Observing Clonal Dynamics across Spatiotemporal Axes: A...

Observing Clonal Dynamics acrossSpatiotemporal Axes: A Prelude to QuantitativeFitness Models for Cancer

Andrew W. McPherson,1,2 Fong Chun Chan,1,2 and Sohrab P. Shah1,2

1Department of Molecular Oncology, BC Cancer Agency, Vancouver V5Z 1L3, Canada2Department of Pathology and Laboratory Medicine, University of British Columbia, Vancouver V6T 2B5,Canada

Correspondence: [email protected]

The ability to accurately model evolutionary dynamics in cancer would allow for predictionof progression and response to therapy. As a prelude to quantitative understanding of evolu-tionary dynamics, researchers must gather observations of in vivo tumor evolution. High-throughput genome sequencing now provides the means to profile the mutational contentof evolving tumor clones from patient biopsies. Together with the development of modelsof tumor evolution, reconstructing evolutionary histories of individual tumors generateshypotheses about the dynamics of evolution that produced the observed clones. In thisreview, we provide a brief overview of the concepts involved in predicting evolutionaryhistories, and provide a workflow based on bulk and targeted-genome sequencing. Wethen describe the application of this workflow to time series data obtained for transformedand progressed follicular lymphomas (FL), and contrast the observed evolutionary dynamicsbetween these two subtypes. We next describe results from a spatial sampling study of high-grade serous (HGS) ovarian cancer, propose mechanisms of disease spread based on theobserved clonal mixtures, and provide examples of diversification through subclonal acqui-sition of driver mutations and convergent evolution. Finally, we state implications of thetechniques discussed in this review as a necessary but insufficient step on the path to pre-dictive modelling of disease dynamics.

Cancer develops through evolutionary pro-cesses (Nowell 1976; Greaves and Maley

2012). Extrinsic and intrinsic factors combinedwith aberrant DNA-repair result in increasedmutation rate in many cancers, leading to cell-specific genomic diversity. Tumor microenvi-ronments, immune surveillance, therapeuticinterventions, and other factors impose selec-tive pressures on the substrate of diverse tumor

clones, resulting in differential proliferation asa function of tumor clone fitness. We suggestthat the desired end-goal of predicting fitnessof tumor clones remains elusive in the field.However, it is well accepted that clonal dynam-ics (defined as the relative abundance of tumorclones over time or in different microenviron-ments in anatomic space) associate with majorevents in tumor progression including onco-

Editors: Charles Swanton, Alberto Bardelli, Kornelia Polyak, Sohrab Shah, and Trevor A. Graham

Additional Perspectives on Cancer Evolution available at www.perspectivesinmedicine.org

Copyright # 2018 Cold Spring Harbor Laboratory Press; all rights reserved; doi: 10.1101/cshperspect.a029603

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genesis, treatment resistance, and metastasis.Thus, observing clonal dynamics and under-standing their nature in different patient con-texts represent a powerful first step on the pathtoward predictive fitness modelling in cancer.

We begin with the notion of generating invivo observations in the form of evolutionaryhistories. A tumor’s evolutionary history com-prises: (1) the genotypes of ancestral and extantclonal populations; (2) the evolutionary treerelating those genotypes; and (3) the distribu-tion of clonal populations through time andanatomic space. Tumor biopsies collected fordiagnostic purposes or during surgical resectionprovide tissues from which observations oftumor evolution can be made. We will focuson high-throughput sequencing methods ap-plied to cancer tissue samples as a means ofprofiling the mutational content of tumorgenomes, and inferring tumor genotypes pre-sent in tumor samples. Because each samplerepresents a population of only extant tumorcells, the evolutionary history of each tumormust be inferred computationally throughreconstruction approaches. Herein, we willreview principles of inferring the clonal geno-types, clone phylogenies, and the distribution ofclones in tumor samples from high-throughputsequencing data. We will then present the appli-cation of these methods in two separate studieson patient tumor samples designed to observeclonal dynamics through time within follicularlymphoma (FL) patients’ clinical histories(Kridel et al. 2016 ) and over anatomic spacein the peritoneal cavity of high-grade serous(HGS) ovarian cancer patients (McPhersonet al. 2016).

FEATURES OF EVOLVING CANCERGENOMES

Genomic features distinguishing a cancer’s ge-nome from its germline progenitor are broadlycategorized into small variants, copy number(CN) changes, and rearrangements. Small vari-ants include somatic point mutations, or singlenucleotide variants (SNVs), and small inser-tions/deletions (InDels). Rearrangements in-volve the reordering of chromosomal segments

and include translocations, inversions, tandemduplications, and deletions. CN changes in-clude deletion or amplification of whole chro-mosomes or smaller chromosomal segments,and are often associated with rearrangements.

Of these three classes of genomic features,SNVs are particularly useful as markers ofclones when studying tumor evolution. Afteracquisition of an SNV, a tumor cell’s progenywill, in general, all harbor the same SNV.Most SNVs can be assumed to be selectivelyneutral, and are thus passengers of a relativelysmall set of coincident driver mutations. Thelarge size of the genome and the relativelysmall per nucleotide mutation rate leads to the“infinite sites assumption”: A specific nucleo-tide in the genome will be affected by mutation,at most, once throughout the life history ofa tumor. Under this assumption, an SNVbecomes an identifying feature of a clade ofthe tumor cell phylogeny, with its detectionan indication of the presence of that clade.However, as is often the case in tumorsharboring deficient DNA repair, deletion ofchromosomal segments will remove concomi-tant SNVs. Thus, CN changes must be account-ed for when assigning an SNV as an identifyingfeature of a tumor clade.

CLONAL EVOLUTION IN CANCER

Mutational processes produce genomicallyheterogeneous populations of tumor cells, pro-viding the necessary substrate for evolution.3

Selective pressures acting on tumor cell popula-tions will result in the expansion of tumor cellswith higher fitness at the expense of less fittumor cells. Over time, populations with high-er fitness will out-compete ancestral popula-tions, resulting in higher representation offit genotypes in the mixture of tumor cells.Additionally, metastasis, invasion, and local-ized immune surveillance properties result inregional differences in clonal abundance acrossanatomic sites.

3Other mechanisms of variation, such as epigenetic modi-fication, are likely contributing to evolution as well, howev-er, we focus only on genomic aberrations here.

A.W. McPherson et al.

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We define a tumor “clone” as a maximal setof tumor cells with shared ancestry.4 Modellingtumor evolution, in terms of clones, is a usefulabstraction that greatly simplifies analysis overexplicit modelling of evolutionary relationshipsbetween individual tumor cells (see Fig. 1).More specifically, modelling evolutionary rela-tionships between ancestral tumor clones allowsresearchers to focus on the important selectionevents that produced a tumor genotype. In re-ality, an ancestral genotype may have arisenthrough successive stages of mutation until ac-quisition of a driver mutation, imposition oftherapy, or some other selection event resultedin extinction of cells with intermediate geno-types and proliferation of cells harboring mul-tiple, serially acquired mutations. However,when observing only the population of extantcells, loss of the intermediate genotypes makes itinfeasible to order sets of mutations selectedtogether, and it becomes convenient to considerthose mutations as part of one ancestral clonalgenotype.

Genomic heterogeneity may thus arise fromthe presence of divergent clones produced dur-ing ancestral selection events. Additionally, mu-tation without selection, or neutral evolution,will result in acquisition of many predominant-ly low-cellular prevalence mutations (Williams

et al. 2016). Estimated mutation rates range inthe 10s to 1000s per cell-division (Williams et al.2016), implying that each cell likely harbors aunique genotype, and could be considered to beits own genomically distinct clone. In practice,it is often preferable to model only extant clonesthat have undergone a selection event and re-sulted in a significantly divergent genotype.Neutral evolution may also result in fixationof selectively neutral mutations caused by thestochastic nature by which future genotypesare sampled from existing genotypes in a birthdeath process. Such mutations will be indis-cernible from the passenger mutations thatwere swept to fixation by the most recent selec-tion event affecting the clonal population. Notethat one of the selective mechanisms is relatedto the experiment itself: Sectioning of biopsiedmaterial for sequencing will sample a subset ofthe tumor cells, resulting in differential repre-sentation of specific genotypes in the sequencedata, particularly if tumor clones are nonran-domly distributed throughout the tumor mass.

SEQUENCING OF HETEROGENEOUSTUMOR SAMPLES

Whole-genome sequencing (WGS) is particu-larly powerful when applied to the study of can-cer evolution as it allows for the identification ofall classes of genomic features mentioned above,and profiles the full length of the genome.However, the information gained from applica-tion of bulk WGS to a tumor biopsy is incom-plete. Tumor cells are lysed, chromosomes arefragmented, and the resulting pool of fragmentsare sequenced en masse, without preserving thecell-specific origin of each fragment. Genomicfeatures identified from sequenced fragmentscan therefore only be assigned to populationsof cells using computational inference. Success-ful assignments of SNVs to cell populations leadto the ability to quantify population abundancewithin the original sample. This ultimatelyenables observations of cellular dynamics overtime, or anatomic space.

The prevalence of each SNV in the cellularpopulation can be approximately assessed bythe fraction of reads with the variant (termed

A B

Figure 1. Phylogeny of individual cells (A) and a cor-responding clone phylogeny (B). The cell phylogenyshows acquisition of mutations (colored circles) se-rially, although intermediate genotypes are extin-guished (gray x) during selection for a clonal geno-type. Neutrally evolving populations produce, inapproximation, a full binary tree structure in thecell phylogeny. The clone phylogeny is a simplifica-tion of the cell phylogeny showing only the genotypessurviving selection events, and a common genotypefor neutrally evolving extant populations.

4Maximality is required, as a clone should include “all”descendants of a common ancestor.

Observing Clonal Dynamics in Cancer

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variant allele fraction [VAF]). The high breadthof WGS often necessitates sequencing to a lowerdepth to allow experiments to remain econom-ically feasible. VAF accuracy is directly relatedto sequencing depth, and thus WGS is not ide-ally suited to quantification of low-prevalenceclones. Targeted high- depth sequencing of asubset of phylogenetically informative SNVs isa useful method for augmenting low-depthWGS datasets, allowing for quantification oflow-prevalence clones. As a result of CNchange, VAF is not equal to the fraction of cellsharboring an SNV, the mutation’s “cellularprevalence,” but is confounded by the SNVloci’s CN (Roth et al. 2014). As a basic example,an SNV with VAF of 0.5 could be heterozygousin 100% of the cells or homozygous in 50% ofthe cells. Accounting for CN is fundamentallyimportant for accurate inference of evolution-ary histories, especially for tumors that showeven a moderate amount of deviation fromdiploid owing to CN change.

CLUSTERING MUTATIONS BY CELLULARPREVALENCE

Clonal evolution will result in increased repre-sentation of specific fit genotypes, and increasedcellular prevalence of mutations present inthose genotypes. In the extreme case, all muta-tions present in the clone that survived the lastselective sweep will be present with cellularprevalence equal to 1 (notwithstanding relevantCN changes deleting those mutations). Thus,within the context of a tumor evolving throughnonneutral clonal dynamics, considerable ben-efit can be gained by clustering mutations withsimilar inferred cellular prevalence, as it allowsfor the discovery of sets of mutations withshared clonal ancestry. As cellular prevalence isnot directly observable, in practice, mutationsare clustered by VAF, while modelling, correct-ing for, or filtering by SNV loci CN. Theresulting mutation clusters represent sets ofmutations (termed clonal clusters) putativelysharing a common evolutionary history: Theyoriginate at the same point between selectivesweeps, and are subject to the same CN changesthat removed the SNVs from descendant sub-

populations. An implicit assumption is that setsof mutations with no common history will notshare the same cellular prevalence by chance.This assumption (termed weak parsimony inDeshwar et al. 2015) becomes less problematicwhen sequencing multiple samples from thesame tumor biopsy. With an increasing numberof samples, sets of mutations are less likelyto have similar cellular prevalence across allsamples by chance, with the corollary beingthat shared prevalences across multiple samplesincreases the likelihood that such sets weregenerated by a common evolutionary history.

Importantly, a mutation cluster does not, ingeneral, correspond to the genotype of anyclone. Instead, a tumor clone’s genotype con-sists of the cluster of mutations acquired imme-diately before the most recent selective sweep, inaddition to any mutations acquired since thegermline progenitor.

CLONAL GENOTYPES AND CLONEPHYLOGENIES

To understand mutation order, convergence,clonal interference, and other evolutionaryproperties of a tumor requires a level of infer-ence beyond mutation clustering to clonal ge-notypes and clone phylogenies. In the contextof tumor evolution, a clone phylogeny refers tothe tree structured graph that represents theevolutionary relationships between extant andancestral tumor clones. Given direct observa-tions of extant clonal genotypes and an appro-priate evolutionary model, it is possible toreconstruct both the evolutionary tree andancestral clonal genotypes using standard phy-logenetic approaches such as maximum parsi-mony. Sequencing multiple tumor samples is apowerful method for measuring the genotypesof tumor clones and reconstructing clonal phy-logenies. If each sequenced sample is populatedby a single tumor clone, the set of mutationsidentified in each sample may be used as a proxyfor extant genotypes, allowing for straight-forward phylogenetic reconstruction.

In general, however, bulk sequencing resultsare confounded by the unknown mixture ofclones in each tumor sample, and the mutations



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identified in a sample represent a superpositionof multiple clonal genotypes. From a biologicalperspective, observing a mixture of clonesgenerates interesting hypotheses. Early prolifer-ation of an emergent clone caused by a recentlyacquired driver mutation, invasion of oneclone’s anatomic space by another clone, orinterference or cooperation between clones,are all plausible interpretations. Thus, methodsthat are able to infer clonal genotypes, clonephylogenies, and sample clone mixtures (evolu-tionary histories) are important for accuratemeasurement of clonal dynamics.

Inference of evolutionary histories fromtumor sequencing data is an ongoing topic ofresearch. CITUP (Malikic et al. 2015), LICHeE(Popic et al. 2015), and SPRUCE (El-Kebir et al.2016) take a combinatorial optimization ap-proach, attempting to build evolutionary histo-ries from a set of mutation clusters in a two-stepprocess. PhyloSub (Jiao et al. 2014), PhyloWGS(Deshwar et al. 2015), and Canopy (Jiang et al.2016) use Markov chain Monte Carlo (MCMC)to sample from the full posterior of evolution-ary histories. The fundamental difficulty of theproblem lies in the size of the search space overwhich methods optimize or generate MCMCsamples. The space of trees is combinatoriallylarge in the number of tumor clones, as is thespace of assignments of mutations to tumorclones. Identifiability is also an issue. Formany datasets, multiple evolutionary historiesprovide an equivalent fit to the data, especiallywhen sequencing a smaller number of samples(Jiao et al. 2014).

WORKFLOW FOR RECONSTRUCTINGEVOLUTIONARY HISTORIES

We synthesized the methods above into a work-flow for reconstructing an evolutionary historyby sequencing multiple tumor samples (Fig. 2).WGS is applied to each sample to discoverpatient-specific SNVs, estimate VAF of eachSNV in each sample, and infer CN changesin each sample. Phylogenetically informativeSNVs are selected uniformly from clusters ofSNVs in the k-dimensional space of VAFs acrossthe k samples. Deep sequencing is applied to the

selected SNVs to provide accurate VAF measure-ments. PyClone (Roth et al. 2014) is applied tothe deep sequenced SNVs to accurately clusterSNVs and estimate the cellular prevalence ofeach clonal cluster.5 Finally, CITUP (Malikicet al. 2015) is applied to the PyClone clustersto simultaneously infer the sets of clonal clus-ters comprising each clonal genotype, the clonephylogeny, and the sample clone prevalences.

Inference of clonal genotypes, and measure-ment of their abundance in bulk tumor sampleshave been used to great effect in observingclonal dynamics in human cancers. Here, wedescribe two recent studies, utilizing the work-flow above, which show the type of inferencethat can be performed to interpret distributionsof clones over time and across anatomic space.

CLONAL DYNAMICS THROUGH TIME:TUMOR EVOLUTION UNDERLYINGHISTOLOGICAL TRANSFORMATION ANDEARLY PROGRESSION OF FOLLICULARLYMPHOMA

In a study of follicular lymphoma (FL), ourgroup recently inferred the clonal dynamicsthrough time of 21 patients with FL whoexperienced disease progression (Kridel et al.2016). Although the majority of FL patientseventually experience disease progression (Kri-del et al. 2012), a subset of patients are markedby early treatment resistance (progressed follic-ular lymphoma [PFL] patients) (Casulo et al.2015a) and/or histological transformation(transformed follicular lymphoma [TFL]) oftheir tumors to a more aggressive form (Casuloet al. 2015b). Both of these clinical inflectionpoints are associated with poor survival. Assuch, profiling and comparing the clonal com-position between FL diagnostic (T1) and re-lapse/transformed (T2) specimens presents anopportunity to study the evolutionary dynam-ics underpinning FL disease progression.

By using WGS and deep sequencing data, inconjunction with bioinformatic methods such

5Although other methods may be used in place of PyClone,one advantage of PyClone is its ability to correct for the CNof each SNV loci.



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as PyClone (Roth et al. 2014) and Citup (Ma-likic et al. 2015), we reconstructed the evolu-tionary history of each tumor and characterizedthe patterns of clonal dynamics associated withtransformation and early progression (Kridelet al. 2016). For TFL patients (n ¼ 15), ourresults showed that the aggressive phenotypewas associated with a vast change in clonalcomposition between the diagnostic and trans-formed specimen (Fig. 3A,B). Specifically, themajority of these patients (13/15, 87%) showeda pattern of a rare clone at diagnosis (,1%clonal prevalence) arising to dominant the clon-al composition at transformation. This strikingpattern was independent of both treatment reg-imen and time to transformation. Importantly,the dominant clone often harbored knowndriver mutations (e.g., CCND3, B2M, EZH2)suggesting that these punctuated expansionsare under positive selection.

In contrast, PFL patients (n ¼ 6) showed adifferent pattern of clonal dynamics betweendiagnostic and early progressed specimens (Fig.3). These patient’s tumors typically harboredreadily detectable clones at diagnosis, whichexpanded to full clonal prevalence during treat-ment with immunochemotherapy. These pat-terns suggest that clones harboring treatmentresistance properties were already present at di-agnosis, and that symptomatic disease progres-sion may be attributed to selection of clones thatwere major constituents of the diagnostic sample.

Collectively, our study reveals divergentmodes of tumor evolution that underlie histo-logical transformation and early progression.For TFL patients, the massive expansion ofclones in T2 samples that were rare or detectablyabsent in T1 samples indicates that diagnosticsamples are not likely to possess reliable predic-tors of transformation in the majority ofcases. Moreover, the results suggest that clonaldynamics occurring after diagnosis likely un-derpin the histological change. As such, todetermine of exact timing of transformationlikely requires more frequent monitoring usingtechniques such as circulating tumor DNA(Scherer et al. 2016).

For PFL patients, there was stability in theclonal architecture between diagnosis and re-

lapsed specimens. This suggests that the fitnesscould be attributed to nongenetic factors or thatthese tumors acquire resistance properties veryearly in their evolutionary histories and inthe absence of therapeutic selective pressure.Importantly, the abundance of these clones atdiagnosis substantiates the feasibility of predict-ing early treatment resistance. Additional stud-ies that comprehensively profiling the clonalarchitecture and associated gene mutations atdiagnosis in PFL patients will be needed for this.

CLONAL DYNAMICS ACROSS ANATOMICSPACE: HIGH-GRADE SEROUS OVARIANCANCER PERITONEAL SPREAD

The distribution of tumor clones resulting fromdisease spread as measured by multisample ge-nome sequencing provides a window into theevolutionary dynamics that shaped a patient’scancer. In a study of HGS ovarian cancer, ourgroup reconstructed the evolutionary historiesof the pretreatment cancers of seven patients(McPherson et al. 2016). HGS is characterizedby widespread and early intraperitoneal spreadto organs, including the omentum and contra-lateral ovary. The genomes of HGS show perva-sive instability because of TP53 loss in nearly allcases (Ahmed et al. 2010), accompanied byhomologous recombination and other DNA re-pair deficiencies in the majority of cases (Patchet al. 2015). Thus, combined dysregulationof apoptosis and DNA repair processes providea mechanism for generating a substrate ofgenomically diverse clones (Bashashati et al.2013; Ha et al. 2014; Schwarz et al. 2015) frommonoclonal aetiology (Jacobs et al. 1992; Kha-lique et al. 2009).

We applied WGS to multiple samples col-lected from the seven HGS patients, and target-ed deep sequencing of phylogenetically infor-mative SNVs identified from WGS for accuratequantification of VAF. We inferred clonal geno-types and clone phylogenies using a combina-tion of PyClone and maximum parsimonyphylogenetic inference within the context of astochastic Dollo model of evolution (Alek-seyenko et al. 2008). The stochastic Dollo modelassumes SNVs originate once within the evolu-



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Figure 3. Modes of evolution in follicular lymphoma. (A, C) Clonal dynamics of a selected transformedfollicular lymphoma (TFL) patient (FL1004) and progressed follicular lymphoma (PFL) patient (FL2008).Progression from SNV cellular prevalences to clonal phylogenies and prevalences. (B, D) Schematic modelsof evolutionary progression in TFL and PFL. (From Kridel et al. 2016, reproduced, with permission from theauthor.)



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tionary history of a tumor (infinite sites as-sumption), and also models the possibilitythat an SNV may be lost as a result of the CNchange in descendant lineages, thus accountingfor the pervasive chromosomal instability thatis typical of HGS. Clone sample prevalence wasestimated using a post hoc MCMC step. Theoutput was a series of clonal “maps,” illustratingthe spreading patterns of each patient (Fig. 4).

We categorized samples as clonally pure orpolyclonal; polyclonal samples were furtherclassified into samples in which multiple cloneswere from within the same phylogenetic clade(monophyletic) or from different clades (poly-phyletic). The majority of samples were mono-phyletic or clonally pure; however, each patientshowed at least one polyphyletic sample. Poly-phyletic samples may be indicative of an ances-tral population having undergone branchedclonal evolution. In patient 9, for example,acquisition of a ERBB2 amplification by a sub-clone of left ovary site 2 was followed by expan-sion of that clone into right ovary and omentalsites (Fig. 4). In an alternative scenario, a poly-phyletic sample may have been seeded eitherserially or simultaneously (polyclonal migra-tion) by multiple clones. In patient 1, for exam-ple, the contralateral left ovary site was populat-ed by both omentum and right ovary-specificclones. The most parsimonious explanation forthis observation is remetastasis of the left ovary.

Accurately inferred clonal phylogenies allowfor the investigation of parallel or convergentevolution of genomic features, an indicationof positive selection toward shared genomictraits. We focused on convergent evolution ofthe structural genome toward amplification orloss of specific genes. Patient 7 showed conver-gent evolution toward loss of heterozygosity(LOH) of chromosome 14, with two distinctevents independently deleting the reference al-lele of a single-nucleotide polymorphism (SNP)affecting a splice site of RAD51B (Fig. 5). BothRAD51B LOH clones coexist in the RUtD3sample of timepoint 1, with clone B eventuallydominating the brain metastasis of timepoint 2,clone D the right pelvic samples of timepoint 3,and RAD51B heterozygous clones extinguishedin the second and third timepoints. Clone B also

harbored an NF1 deletion that may have drivenmetastasis and expansion of that clone in thepatient’s brain, providing of an example of clon-al interference between the RAD51B LOH eventof clone D and the NF1 deletion/RAD51B LOHgenotype of clone B.

In patient 2, presence of breakpoints withinthe CCNE1-amplified region recapitulated theclone phylogeny identified from SNVs. All28 breakpoints within the CCNE1-amplifiedregion were determined to be specific to eitherthe right ovary or omentum. As evidence ofthe association between the breakpoints andCN changes, break-ends within the CCNE1-amplified region coincided with significantlyhigher CN change in samples in which theywere predicted as present, compared with sam-ples in which they were predicted as absent (Fig.5). The combined effects of these breakpoints inboth the right ovary and omentum was highlevel amplification of CCNE1, a known driverevent in HGS.

CONCLUSIONS

The methods and examples we illustrate hereexemplify progress in enumerating clones incancer tissues and measuring their distributionacross spatial and temporal axes. Interpretationof results obtained through analysis of ourmodestly sized cohorts is facilitated by leverag-ing prior information gained from studiesin larger cohorts. Specifically, known drivermutations associated with emergence of moreaggressive tumor clones in TFL, and convergentevolution in HGS, are suggestive of commonpatterns of evolution in these cancers. Never-theless, we view the primary objective of ourinitial work as observational, necessary for pro-viding an initial window into the evolutionarycomplexity of the diseases studies and generat-ing additional important and unresolved ques-tions to be addressed in future studies. Forexample, can we predict which clones mightexpand in different microenvironments? Howdo clonal dynamics relate to immunodynamics?Which clones might expand over a patient’sclinical trajectory? Under what selective pres-sures are some clones more fit than others? We



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Figure 4. Spatial distribution of high-grade serous (HGS) clones in seven patients. The anatomy of each patientis depicted in the center of each diagram, with a presentation of the clonal mixture by color within the innercircle, and the clones present in the sample overlaid on the clone phylogeny on the outer circle. The full clonephylogeny is shown at the top right for each patient. (From McPherson et al. 2016, reproduced, with permissionof the author.)



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Figure 5. Examples of convergent evolution of copy number (CN). (A) Major (red line) and minor (blue line)allele-specific CNs with experimentally validated breakpoints (colored lines/arrows) for patient 7, chromo-somes 14, 8, 19, and 16. Both the brain metastasis (BrM) and right pelvic mass (RPvM) show loss of hetero-zygosity (LOH) of distinct segments of chromosome 14, corroborated by the presence of distinct sets ofbreakpoints. (B) The top plot shows total CN for omentum (Om1, Om2) and right ovary samples (ROv1,ROv2) in patient 2. The bottom plot shows the presence (blue) or absence (white) of rearrangement break-points, with break-ends in the CCNE1 amplified region. Green lines show correspondence between rearrange-ment breakpoints in the heatmap and positions of break-ends, highlighting the association between break-points and CN transitions. (C) Break-ends are associated with significantly higher CN change for samples inwhich they are predicted as present compared with absent. Shown is the distribution of the difference in CNbetween segments on the right and left of each break-end, correcting for break-end orientation. Higher CNdifference indicates higher CN change induced by the breakpoint. For each break-end in each sample, wepredicted whether the break-end exists in that sample. We then compare the CN difference in each sample forbreak-ends that are predicted as absent (left) versus present (right) in those samples. (From McPherson et al.2016, reproduced, with permission from the author.)



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suggest that the methods and examples present-ed here offer a prelude to future work that mightelucidate progress addressing these questions.

As part of future efforts to build predictivemodels of clonal dynamics, it will be necessaryto tackle both the complexity of fitness land-scapes and the heterogeneity between cancersand patients. The extensive clinical heterogene-ity in many cancers weakens our ability to makepredictive statements from clonal phylogeniesof a small number of patients. We proposethat future studies involving orders of magni-tude more patients for which clonal analysis isstandard may allow researchers to build predic-tive models robust to the many factors that cur-rently confound such analyses. Furthermore,the complex effects of genetic backgrounds,tumor microenvironments, and immune sur-veillance, all impact the observed clonal mix-tures in each patient. We can envision futuredatasets that attempt to capture and providean integrated analysis of each of these factors,and model their effects on fitness landscapes,providing additional power for the creation ofaccurate predictive models.

Finally, high-fidelity physical models ofcancer will allow for controlled replicate exper-iments, providing the reproducibility that is aperquisite for predictive science. A recent studyby our group provides a useful illustrative ex-ample. Patient derived immunodeficient mousexenograft (PDX) systems offer the opportunityto study cancer cell populations in laboratorysettings, where repeated experiments can beperformed. Using the methods described inthis review, we reported that clonal dynamicsin serially passaged breast cancer PDX modelsare reproducible in parallel PDX lines (Eirewet al. 2014). This important result establishes astrong likelihood of determinism, setting thestage for measuring reproducible dynamics ininterventional PDX studies using pharmacolog-ic or genetic perturbation. We suggest thatreproducible dynamics in the context of con-trolled interventional studies will provide asubstrate for quantitative fitness models of can-cer. If successful, these models will ultimatelypermit prediction of clonal response profilesof treatment interventions, significantly aug-

menting quantitative understanding on thepath from observations of dynamics towardmechanistic insight.

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