter JG, Sun R, Hu Z, Ma Z, * * Ding J, Suarez CJ, Tilk S, Raghavendra A, et al.: Clonal replacement and heterogeneity in breast tumors treated with neoadjuvant HER2-targeted therapy. Nat Commun 2019, 10: 657. Three-dimensional agent-based modeling coupled to parameter inference via Approximate Bayesian Computing aids the interpretation of genomic sequencing data. 54. Stephens PJ, Greenman CD, Fu B, Yang F, Bignell GR, Mudie LJ, Pleasance ED, Lau KW, Beare D, Stebbings LA, et al.: Massive genomic rearrangement acquired in a single catastrophic event during cancer development. Cell 2011, 144:27–40. 55. Rausch T, Jones DT, Zapatka M, Stütz AM, Zichner T, Weischenfeldt J, Jäger N, Remke M, Shih D, Northcott PA, et al.: Genome sequencing of pediatric medulloblastoma links catastrophic DNA rearrangements with TP53 mutations. Cell 2012, 148:59–71. 56. Ohtsuki H, Innan H: Forward and backward evolutionary pro* cesses and allele frequency spectrum in a cancer cell population. Theor Popul Biol 2017, 117:43–50. Extends the model of Ref. 9** to account for fully stochastic clonal expansions. 57. Tarabichi M, Martincorena I, Gerstung M, Leroi AM, Markowetz, , * PCAWG Evolution and Heterogeneity Working Group, Spellman PT, Morris QD, Lingjærde OC, Wedge DC, et al.: Neutral tumor evolution? Nat Genet 2018, 50:1630–1633. Refs 57–59 discuss potential limitations of the null model for VAF distributions generated by neutral drift proposed in Ref. 9** 58. McDonald TO, Chakrabarti S, Michor F: Currently available bulk * sequencing data do not necessarily support a model of neutral tumor evolution. Nat Genet 2018, 50:1620–1623. Refs 57–59 discuss potential limitations of the null model for VAF distributions generated by neutral drift proposed in Ref. 9** 59. Noorbakhsh J, Chuang JH: Uncertainties in tumor allele fre* quencies limit power to infer evolutionary pressures. Nat Genet 2017, 49:1288–1289 *. Refs 57–59 discuss potential limitations of the null model for VAF distributions generated by neutral drift proposed in Ref. 9**. 60. Hata AN, Niederst MJ, Archibald HL, Gomez-Caraballo M, Siddiqui FM, Mulvey HE, Maruvka YE, Ji F, Bhang HC, Krishnamurthy Radhakrishna V, et al.: Tumor cells can follow distinct evolutionary paths to become resistant to epidermal growth factor receptor inhibition. Nat Med 2016, 22:262–269. 61. Burger JA, Landau DA, Taylor-Weiner A, Bozic I, Zhang H, Sarosiek K, Wang L, Stewart C, Fan J, Hoellenriegel J, et al.:

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