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Jul 23, 2015 - Dynamics of Tumor Heterogeneity Derived from Clonal Karyotypic Evolution. Ashley M. Laughney,1 Sergi Elizalde,2 Giulio Genovese,3,4 and ...
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Dynamics of Tumor Heterogeneity Derived from Clonal Karyotypic Evolution Graphical Abstract

Authors Ashley M. Laughney, Sergi Elizalde, Giulio Genovese, Samuel F. Bakhoum

Correspondence [email protected]

In Brief Chromosomal instability (CIN) is a hallmark of cancer. Laughney et al. developed a stochastic model of clonal karyotypic evolution, revealing that CIN optimizes tumor growth through the generation of heterogeneity. This rapidly shapes the evolution of clonal populations and enables spontaneous convergence onto favorable karyotypes frequently observed in cancer.

Highlights d

Chromosomal instability (CIN) underlies tumor heterogeneity and subclonal diversity

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Optimal chromosome missegregation rates balance phenotypic diversity with survival

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Whole-genome duplication is a path to a commonly observed near-triploid state

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Karyotypic evolution shapes chromosomal translocation patterns

Laughney et al., 2015, Cell Reports 12, 809–820 August 4, 2015 ª2015 The Authors http://dx.doi.org/10.1016/j.celrep.2015.06.065

Cell Reports

Article Dynamics of Tumor Heterogeneity Derived from Clonal Karyotypic Evolution Ashley M. Laughney,1 Sergi Elizalde,2 Giulio Genovese,3,4 and Samuel F. Bakhoum5,* 1Cancer

Biology and Genetics, Memorial Sloan Kettering Cancer Center, New York, NY 10065, USA of Mathematics, Dartmouth College, Hanover, NH 03755, USA 3The Broad Institute of Harvard and MIT, Cambridge, MA 02142, USA 4Department of Genetics, Harvard Medical School, Boston, MA 02115, USA 5Department of Radiation Oncology, Memorial Sloan Kettering Cancer Center, New York, NY 10065, USA *Correspondence: [email protected] http://dx.doi.org/10.1016/j.celrep.2015.06.065 This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). 2Department

SUMMARY

Numerical chromosomal instability is a ubiquitous feature of human neoplasms. Due to experimental limitations, fundamental characteristics of karyotypic changes in cancer are poorly understood. Using an experimentally inspired stochastic model, based on the potency and chromosomal distribution of oncogenes and tumor suppressor genes, we show that cancer cells have evolved to exist within a narrow range of chromosome missegregation rates that optimizes phenotypic heterogeneity and clonal survival. Departure from this range reduces clonal fitness and limits subclonal diversity. Mapping of the aneuploid fitness landscape reveals a highly favorable, commonly observed, near-triploid state onto which evolving diploid- and tetraploid-derived populations spontaneously converge, albeit at a much lower fitness cost for the latter. Finally, by analyzing 1,368 chromosomal translocation events in five human cancers, we find that karyotypic evolution also shapes chromosomal translocation patterns by selecting for more oncogenic derivative chromosomes. Thus, chromosomal instability can generate the heterogeneity required for Darwinian tumor evolution. INTRODUCTION Cancer is an evolutionary disease whose clonal nature has long been appreciated (Nowell, 1976). For Darwinian selection to occur, tumor cells must preserve the aptitude to maintain phenotypic heterogeneity through genomic instability (Yates and Campbell, 2012). A prevalent, yet understudied, form of instability is numerical (whole) chromosomal instability, whereby cancer cells rapidly vary the number of chromosome copies (karyotype) through whole-chromosome missegregation during mitosis (Bakhoum et al., 2014b; Lengauer et al., 1997). This karyotypic heterogeneity engenders transcriptomic and proteo-

mic imbalance (Pavelka et al., 2010b; Stingele et al., 2012; Upender et al., 2004). It is postulated that the cumulative potency and distribution of pro- and anti-proliferative genes encoded on individual chromosomes leads to tumor cells with varying fitness levels (Davoli et al., 2013; Pavelka et al., 2010a). Tumors are made up of subclonal populations that grow side by side in a branched manner and experience divergent evolutionary paths shaped by selective pressures (Gerlinger et al., 2012; Wang et al., 2014; Yates and Campbell, 2012). These subclones have been defined by chromosomal translocations or somatic mutations in key oncogenes and tumor suppressor genes. Unlike the firmly established role of somatic mutations during tumor evolution, the contribution of karyotypic instability at the single-cell level is poorly understood. Direct comparison of the prevalence and phenotypic consequences of somatic mutations and whole-chromosome missegregation might shed some light on their respective roles: most tumor cells exhibit somatic mutation rates similar to those of normal cells, and it was estimated that highly mutable tumors experience approximately eight somatic mutations per cell division (Wang et al., 2014). However, the majority of these are passenger mutations that rarely alter cellular phenotype over the span of a single cell division (Tomasetti et al., 2013), and the frequency of driver mutations is estimated to be on the order of 3.4 3 105 per cell division (Bozic et al., 2010). On the other hand, whole-chromosome missegregation events in unstable cancer cells occur approximately once every two to five cell divisions, much more frequently than in normal cells (Bakhoum et al., 2009b; Lengauer et al., 1997; Thompson and Compton, 2008), leading to altered expression of hundreds to thousands of genes. Therefore, we postulate that karyotypic instability can provide clonal populations with significant phenotypic diversity over the span of a few generations. Under this proposition, chromosome missegregation would complement mutation-derived changes by affording an added dimension of rapidly acquired phenotypic heterogeneity, thereby allowing tumor cells to adapt within a short time span. Experimental limitations represent a significant challenge to our understanding of the nature and dynamics of karyotypic heterogeneity at the single-cell level. As a result, fundamental questions about the evolution of chromosomally unstable clonal populations remain unanswered. To address these questions, we developed an experimentally inspired stochastic model of Cell Reports 12, 809–820, August 4, 2015 ª2015 The Authors 809

Figure 1. Numerical Chromosomal Instability in Clonal Population (A) Cancer cells frequently missegregate whole chromosomes leading to karyotypic heterogeneity. Depending on the oncogenic and tumor suppressive effect of genes encoded by individual chromosomes, individual karyotypes will have distinct proliferative states, leading to subclonal heterogeneity and shaping the overall fitness of the population. (B) Flowchart of the Monte Carlo stochastic model. D1 and D2 denote the two daughter cells, which either gain (D + missegregated chromosome) or lose (D – missegregated chromosome) one copy of the given chromosome that underwent a missegregation event. WGD, whole-genome duplication; Y, yes; N, no.

clonal evolution that traces single-cell karyotypes over hundreds of generations, while allowing chromosomally unstable cells to constantly sample the aneuploid fitness landscape. This landscape is defined by the aggregate oncogenic or tumor suppressive potential dictated by single-cell karyotypes, which are defined by the number of possible copies of each of the 23 human chromosomes (nchrom). For instance, given nchrom % 8, the aneuploid landscape includes 823 possible states, thus providing immense potential for chromosomally unstable cells to evolve. We then used this model to understand key parameters that govern the dynamics of tumor heterogeneity derived from clonal karyotypic evolution. RESULTS Basic Characteristics of Clonal Karyotypic Evolution Single cells contained nchrom copies of each of the 23 human chromosomes, summing to a total number of chromosomes 810 Cell Reports 12, 809–820, August 4, 2015 ª2015 The Authors

P per cell, Nchrom = 23 We i = 1 nchrom ðiÞ. assumed exponential cell growth so that each dividing cell gave rise to two daughter cells. Single chromosome copies missegregated at a given probability, pmisseg. When a missegregation event occurred during cell division, it led to disproportionate inheritance whereby the two daughter cells ended up with one too many or one too few copies of the missegregated chromosome (Figures 1A and 1B). We assumed that (1) cells were unviable if they completely lost all copies of any given chromosome (nchrom = 0), as they would be missing a number of essential genes (Davoli et al., 2013). (2) Cells could not have more than eight copies of any given chromosomes (nchrom % 8 or Nchrom % 184 chromosomes/cell). We performed sensitivity analyses for the first two assumptions for key conclusions. (3) pmisseg was the same across all 23 human chromosomes; this is based on the stochastic nature of microtubule attachments to kinetochores during mitotic chromosome missegregation (Bakhoum et al., 2009a). A key experimental approach to studying karyotypic heterogeneity has been to propagate single cells and then use chromosome-specific probes to measure the proportion of the derived clonal population that deviates from its modal chromosome number for any given chromosome (Lengauer et al., 1997). For instance, in chromosomally unstable U2OS cells, approximately one in four cells deviate from modal chromosome numbers for any given chromosome after 25 generations. This is observed at chromosome missegregation rates of 9.4 3 103 per chromosome type (Bakhoum et al., 2009b), which are equivalent to a pmisseg 2.5 3 103 per chromosome copy when accounting for cellular ploidy (Table S1). In these experiments, population deviance proportionately decreases when chromosome missegregation is experimentally suppressed.

Figure 2. Basic Characteristics of Numerical Chromosomal Instability in Clonal Populations (A) Percentage of cells that deviate from modal chromosome numbers as a function of chromosome missegregation probabilities (pmisseg). Bars represent mean ± SEM. (B) Predicted (red) and experimental (blue, U2OS cells) percentage of cells that deviate from the modal chromosome number after 25 generations. In the predicted cohort, an example from one iteration is shown. *, > mean + 2SD. (C) Percentage of cells that deviate from modal chromosome number for any given chromosome as a function of the first cell division at which this chromosome underwent a missegregation event for the first time. Solid red line shows mean; dotted lines denote 95% confidence interval (CI). Data points represent individual chromosomes from 1.05 3 109 cells generated from 1,000 clonal populations. (D) Percentage of cells that deviate from modal chromosome number as a function of number of cell divisions (generations). Lines denote individual chromosomes in a single clonal population. (E) Percentage of cells that deviate from modal chromosome number as a function of the number of cell divisions for two different chromosome missegregation probabilities. Lines represent averages of all chromosomes in three separate replicates. Thickness of the line represents 95% CI of the fitted curve.

To establish whether our model approximates experimental conditions in its most basic form, we simulated clonal growth for 25 generations at three different pmisseg values for which experimental data were available. At pmisseg = 2.5 3 103, 20% of the population deviated from modal chromosome numbers, and this deviance decreased at lower missegregation rates, closely mirroring experimental values under similar conditions (Figure 2A). We frequently observed random outlier chromosomes for which population deviance was much greater than expected, also consistent with experimental observations (Figure 2B). We reasoned that these chromosomes might have experienced early missegregation events during clonal expansion. Consequently, we indexed the generation of the first missegregation event per chromosome and found that a missegregation event during the first approximately five generations had a profound impact on population deviance for the early missegregating chromosome (Figure 2C). This relationship was significant for

as many as 250 generations, after which it became less consequential (Figure 2D). To determine the temporal dependence of karyotypic heterogeneity on chromosome missegregation rates, we simulated clonal growth for 1,000 generations at two different pmisseg values. Lower chromosome missegregation rates delayed population deviance from reaching an ultimately stable asymptote (Figure 2E). A Markov chain model was then developed to predict the probability that a randomly chosen cell will have nchrom copies of a given chromosome at the gth generation (see Supplemental Experimental Procedures). Using this alternative approach, we validated that population deviance stabilizes at an asymptote over time irrespective of pmisseg (Figure S1A). Interestingly, this steady-state value was also independent of the nchrom of the founder clone (Figures S1B and S1C). Therefore, given sufficient time, even low chromosome missegregation rates are capable of generating maximum karyotypic heterogeneity. Cell Reports 12, 809–820, August 4, 2015 ª2015 The Authors 811

Dependence of Clonal Fitness on Chromosome Missegregation Rates The above analysis does not account for karyotype-specific viability, even though each chromosome is hypothesized to have a distinct pro- or anti-proliferative tendency based on the cumulative oncogenic or tumor-suppressive effects of the genes it harbors. Therefore, an oncogenic or tumor suppressive value (ChromTSG-OG), derived from a recent genomic analysis, was assigned to individual chromosomes based on the potency and chromosomal distribution of the oncogenes and tumor suppressor genes they carry (Davoli et al., 2013). Positive ChromTSG-OG scores indicated chromosomes with an oncogenic tendency, whereas negative scores defined tumor suppressive propensity (Table S2). In this analysis, ChromTSG-OG scores correlated with chromosome amplification frequencies observed in cancer. Individual cell scores were then defined according to the cumulative score of all chromosomes weighted by the copy number of each chromosome, such that P cell score = 23 i = 1 nchrom ðiÞ ChromTSGOG ðiÞ (Table S1). Each cell score was translated into a survival probability by mapping the cell score distribution to quantitative measurements of apoptotic indices observed in a variety of human tumors (Figure 1B; Figures S2A–S2C; Experimental Procedures). In this model, changes in the relative dosage of oncogenes and tumor suppressor genes led to corresponding alterations in cellular viability. To determine whether pmisseg influenced the viability of chromosomally unstable clones, 60 clonal populations derived from either diploid (nchrom = 2 for all chromosomes) or tetraploid (nchrom = 4 for all chromosomes) founder cells were expanded for 1,000 generations (g) with pmisseg varying from 107 to 101. The growth of clonal populations was then characterized by measuring the surviving fraction, fsurviving = ðng =2g Þ, where ng is the total cell number at the gth generation of cell division (Table S1; Experimental Procedures), the average cell score, and the Shannon-Weaver diversity index (H) of the cell scores as an estimate of phenotypic heterogeneity. Here, P H =  165 i = 1 pcell score ðiÞln pcell score ðiÞ, where pcell score(i) represented the probability of a given state i within the population, and i represented the possible range of possible cell scores (72 to +93) discretized into 165 integer states (Figures 3A– 3C). Interestingly, we observed that a narrow range of chromosome missegregation rates maximized cell viability and clonal heterogeneity; fsurviving peaked at pmisseg 103 before precipitously decreasing at higher missegregation probabilities (Figures 3A and 3D). On the other hand, H increased with increasing chromosome missegregation probabilities, reaching a plateau at pmisseg values between 103 and 104 (Figures 3C and 3D). Clonal fitness was then defined as the product of cell survival and heterogeneity integrated over clonal lifetime, such that P fitness = 1000 g = 1 fsurviving HðgÞ. Optimal clonal fitness was achieved at pmisseg = 1.4 3 103 and pmisseg = 3.0 3 103 for diploid and tetraploid-derived populations, respectively (Figure 3E). This peak was independent of the number of generations, g, and the upper boundary condition (nchrom % 8) (Figure S3A), but was defined by the lethality of nullisomy (nchrom = 0), when all copies of any given chromosome were lost (Figure S3B). Therefore, increasing chromosome missegregation rates enhances 812 Cell Reports 12, 809–820, August 4, 2015 ª2015 The Authors

clonal fitness up to a point beyond which clonal viability is curtailed by frequent nullisomy. We used an orthogonal approach to validated the existence of an optimal missegregation rate for clonal expansion by measuring the difference between the cell score of the founder cell, mcell score (g0), and the average cell score of the resultant population after g generations, mcell score (g) (Figure 3B). This difference represents the ability of a clonal population to mobilize across the aneuploid fitness landscape, a property we termed adaptive capacity = mcell score ðgÞ  mcell score ðg0 Þ (Table S1). Similarly, the adaptive capacity reached a peak at pmisseg 1.5 3 103 (Figure 3F). This peak was conserved for 5,000 generations (Figure S3C) and was defined by both upper and lower boundary conditions of nchrom (Figures S3D and S3E). Chromosome missegregation rates experimentally measured in human-cancer-derived cell lines (Bakhoum et al., 2009b; Thompson and Compton, 2008) were then surveyed and found to fall within, or very close to, our predicted range of optimal chromosome missegregation probability (Figure 3G). Put together, these findings strongly suggest the existence of a narrow range of chromosome missegregation frequencies that is optimal for clonal evolution. Clonal growth patterns were then evaluated while random mutations, which were introduced at probabilities (pmutation) ranging from 1 3 106 to 1 3 103, altered either the cell-cycle duration or chromosome missegregation rates. Surprisingly, clonal growth characteristics were insensitive to mutations that led to a 2-fold change in cell-cycle duration; clonal heterogeneity and adaptive capacity remained largely unchanged (Figures S4A and S4B). Furthermore, the fraction of rapidly and slow cycling populations remained at equilibrium for up to 4,000 generations (Figure S4C). On the other hand, clonal populations were exquisitely sensitive to mutations that spontaneously altered pmisseg, resulting in a nearly 100-fold change in fsurviving after 1,000 generations (Figures S5A–S5C). This was due to the enhanced fitness of subclonal populations whose pmisseg shifted towards the optimal value. Finally, we found that clonal characteristics were relatively robust to small perturbations in the cost of aneuploidy on cell survival (Figures S6A–S6C). However, when apoptotic indices, to which cell scores were mapped, were varied by up to 3-fold, clonal adaptation was accelerated given increased selective pressures at higher apoptotic indices (as high as 18%). This came at a significant cost to growth rates (Figures S6D–S6F). Missegregation rates optimal for fitness remained relatively robust over a wide range of apoptotic indices (Figures S6G and S6H). This range of apoptotic indices (0%–18%) encompasses recently predicted values for the average fitness reduction of aneuploidy in cancer cells being on the order of 6% (Valind et al., 2013). Clonal Sampling of the Aneuploid Fitness Landscape We then sought to determine the kinetics by which chromosomally unstable clones navigate the aneuploid fitness landscape depending on their ‘‘ground state’’ fitness level. Copy numbers of the 23 chromosomes were randomized to create 25 near-diploid (1 % nchrom % 3) and 25 near-tetraploid (3 % nchrom % 5) founder cells. Nchrom ranged from 41 to 52 and 84 to 100 for near-diploid and near-tetraploid cells, respectively

Figure 3. Influence of Chromosome Missegregation Rates on Clonal Fitness (A–C) The surviving fraction (fsurviving) (A), cell score (B), and the Shannon diversity index (H) (C) of 30 representative clonal populations dividing with different rates of chromosome missegregation (pmisseg). Gray lines represent pmisseg values that fall in between colored lines; only a few pmisseg values were colored and labeled for clarity. (D) fsurviving and H at the 1,000th generation as a function of pmisseg. Data points represent mean ± SD, total of 90 iterations. (E and F) Clonal fitness (integrated by measuring the area under the curve for 1,000 generations, E) and the adaptive capacity (F) of diploid and tetraploid cell clones as a function of pmisseg, data points represent mean ± SD, total of 90 iterations for each panel. (G) The predicted optimal pmisseg range for clonal fitness and adaptation (derived from two orthogonal approaches) in comparison with chromosome missegregation rates experimentally observed in cancer-derived cell lines.

(Figure S7A). Each founder cell had a distinct karyotypic makeup and consequently, a unique starting fitness level (Figure 4A). These cells were propagated for 1,000 generations at pmisseg = 2.5 3 103. Mean population cell scores progressively increased in all clonal populations over time (Figure 4A) and converged onto a narrow range of cell scores regardless of their initial ground state. This asymptote was conserved for up to 5,000 generations (Figure 4A; Figure S7B).

To our surprise, all clones converged onto a near-triploid karyotype regardless of their starting state and this karyotype remained stable for up to 5,000 generations (Figure 4B; Figure S7A), suggesting a global minimum in the aneuploid fitness landscape. We then used the Markov chain model to precisely determine the limiting distribution of chromosome copy numbers given ChromTSG-OG and a pmisseg = 2.5 3 103 and found that, as the number of generations approached infinity, the average Cell Reports 12, 809–820, August 4, 2015 ª2015 The Authors 813

Figure 4. Clonal Sampling of the Aneuploid Fitness Landscape (A) Average cell score of 50 randomly derived near-diploid or near-tetraploid clonal populations as a function of time. (B) Total chromosome numbers/cell for six randomly chosen near-diploid or near-tetraploid clonal populations over 5,000 generations. (C) The limiting distribution of chromosome copy numbers derived form the Markov chain model averaged across all chromosomes as the number of generations approaches infinity, yielding a mean value of 3.16 copies/human chromosome. (D) Modal chromosome numbers as a function of chromosome-specific scores (ChromTSG-OG) after 1,000 generations. Data points represent mean ± SD for 50 clonal populations. (E) The limiting distribution of chromosome copy numbers derived form the Markov chain model as a function of chromTSG-OG score as the number of generations approaches infinity. (F) The number of generations elapsed until diploid and tetraploid-derived clonal populations achieve a mean karyotype of 67–75 chromosomes/cell (50 iterations). (G) The surviving fraction as a function of distance traveled on the aneuploid fitness landscape (Dcell score) for populations derived form near-diploid and neartetraploid founder clones. Dashed lines depict the 95% CI of the curve fit. (H) Distribution of 1,260 tumor karyotypes from the Mitelman database. The blue line is the predicted optimal chromosomal content derived from (B).

nchrom value equaled 3.16 which corresponds to 72.7 chromosomes/cell (Figure 4C). Using both the forward stochastic model and the Markov model, we showed that this near triploid state did not merely consist of three copies per chromosome but rather maximized the copies of oncogenic chromosomes and minimized the copies of tumor suppressive ones (Figures 4D and 4E). Interestingly, the time required to reach this near-triploid state was the same for diploid and tetraploid-derived populations and was inversely proportional to pmisseg (Figure 4F). However, the survival cost to reach this state was nearly two orders of magnitude higher for populations derived from neardiploid founders compared to their near-tetraploid-derived counterparts (Figure 4G). Accordingly, when diploid and tetraploid founder clones were propagated side by side, the tetraploid-derived populations rapidly overtook their diploidderived counterparts (Figures S7C and S7D). At chromosome missegregation rates commonly observed in cancer-derived cell lines, tetraploid-derived cells represented >85% of the total population after 1,000 generations. To assess whether a near-triploid state might also be favored in human tumors, we surveyed 1,260 tumor karyotypes reported in the Mitelman database for breast, gastrointestinal, pancreatic, ovarian, and lung cancers and melanoma. Tumor karyotypes centered around two peaks: one near-diploid, likely representing 814 Cell Reports 12, 809–820, August 4, 2015 ª2015 The Authors

chromosomally stable or early stage tumors. A second peak emerged at 71 chromosomes/cell (Figure 4H), falling very closely to the karyotype onto which all clones eventually converge, as predicted by our model. These findings suggest that clonal populations drift towards a favorable near-triploid karyotype that likely confers a selective advantage in tumors. This state can be achieved by diploid and tetraploid derived populations alike, albeit at a much lower fitness cost for the latter. A large proportion of chromosomally unstable human tumors are postulated to have undergone genome duplication events during their evolutionary history (Carter et al., 2012; Dewhurst et al., 2014) (Figure 1A). We postulated that passage through a tetraploid-intermediate might serve as a faster path to a near-triploid chromosomal state. The probability of wholegenome duplication events (pGD) was varied across 30 orders of magnitude for sensitivity analysis (Figure 1B). An optimal genome duplication rate (pGD = 4.8 3 104 ± 2.2 3 105) was found to maximize clonal survival and time to reach a near-triploid karyotype (Figures S8A and S8B). This optimal pGD peak was not influenced by either the upper (nchrom > 0) or lower (nchrom % 8) boundaries (Figures S8C and S8D). Beyond this peak, reduction in fsurviving was primarily due to increased frequency of genome duplication without an increase in cell number.

Figure 5. Subclonal Heterogeneity in Chromosomally Unstable Clones (A) Unsupervised clustering of 1.59 3 105 cells from clone 13 (Figure S9A) with 3.18 3 104 cells from two reference clones (Figure S10D) reveals 67 distinct subclones. (B) Number of subclones as a function of chromosome missegregation probability (pmisseg). Data points represent mean ± SD, total of 90 iterations. (C) Population fraction of each of the 67 subclones in clone 13 over 5,000 generations propagating at pmisseg = 2.5 3 103. (D) Mean subclone lifetime (in generations) as a function of pmisseg. Data points represent mean ± SD (51 iterations). (E) Subclonal population fraction at various pmisseg values as a function of the Shannon diversity index (H). Each data point represents a subclone, and each line represents a different chromosome missegregation rate. (F) Heatmap of (H) over 5,000 generations for all 67 subclones at three missegregation rates.

Branched Evolution of Chromosomally Unstable Subclones Tumors are made up of co-evolving and competing subclones. We reasoned that experimental methods that estimate karyotype information by simply measuring the most common chromosome copy numbers for a tumor might not accurately reflect the population karyotype which is made up of diverse subclones. To test this hypothesis, we computed modal chromosome numbers for all of the 23 chromosomes in 50 diploid and tetraploid derived clonal populations. For each of the clonal populations, we found striking disparity between the cell scores derived from the modal values of each of the 23 chromosomes and the true average of individual cell scores (Figures S9A and S9B). This discrepancy was more notable in tetraploid-derived clones and suggests that modal chromosome numbers do not accurately represent the average cellular karyotype in a population. The subclonal makeup of clonal populations was determined by unsupervised clustering of chromosome copy numbers of single cells using a trained-neural network algorithm followed

by neighbor-joining method (Figures S10A–S10D; Supplemental Experimental Procedures). Essentially, this method treated chromosome missegregation events as a clock to determine the evolutionary path of the clonal population. For validation, the progeny of clonal populations derived from 20 distinct founder clones (evolved for 50 generations) were randomly mixed and then classified via unsupervised clustering with an accuracy >0.998 (Figure S10E). We subsequently applied this methodology to identify subclones within founder clone 13, which exhibited marked divergence between the modal cell score (45.9) and average cell score (27.0) (Figure S9A). To calibrate Euclidean distances between subclones, phylogenic trees were computed relative to cells from two distinct reference clones. Clustering of 1.58 3 105 cells sampled from clone 13 revealed 67 distinct subclones with diverse karyotypes and highly variable average cell scores (Figure 5A; Figures S11A and S11B). This analysis was then repeated at varying missegregation rates, revealing that chromosome missegregation can rapidly lead to the emergence of diverse subclones. Furthermore, the maximal subclonal diversity emerged at lower pmisseg values Cell Reports 12, 809–820, August 4, 2015 ª2015 The Authors 815

Figure 6. CIN Shapes Chromosome Translocation Patterns (A) Schematic diagram of peri-centromeric chromosomal translocations. (B) Frequency of translocation events yielding a higher (red, higher D) versus lower (blue, lower D) differences in ChromTSG-OG scores between derivative chromosomes. (C) Frequency at which the more oncogenic (red, higher CS [chromosome score]) versus less oncogenic (blue, lower CS) derivative chromosome is retained after reciprocal translocation. (D) Frequency at which a derivative chromosome will have an oncogenic (ChromTSG-OG > 0, red, OG) versus tumor suppressive (ChromTSG-OG > 0, blue, TSG) scores. *p < 0.05, c2 test. (E) Mean and SD of ChromTSG-OG scores of derivative chromosomes, *p < 0.05; **p < 0.0001 (twotailed t test, H0; average ChromTSG-OG = 0). (F) Distribution of cell scores for near-diploid and near-triploid subclones in a pancreatic tumor. (G) Frequency of gains and losses of all chromosomes (All chrom) and derivative chromosome (Derivative chrom) in 35 subclones of a pancreatic tumor as a function of the ChromTSG-OG score (CS). *p < 0.0001, c2 test.

cell scores, survived until 5,000 generations (Figures 5E and 5F; Figures S11D and S11E).

for tetraploid-derived populations compared to their diploidderived counterparts (Figure 5B). To determine factors that influence subclonal viability and composition, 67 subclones from clone 13 were then tracked for an additional 5,000 generations. By that time, many subclones became extinct (Figure 5C). While important for generating subclonal heterogeneity, increasing chromosome missegregation led to a significant decrease in both subclonal lifetime and fitness as measured by mean cell score (Figure 5D; Figure S11C). The strongest determinant for subclonal viability was intra-subclonal heterogeneity, where only the most heterogeneous clones, and not necessarily the ones with the highest 816 Cell Reports 12, 809–820, August 4, 2015 ª2015 The Authors

Chromosomal Instability Shapes Chromosomal Translocation Patterns Numerical chromosomal instability does not exist in isolation; tumors with unstable karyotypes simultaneously exhibit numerical and structural chromosomal instabilities (Bakhoum et al., 2014a; Burrell et al., 2013; Crasta et al., 2012). Experimental data on rates of chromosomal rearrangements and translocations at the singlecell level are lacking, precluding our ability to incorporate it into our model. Yet, it has been proposed that tumor-defining chromosome translocation events most likely occur prior to major chromosome copynumber changes (Carter et al., 2012). We postulated that, once formed, centromere-containing derivative chromosomes would missegregate at rates similar to those of normal chromosomes during mitosis, and, as such, karyotypic evolution may also shape translocation patterns to favor the generation, and amplification, of more oncogenic derivative chromosomes. When two chromosomes undergo reciprocal translocations they can produce two pairs of derivative chromosomes depending on the location of the breakpoints with respect to the centromere (Figure 6A, left). We posited that these translocation events represent an opportunity to pair two highly oncogenic chromosome arms together and two tumor suppressive arms together,

loid subclones had higher overall cell scores and exhibited more interclonal variability (Figure 6G). In these subclones, net oncogenic ChromTSG-OG scores were associated with a 26.7fold likelihood of chromosome gain rather than loss (p < 0.0001). This was also the case within the subset of derivative chromosomes (odds ratio = 93.3, p < 0.0001) (Figure 6H). Collectively, these data demonstrate that derivative chromosomes are subject to strong selective pressures in chromosomally unstable cancers, and they address a long-standing question regarding the fate of reciprocal products of chromosomal translocation events, and why such products are frequently lost in solid tumors (Rego and Pandolfi, 2002). DISCUSSION Figure 7. Tumor Heterogeneity Derived from Clonal Karyotypic Evolution (A) Schematic comparison of the phenotypic penetrance and expressivity of somatic mutation events (dark red) and chromosome missegregation events (shades of red). (B) Clonal population experiencing a somatic mutation event (dark red) leading to early subclonal speciation. Both subclones undergo chromosome missegregation events leading to an additional layer of intra-tumor heterogeneity.

leading to subsequent amplification of the former and suppression, or loss, of the latter. We asked whether selective pressures during karyotypic evolution favors chromosomal breakpoint configurations that yield larger differences in ChromTSG-OG scores (DChromTSG-OG) between the two derivative chromosomes (Figure 6A, left). To address this question, we analyzed 1,368 unique chromosomal translocations reported in the Mitelman database found in breast, lung, gastrointestinal, and pancreatic cancers and melanoma. Our analysis focused on breakpoints near the centromeres (p1 or q1 regions) as they involved the translocation of nearly an entire chromosome arm. Indeed, there was 1.27-fold enrichment for translocation events that derived from breakpoint configurations that maximized DChromTSG-OG between the two derivative chromosomes (Figure 6B, p = 6.5 3 103). Once a translocation event occurs, regardless of breakpoint arrangements, tumor cells can either keep both derivative chromosomes or lose one of them (Figure 6A, middle). In the event that one of the two derivatives were lost, tumors were 1.46fold more likely to retain the more oncogenic derivative chromosome (Figure 6C, p = 1 3 106). Overall, 61% of all derivative chromosomes observed had an oncogenic ChromTSG-OG score, whereas only 39% had a tumor suppressive ChromTSG-OG score (Figure 6A, right, and Figure 6D, p < 1 3 106). Further, ChromTSG-OG scores for derivative chromosomes found in all tumor types surveyed were on average oncogenic (mChromTSG-OG > 0) (Figure 6E). Finally, we analyzed 572 chromosomal alterations in a single pancreatic ductal adenocarcinoma tumor for which karyotype information on 33 subclones was available (Gorunova et al., 1998). In this tumor, 16 subclones were near-diploid, 13 were near-triploid, and four were polyploid. Karyotypic changes involved gains and losses of whole chromosomes or derivative chromosomes. Compared to the near-diploid clones, near-trip-

We have developed a stochastic model of clonal karyotypic evolution to explore, in silico, the dynamics by which numerical chromosomal changes contribute to clonal and subclonal fitness and diversification. Our model is distinct from prior modeling efforts in two key aspects (Gusev et al., 2001). First, it incorporates a measure of cellular viability based on chromosomal content, as well as the potency and relative distribution of oncogenes and tumor suppressor genes on each chromosome (Davoli et al., 2013). Second, it employs a Markov chain model that lends a mathematical proof to the main conclusions derived from the stochastic Monte Carlo simulations. We show that chromosomal content in human cancer, as well as chromosome missegregation rates in cancer-derived cell lines, are heavily shaped by selection imparted during clonal karyotypic evolution. While the primary speciation events in tumors are broadly defined by key somatic mutations or rare translocation events (Carter et al., 2012), we demonstrate that karyotypic evolution can endow the tumor cell population with an added dimension of phenotypic heterogeneity that facilitates rapid adaptation. This model is based on both the relative penetrance and expressivity of somatic mutations and wholechromosome missegregation events (Figure 7A); most somatic mutations are passenger mutations and thus, as single events, have low phenotypic penetrance. Yet, the rare and consequential ones often have high expressivity (Bozic et al., 2010; Tomasetti et al., 2013). In contrast, whole-chromosome missegregation events remain highly penetrant and with variable expressivity. These multidimensional genomic alterations would ensure that clonal populations constantly sample a wide array of fitness states, thereby enabling rapid genomic drifts under selective pressures (Figure 7B) (Bakhoum and Compton, 2012; Chen et al., 2012, 2015). We show that chromosome missegregation rates commonly observed in cancer are sufficient to generate maximal cellular and subclonal heterogeneity over timescales relevant to tumor evolution. These rates, however, must balance the emergence of new subclones with clonal fitness and they are defined, in part, by the deleterious consequences of nullisomy. As the overall clonal population remains unstable, it continues to beget subclones with variable fitness levels, out of which only the most heterogeneous survive. The notion of an optimal missegregation rate is supported by multiple experimental and clinical observations. Inducing Cell Reports 12, 809–820, August 4, 2015 ª2015 The Authors 817

chromosome missegregation in otherwise normal cells can enhance proliferation in vivo and accelerate tumorigenesis (Foijer et al., 2014; Sotillo et al., 2007; Weaver et al., 2007), whereas excessive chromosome missegregation is often lethal (Janssen et al., 2009; Silk et al., 2013). Clinically, chromosomal instability is associated with poor prognosis and therapeutic resistance (Bakhoum et al., 2011; Lee et al., 2011; Ryan et al., 2012); however, excessive instability results in a superior treatment response (Bakhoum et al., 2015; Birkbak et al., 2011; Roylance et al., 2011; Zaki et al., 2014). Our work provides experimentally testable predictions and sheds quantitative insight into ongoing efforts that aim to specifically target chromosomally unstable and aneuploid cancer cells (Janssen et al., 2009; Tang et al., 2011). By allowing clonal populations to sample the aneuploid fitness landscape, we validate that a karyotype of 72 chromosomes/ cell represents a relatively favorable state that maximizes the copies of oncogenic chromosomes and minimizes those with a tumor suppressive propensity. While both diploid and tetraploid-derived populations can achieve this near-triploid state, the latter do so at a much lower fitness cost. This lends evolutionary support to the hypothesis that a near-tetraploid intermediate represents a faster and a more viable path toward the favorable near-triploid karyotype frequently observed in cancer (Carter et al., 2006; Dewhurst et al., 2014). Incremental chromosome gains and losses might not be the only path toward an optimal near-triploid state; sequential rounds of whole-genome duplication events followed by cytoreductive mitosis may also represent a rapid path to such a state. In addition to numerical changes in chromosomal content, chromosome missegregation during mitosis can lead to chromosome pulverization and massive rearrangements, a process known as chromothripsis (Crasta et al., 2012; Stephens et al., 2011). Experimental data on the frequency of these events at the single-cell level are lacking, precluding our ability to incorporate it in our model. It is likely that these punctuated chromosomal alterations frequently represent catastrophic events to tumor cells. Nonetheless, they may at times generate strong selective advantage, such as massive amplification of oncogenes on double minute chromosomes. If such events were to occur, clonal populations would experience significant genomic shifts amidst cycles of incremental genomic drift both of which resulting from chromosome missegregation during mitosis. EXPERIMENTAL PROCEDURES Stochastic Model of Chromosome Missegregation in Clonal Populations Single-cell karyotypes were tracked during exponential population growth using a matrix representation of chromosome copy numbers. Given the number of cells (ng) at generation g, let nchrom(j,i) be the copy number per cell j for each of the 23 chromosomes indexed by i, for 1 % i % ng. Let pmisseg be the probability of missegregation of a chromosome copy per cell division. The probability of missegregation per chromosome type (i.e., human chromosomes 1 to 23), pweighted(j,i), was weighted by the absolute copy number of each chromosome nchrom(j,i), such that pweighted ðj; iÞ = 1  ð1  pmisseg Þnchrom ði; jÞ . A pseudorandom matrix of values rand(j,i) was drawn from a standard uniform distribution over the open interval (0,1) with the dimensions of pweighted(j,i). A missegregation event occurred whenever randðj; iÞ%pweighted ðj; iÞ.

818 Cell Reports 12, 809–820, August 4, 2015 ª2015 The Authors

During cell division, nchrom was replicated and stacked so that it had dimensions 2ng 3 23. For all missegregation events, one copy of each missegregated chromosome was disproportionately assigned to one of the two daughter cells in a random fashion. Our forward stochastic model did not preclude multiple missegregation events of different chromosomes in a single cell division, although the probability of such events was significantly lower. In its most basic form, the survival of each cell, j, was determined according to its karyotype; cell death was certain whenever nchrom(j,i) = 0 or nchrom(j,i) > 8 for any given chromosome type, i, unless stated otherwise. A new seed was selected for the pseudorandom number generator at every instance of cell division to ensure a stochastic model. To manage the computational memory requirements for exponential cell growth, a sampling strategy was implemented whenever ng > 5 3 105 cells. Prior to implementing the selection imparted by cell survival probabilities, a fraction of the cell population (fsampled = 0.125) was randomly sampled for unbiased representation of the total cell population. The number of cells sampled (ng,sampled) and the number of sampling events were indexed (indexsampled) per generation to extrapolate the true cell count in the absence of sampling, ng = ng;sampled ð1=fsampled Þindexsampled . Therefore, surviving fraction at generation g was computed according to fsurviving = ðng =2g Þ, where 2g represents the maximum cell number at generation g assuming exponential cell growth with survival probability = 1. Modeling Clonal Evolution within the Aneuploid Fitness Landscape A forward Monte Carlo model simulating cell proliferation and death according to stochastic survival probabilities was then developed to computationally explore how chromosomal instability shapes clonal karyotypic evolution. We employed chromosome-specific scores (ChromTSG-OG with dimensions 23 3 1) derived from a recent genomic analysis, which assigned an oncogenic or tumor suppressive score to individual chromosomes based on the potency and chromosomal distribution of oncogenes and tumor suppressor genes (Davoli et al., 2013) (Table S2). Overall cell score was defined as the matrix product of nchrom and ChromTSG-OG. To relate this cell score to cell survival, we assigned a survival probability (psurvival) to each cell according to its unique chromosomal karyotype, which made up the overall cell score. The distribution of psurvival was derived from apoptotic indices commonly observed in a number of human tumors (Soini et al., 1998), such that psurvival = 1-apoptotic index. The normal distribution of possible cell scores was then linearly translated to the log-transformed psurvival distribution (Figure S2). Cells continued to proliferate or die as influenced by psurvival and within the initial viability constraints (0 < nchrom % 8). With this translation, the probability of survival per cell karyotype was computed according to: psurvival ðjÞ = where ðnchrom ChromTSGOG Þj = ðeð0:00039ðnchrom ChromTSGOG Þj + 4:5909Þ =100Þ, P23 i = 1 nchrom ðj; iÞChromTSGOG ðiÞ. Again, a pseudorandom array of length ng was drawn from a standard uniform distribution over the open interval (0,1) at every generation to determine whether a cell with a given probability of survival, psurvival(j), in fact, dies (cell death if rand(j) % psurvival(j)). Cells that die were removed from the matrix nchrom; remaining cells continued to proliferate exponentially. Genome Duplication Events To vary whole-genome duplication events, a pseudorandom array of length ng was drawn from a standard uniform distribution over the open interval (0, 1) at every generation to determine whether a cell with a given pGD experiences a genome duplication event, which entailed doubling of the entire chromosomal content without cell division. These cells resumed normal cell division in subsequent generations. All simulations were performed using MATLAB (MATLAB and Statistics Toolbox Release 2013b, The MathWorks). SUPPLEMENTAL INFORMATION Supplemental Information includes Supplemental Experimental Procedures, 11 figures, and two tables and can be found with this article online at http:// dx.doi.org/10.1016/j.celrep.2015.06.065.

AUTHOR CONTRIBUTIONS S.F.B. and A.L.M. conceived of the project, A.L.M. designed and executed the forward stochastic model, S.E. derived the Markov model, S.F.B., A.L.M., G.G., and S.E. analyzed the data, S.F.B. and A.L.M. wrote the manuscript with help from G.G. and S.E. S.F.B. supervised the entire project. ACKNOWLEDGMENTS This work was supported by the William H. Neukom 1964 Institute for Computational Sciences. We thank Lewis C. Cantley, PhD (Weill Cornell Medical College), Joan Massague´, PhD (MSKCC), Neil Taunk, MD (MSKCC), and Duane Compton, PhD (Dartmouth) for critical feedback. Received: January 30, 2015 Revised: May 18, 2015 Accepted: June 22, 2015 Published: July 23, 2015 REFERENCES Bakhoum, S.F., and Compton, D.A. (2012). Chromosomal instability and cancer: a complex relationship with therapeutic potential. J. Clin. Invest. 122, 1138–1143. Bakhoum, S.F., Genovese, G., and Compton, D.A. (2009a). Deviant kinetochore microtubule dynamics underlie chromosomal instability. Curr. Biol. 19, 1937–1942. Bakhoum, S.F., Thompson, S.L., Manning, A.L., and Compton, D.A. (2009b). Genome stability is ensured by temporal control of kinetochore-microtubule dynamics. Nat. Cell Biol. 11, 27–35. Bakhoum, S.F., Danilova, O.V., Kaur, P., Levy, N.B., and Compton, D.A. (2011). Chromosomal instability substantiates poor prognosis in patients with diffuse large B-cell lymphoma. Clin. Cancer Res. 17, 7704–7711. Bakhoum, S.F., Kabeche, L., Murnane, J.P., Zaki, B.I., and Compton, D.A. (2014a). DNA-damage response during mitosis induces whole-chromosome missegregation. Cancer Discov 4, 1281–1289. Bakhoum, S.F., Silkworth, W.T., Nardi, I.K., Nicholson, J.M., Compton, D.A., and Cimini, D. (2014b). The mitotic origin of chromosomal instability. Curr. Biol. 24, R148–R149.

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Cell Reports Supplemental Information

Dynamics of Tumor Heterogeneity Derived from Clonal Karyotypic Evolution Ashley M. Laughney, Sergi Elizalde, Giulio Genovese, and Samuel F. Bakhoum

SUPPLEMENTARY  FIGURES  AND  LEGENDS  

  Figure  S1.  Determinants  of  population  deviance  from  modal  chromosome  copy  number   (A)  Population  deviance  from  modal  chromosome  copy  number  over  time  for  two  chromosome   missegregation  rates  (pmisseg)  as  predicted  using  Markov  Chain  method.  Founder  clones  had  nchrom  =   4  for  all  chromosomes.  This  is  in  direct  comparison  with  Figure  2E  of  the  main  text  where  this   information  was  derived  instead  from  the  forward  stochastic  model.  (B)  Population  deviance  from   modal  chromosome  copy  number  over  time  for  founder  clones  with  a  different  chromosome  copy   numbers  (nchrom)  as  predicted  using  Markov  chain  method  expanding  at  pmisseg  =  0.0025.  (C)   Population  deviance  from  modal  chromosome  copy  number  over  time  for  founder  clones  with   different  chromosome  copy  numbers  (nchrom)  as  predicted  using  Markov  chain  method  expanding  at   pmisseg  =  0.0025  taking  into  account  chromTSG-­‐OG  for  each  of  the  23  human  chromosomes  (Table  S2).   Please  refer  to  experimental  extended  procedures  for  full  description  of  the  Markov  model  used  to   derive  these  graphs.      

 

 

2  

  Figure  S2.  Fitting  the  chromosome  score  to  cellular  survival  probability  used  in  Figures  3-­‐5   of  the  main  text.     (A)  Distribution  of  cell  scores  for  randomly  generated  1x107  cells  (0  0.      

 

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