Author response: Quantifying chromosomal instability from intratumoral karyotype diversity using agent-based modeling and Bayesian inference
Year: 2021
Type: peer-review
Abstract: Article Figures and data Abstract Editor's evaluation eLife digest Introduction Results Discussion Materials and methods Data availability References Decision letter Author response Article and author information Metrics Abstract Chromosomal instability (CIN)—persistent chromosome gain or loss through abnormal mitotic segregation—is a hallmark of cancer that drives aneuploidy. Intrinsic chromosome mis-segregation rate, a measure of CIN, can inform prognosis and is a promising biomarker for response to anti-microtubule agents. However, existing methodologies to measure this rate are labor intensive, indirect, and confounded by selection against aneuploid cells, which reduces observable diversity. We developed a framework to measure CIN, accounting for karyotype selection, using simulations with various levels of CIN and models of selection. To identify the model parameters that best fit karyotype data from single-cell sequencing, we used approximate Bayesian computation to infer mis-segregation rates and karyotype selection. Experimental validation confirmed the extensive chromosome mis-segregation rates caused by the chemotherapy paclitaxel (18.5 ± 0.5/division). Extending this approach to clinical samples revealed that inferred rates fell within direct observations of cancer cell lines. This work provides the necessary framework to quantify CIN in human tumors and develop it as a predictive biomarker. Editor's evaluation The authors have developed a framework to quantify rates of chromosomal instability (CIN) in human tumors by fitting karyotype distributions inferred from low-depth DNA-sequencing to in silico models of CIN with karyotype selection pressures, sweeping through parameter space. This is particularly useful for the development of biomarkers for CIN, which is associated with cancer metastasis and drug resistance. https://doi.org/10.7554/eLife.69799.sa0 Decision letter Reviews on Sciety eLife's review process eLife digest DNA contains all the information that cells need to function. The DNA inside cells is housed in structures called chromosomes, and most healthy human cells contain 23 pairs. When a cell divides, all chromosomes are copied so that each new cell gets a complete set. However, sometimes the process of separating chromosomes is faulty, and new cells may get incorrect numbers of chromosomes during cell division. Cancer cells frequently exhibit this behavior, which is called chromosomal instability', or CIN. Chromosomal instability affects many cancer cells with varying severity. In cancers with high chromosomal instability, the number of chromosomes may change almost every time the cells divide. These cancers are often the most aggressive and difficult to treat. Scientists can estimate chromosomal instability by counting differences in the number of chromosomes across many cells. However, many cells that are missing chromosomes die, resulting in inaccurate measures of chromosomal instability. To find a solution to this problem, Lynch et al. counted chromosomes in human cells with different levels of chromosomal instability and created a computer model to work out the relationship between chromosomal instability and chromosome number. The model could account for both living and dead cells, which gave more accurate results. Lynch et al. then confirmed the accuracy of their approach by using it on a group of cells treated with a chemotherapy drug that causes a known level of chromosomal instability. They also used existing data from breast and bowel cancer, which revealed that levels of chromosomal instability varied between one mistake per three to twenty cell divisions. Lower levels of chromosomal instability can be linked to a better prognosis for cancer patients, but it currently cannot be measured reliably. These results may help to reveal the causes of chromosomal instability and the role it has in cancer. If this method is successfully applied to patient samples, it could also improve our ability to predict how each cancer will progress and may lead to better treatments. Introduction Chromosomal instability (CIN) is characterized by persistent whole-chromosome gain and loss through mis-segregation during cell division. Genome instability is a hallmark of cancer (Hanahan and Weinberg, 2011) and one type, CIN, is the principal driver of aneuploidy, a feature of ~80% of solid tumors (Hancock et al., 2004; Knouse et al., 2017; Weaver and Cleveland, 2006). CIN potentiates tumorigenesis (Foijer et al., 2017; Levine et al., 2017; Silk et al., 2013) and associates with therapeutic resistance (Ippolito et al., 2020; Lee et al., 2011; Lukow et al., 2020; Pavelka et al., 2010), metastasis (Bakhoum et al., 2018) and poor survival outcomes (Bakhoum et al., 2011; Denu et al., 2016; Jamal-Hanjani et al., 2017). Thus, CIN is an important characteristic of cancer biology. Despite its importance, CIN has not emerged as a clinical biomarker, in part because it is challenging to quantify. Although CIN has classically been characterized as binary—tumors either have it or not—recent evidence highlights the importance of the rate of chromosome mis-segregation and the specific aneuploidies it produces. For example, clinical outcomes partially depend on aneuploidy of specific chromosomes (Davoli et al., 2013; Sheltzer et al., 2017; Vasudevan et al., 2020). Further, higher levels of CIN suppress tumor growth when they surpass a critical threshold, thought to be due to lethal loss of essential genes and irregular expression due to imbalanced gene dosage (Funk et al., 2021; Silk et al., 2013; Weaver and Cleveland, 2008; Zasadil et al., 2014). Moreover, baseline CIN may predict chemotherapeutic response to paclitaxel (Janssen et al., 2009; Swanton et al., 2009) and is proposed to both promote detection by or evasion from the immune system (Davoli et al., 2017; Santaguida et al., 2017). No single or standardized analytically valid measure of CIN has emerged and this gap has precluded its clinical validation as a prognostic or predictive biomarker. Prior measures of CIN use various means to compare levels in tumors or populations, but do not establish a standardized quantitative rate. These prior measures include histologic analysis of mitotic defects (Bakhoum et al., 2011; Jin et al., 2020), fluorescence in situ hybridization (FISH) with probes to detect individual chromosomes (Thompson and Compton, 2008), and gene-expression methodologies like CIN scores (Carter et al., 2006). While these methods are readily accessible, they have significant drawbacks for clinical application. FISH and mitotic visualization approaches are laborious. Direct visualization of mitotic defects to measure CIN is only possible in the most proliferative tumors where enough cells are captured in short-lived mitosis. FISH typically quantifies only a subset of chromosomes, which will be misleading if there is bias toward specific chromosome gains/losses (Dumont et al., 2020). While gene expression scores are proposed as indirect measures of CIN, they are not specific to CIN and correlate highly with proliferation and structural aneuploidy (Carter et al., 2006; Sheltzer, 2013). Single-cell sequencing promises major advances in quantitative measures of CIN by displaying cell-cell variation for each chromosome across hundreds of cells (Navin et al., 2011; Wang et al., 2014). However, selection poses another complication. To date, single-cell analyses have identified surprisingly low cell-cell karyotype variation, even when mitotic errors are directly observed by microscopy (Bolhaqueiro et al., 2019; Gao et al., 2016; Kim et al., 2018; Nelson et al., 2020; Wang et al., 2014). These observations highlight the confounding role of selection against aneuploid karyotypes in measuring CIN in human tumors. Indeed, selection reduces karyotype variance in cancer cell populations that directly exhibit mitotic errors (Gerstung et al., 2020; Ippolito et al., 2020; Lukow et al., 2020). Here, we seek to overcome gap by modeling chromosomal instability and explicitly considering the evolutionary selection of aneuploid cells, to derive a quantitative measure. We describe a quantitative framework to measure CIN by sampling population structure and cell-cell karyotypic variance in human tumors, accounting for selection on aneuploid karyotypes. We built our framework on the use of phylogenetic topology measures to quantify underlying evolutionary processes (Mooers and Heard, 1997); in this case to quantify CIN from both the diversity and the aneuploid phylogeny within a tumor. Using an agent-based model of CIN, we determine how distinct types and degrees of selective pressure shape the karyotype distribution and population structure of tumor cells at different rates of chromosome mis-segregation. We then use this in silico model as a foundation for parameter inference to provide a quantitative estimate of CIN as the numerical rate of chromosome mis-segregation per cell division. We apply this model to quantify CIN caused by the chemotherapeutic paclitaxel in culture. Next, using existing single-cell whole-genome sequencing data (scDNAseq), we measure CIN in cancer biopsy and organoid samples. As a whole, this work provides a framework to quantify CIN in human tumors, a first step toward developing CIN as a prognostic and predictive biomarker. Results A framework for modeling CIN and karyotype selection To assess intratumoral CIN via cell-cell karyotype heterogeneity, we considered how selection on aneuploid karyotypes impacts observed chromosomal heterogeneity within a tumor. By modeling fitness of aneuploid cells, we observe chromosomal variation in a population of surviving cells. The selective pressure of diverse and specific aneuploidies on human cells has not been, to our knowledge, directly measured. Therefore, we employ previously developed models of selection. In models of CIN, fit karyotypes are selected while unfit aneuploid karyotypes are eliminated over time (Ippolito et al., 2020; Ravichandran et al., 2018; Sheltzer et al., 2017; Vasudevan et al., 2020). We use two previously proposed models of aneuploidy-associated cellular fitness, as well as hybrid and neutral selection models. The Gene Abundance model is based on the relatively low incidence of aneuploidy in normal tissues and assumes cellular fitness declines as the cell's karyotype diverges from a balanced euploid karyotype (Sheltzer and Amon, 2011; Zhu et al., 2012). When an individual chromosome diverges from euploid balance (2 N, 3 N, 4 N, for example), its contribution to cellular fitness is weighted by its abundance of genes (Figure 1—figure supplement 1A, left). Alternatively, the Driver Density model assumes that each chromosome's contribution to cellular fitness is weighted by its ratio of Tumor suppressor genes, Oncogenes, and Essential genes (TOEs)(Davoli et al., 2013; Laughney et al., 2015). For example, Driver Density selection will favor loss of chromosomes with many tumor suppressors and favor gain of chromosomes replete with oncogenes and essential genes (Figure 1—figure supplement 1A, right). The hybrid averaged model accounts for both karyotypic balance and TOE densities (Figure 1—figure supplement 1A, middle). Using these fitness models, we assigned chromosome scores to reflect each chromosome's value to cellular fitness (Figure 1—figure supplement 1B, Table 1), the sum of which represent the total fitness value for the cell, relative to a value of 1 for a euploid cell. Further, we scaled the impact of cell fitness with a scaling factor, S, ranging from 0 (no selection) to 100 (high selection). While these models are approximations, they are nevertheless useful to estimate how mis-segregation and selective pressure cooperate to mold karyotypes in the cell population. Table 1 Base chromosome-specific fitness scores for individual models. Selection modelCHR ARMGene AbundanceDriver DensityHybrid1p0.04780162–0.00240180.022699921q0.043403210.032443620.037923412p0.027336550.029357170.028346862q0.042440540.039432670.04093663p0.023104120.032896950.028000533q0.02997560.054167360.042071484p0.012381950.017849090.015115524q0.031817960.029013240.03041565p0.011784430.042811660.027298055q0.037876150.019499340.028687756p0.025577190.023986190.024781696q0.025543990.000116250.012830127p0.01795880.098892840.058425827q0.032315890.069333140.050824518p0.015917280.027695640.021806468q0.02549420.058614270.042054239p0.01301266–0.00129410.005859299q0.025726570.047026810.0363766910 p0.0112201–0.0364218–0.012600810q0.027502530.011426880.0194647111 p0.019618580.038186210.028902411q0.036299360.018987840.027643612 p0.01425750.05515510.034706312q0.036598120.062737860.0496679913 p00013q0.02333649–0.01015390.0065912814 p1.66E-0508.30E-0614q0.037925940.025574390.0317501615 p00015q0.037013060.02065660.0288348316 p0.023834420.043347360.0335908916q0.01900446–0.00714440.0059300517 p0.01548573–0.00859750.0034441417q0.035535860.043634740.039585318 p0.006273960.005336970.0058054718q0.01434049–0.0263632–0.006011319 p0.021593720.053714160.0376539419q0.028133250.005503380.0168183120 p0.00896280.043510250.0262365320q0.015269960.049935930.0326029521 p0.0023236900.0011618521q0.01233215–0.00330920.0045114722 p0.0001327806.64E-0522q0.02297134–0.00515810.0089066Xp0.0155521300.00777606Xp0.0249962700.01249813 We employed these selection models in an agent-based model of exponential population growth wherein each cell has its own karyotype (Figure 1 and Figure 1—figure supplement 1). Briefly, simulations started with 100 euploid cells and were run in discrete time steps with variable rates of selective pressure, S, and rates of chromosome mis-segregation (Pmisseg, see definitions in Table 2). The rate—or probability—of mis-segregation events, Pmisseg, is the measure of CIN. During each time step, cells have a Pdivision ( = 0.5 for euploid) chance of dividing. Each dividing cell has a Pmisseg chance of improper segregation of each chromosome. Segmental chromosome breaks occur with a probability Pbreak, set at 0 or 0.5. After division, fitness (F) of each daughter is assessed. Cells are removed from the population if any given chromosome has copy number 0 or >6. The Pdivision value of the remaining viable cells is adjusted by the cell's fitness under selection (FS). Due to computational limitations, pseudo-Moran or Wright-Fisher models are employed to limit the modeled cell population (Figure 1—figure supplement 1C, D). These limits did not significantly affect the measures extracted from these populations (Figure 1—figure supplement 2). Thus, these models simulate an evolving population of aneuploid cells under given rates of CIN, Pmisseg, and models and strength of selection. Table 2 Parameters varied during agent-based modeling. ParameterDescriptionPmissegProbability of mis-segregation per chromosome per divisionPbreakProbability of chromosome breakage after mis-segregationPdivisionProbability of cellular division per time stepSMagnitude of selective pressure on aneuploid karyotypes Figure 1 with 2 supplements see all Download asset Open asset A framework for modeling CIN and karyotype selection. (A) Chromosome arm scores for each model of karyotype selection. Gene Abundance scores are derived from the number of genes per chromosome arm normalized to the number of all genes. Chromosome arms 13 p and 15 p did not have an abundance score and were set to 0. Driver Density scores come from the pan-cancer chromosome arm scores derived in Davoli et al., 2013, and normalized to the sum of chromosome arm scores for chromosomes 1-22,X. Chromosome arms 13 p, 14 p, 15 p, 21 p, 22 p, and chromosome X did not have driver scores and were set to 0. Hybrid model scores are set to the average of the Driver and Abundance models. The neutral model (not displayed) is performed with all cell's fitness constitutively equal to 1 regardless of karyotype. (B) Framework for the simulation of and selection on cellular populations with CIN. Cells divide (Pdivision starts at 0.5 in the exponential pseudo-Moran model and is constitutively equal to 1 for the constant Wright-Fisher model) and probabilistically mis-segregate chromosomes (Pmisseg ∈ [0, 0.001… 0.05]). After, cells experience selection under one of the selection models, altering cellular fitness and the probability (Pdivision) a cell will divide again (green check). Additionally, cells wherein the copy number of any chromosome falls to zero or surpasses 6 are removed (red x). After this, the cycle repeats. See Materials and methods for further details. Evolutionary dynamics is imparted by CIN To understand the interplay between CIN and selection, we simulated 100 steps of cell growth with CIN under each selection model. We varied the rate of CIN (Pmisseg,c ∈[0, 0.001… 0.05] per chromosome; or 0–2.3 chromosome mis-segregations per division) and selective pressure ranging from none to heavy selection (S ∈[0, 2… 100]). As expected, the simulated cell number increases rapidly to the pseudo-Moran cap of 3000, where it remains (Figure 2A). As displayed in Figure 2B, diversity of the cell population, expressed as mean karyotypic variance increases over time, but also depends on mis-segregation rate, and selection levels (Figure 2B). As expected, high mis-segregation rates (Pmisseg, Y axis) and low selection (S = 0; top row) enhance the variance of the population. Further, without selection (S = 0; top row) all models returned comparable profiles over time, resembling neutral selection. However, when selective pressure is applied (S > 0), the distinct profiles appear. The abundance model (first column) negatively selects against all aneuploid karyotypes and yields low heterogeneity that increases modestly with mis-segregation rate. With the Driver model (second column), there is a sharp increase in heterogeneity even at low mis-segregation rates, as this model favors specific aneuploid states that maximizes oncogenes and minimizes tumor suppressors. The Hybrid model falls between the other two. Results were not specific to the pseudo-Moran process of capping at 3000 cells—dynamics were similar in the constant-population Wright-Fisher model (Figure 2—figure supplement 1A, B). These data illustrate how CIN and selection operate together to shape the karyotype diversity in the cell population. Figure 2 with 2 supplements see all Download asset Open asset Evolutionary dynamics imparted by CIN. (A) Population growth curve in the absence of selective pressure (Pmisseg = 0.001, S = 0, n = 3 simulations). The steady state population in null selection conditions is 3000 cells. (B) Heatmaps depicting dynamics of karyotype diversity as a function of time (steps), mis-segregation rate (Pmisseg), and selection (S) under each model of selection. Columns represent the same model; rows represent the same selection level. Mean karyotype diversity (MKV) is measured as the variance of each chromosome averaged across all chromosomes 1–22, and chromosome X. Low and high MKV are shown in white and blue respectively (n = 3 simulations for every combination of parameters). (C) Population growth under each model, varying Pmisseg and S. Pmisseg∈ [0.001, 0.022, 0.050] translate to about 0.046, 1, and 2.3 mis-segregations per division respectively for diploid cells. (D) Dynamics of the average ploidy (total # chromosome arms / 46) of a population while varying Pmisseg and S. (E) Dynamics of ploidy under each model for diploid and tetraploid founding populations. Pmisseg∈ [0.01, 0.02] translate to about 0.46 and 0.92 mis-segregations for diploid cells and 0.92 and 1.84 mis-segregations for tetraploid cells. (F) Fitness (FS) over time for diploid and tetraploid founding populations evolved under each model. (G) Karyotype diversity dynamics for diploid and tetraploid founding populations. MKV is normalized to the mean ploidy of the population at each time step. Plotted lines in C-G are local regressions of n = 3 simulations. High levels of selection against aneuploid cells are expected to impede cell growth. To visualize this, we quantified the population of viable cells with distinct models (Figure 2C). As expected with the Abundance model at S = 10 and S = 100, cells proliferated more slowly with higher rates of mis-segregation. By contrast, the Driver model saw no growth defect as they favored specific aneuploid states that are easily reached with missegregation. As before, the Hybrid model, is intermediate, and findings are not impacted by pseudo-Moran or Wright-Fisher restrictions on cell number (Figure 2—figure supplement 1C). To further assess model we of average cellular number of chromosomes by In many the mean ploidy of the populations to increase over time (Figure Figure 2—figure supplement particularly in the absence of selection (S = 0; This is due to a higher to chromosome in our model cells with or any chromosome the is With selection (S = S = 100 the models In the abundance model, populations With the Driver model, the average ploidy increases more rapidly due to aneuploidy states that favor high oncogenes and low tumor with computational models built on chromosome-specific driver densities (Davoli et al., 2013; Laughney et al., 2015). the Hybrid model, ploidy increases are with the constant-population Wright-Fisher model (Figure 2—figure supplement In selection and mis-segregation cooperate to shape the aneuploid karyotypes cell proliferation and average ploidy in a population of cells, or a human tumor. Further, sampling karyotypes in a cell population not direct of mis-segregation rates, as their diversity is by other as selective pressure, selection and In tumors, in tumor relative to other copy number et al., 2018; et al., 2020). Genome is for example, by by or by cell-cell Genome against loss of chromosomes and favors aneuploidy. To determine how impacts in our model, we diploid and tetraploid (Figure and to toward the state as observed in many human cancers (Carter et al., this is to a with the Abundance and Hybrid models. with diploid cells, against the of cellular fitness in the Abundance model, similar levels of diversity over time (Figure and this is more when Pmisseg = in Pmisseg = in to the number of chromosome mis-segregations per division. This is with the that as an a karyotype that is in many cancers et al., 2018; et al., 2020). By contrast, in the Driver model, did not provide a selective to tumors (Figure fitness, karyotype and ploidy increases were with a Wright-Fisher model of population growth (Figure 2—figure supplement Figure 2—figure supplement 2). the agent-based model expected of tumor to our model. Further, they illustrate the of mis-segregation rates directly from variation in karyotypes in human cancer. this model provides a framework to selection to measure CIN through quantitative inference from the observed as we will karyotype diversity depends on selection measures of CIN are derived from karyotype diversity in the population. our model that selection pressure will shape this diversity. To further understand the of karyotype diversity under selection, we their they exhibit and populations simulated under each model on a karyotype. We simulated diploid and tetraploid populations for 3000 time steps at a mis-segregation rate, in an for of chromosome arms (Pmisseg = = (Bakhoum et al., 2009; et al., 2019; Weaver et al., and S ∈ (Figure We karyotypes of cells from the population. As expected, population diversity is under the Abundance model (Figure after 3000 time only a number of and ( 13 as they no fitness in this model. Moreover, the karyotype average of cells across a diploid karyotype (Figure 1), that the Abundance model provides selection the euploid karyotype. In populations simulated under this model with selection (S = a level of karyotype diversity and fitness while with the selection (S = a time to this and have similar levels of karyotype diversity and fitness as the other models (Figure supplement 1). To identify any that may affect these we performed the same simulation using of our model. We this steady state to be for tetraploid cells as well as when we the ploidy from = 6 to an = when we a fitness for all cells with a and when we simulated populations under the Wright-Fisher model (Figure rows Figure 3 with 1 supplement see all Download asset Open asset Karyotype diversity depends on selection (A) to assess dynamics of karyotype and karyotype (B) Heatmaps depicting the chromosome copy number profiles of a subset (n = out of of the simulated population with CIN over time under each model of karyotype selection. (C) the average copy number across the for the the model with the copy number limit set to the model that a for any cell with a and the Wright-Fisher model. Pmisseg = S = model; S = ploidy = The Driver Density and Hybrid models more diversity (Figure but nevertheless by (Figure supplement 1). selection there is high diversity and no over these a high on the model of selection. However, the models are not highly on ploidy or on selection of or Wright-Fisher of cell populations are by the model of karyotype selection for a given Pmisseg, but relatively to other of the model. This our approach of varying only the selection model, the of selection and Pmisseg to infer parameters from data via phylogenetic topology and Bayesian of simulated CIN rate and karyotype selection a model of diversity and selective pressures, we to infer Pmisseg as a measure of CIN from an observed population of cells. provide evolutionary processes of and selection. Moreover, the topology of the phylogenetic has been used as a quantitative measure of the underlying evolutionary processes and 2018; and et al., et al., et al., 2020). Here, chromosome mis-segregation to karyotype heterogeneity, and the population of cells is then by selection. To this, we use chromosome copy phylogenetic rates are not high enough in tumors to infer cellular particularly with are from simulated and populations, the can be These include that a direct with three (Figure Additionally, we considered a of the which measures the or of the To understand how these measures are by selection in simulated populations, we from cells from each population simulated with a of selective at time steps under Hybrid Figure As aneuploidy and mean karyotypic variance (MKV) with selective pressure, a that is at high mis-segregation rates (Figure By contrast, increase with mis-segregation rate
Source: eLife
Language: English
Subfield: Cell Biology
Domain: Life Sciences
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