Heritable tumor cell division rate heterogeneity induces clonal dominance

<div><p>Tumors consist of a hierarchical population of cells that differ in their phenotype and genotype. This hierarchical organization of cells means that a few clones (i.e., cells and several generations of offspring) are abundant while most are rare, which is called <i>clonal dominance</i>. Such dominance also occurred in published <i>in vitro</i> iterated growth and passage experiments with tumor cells in which genetic barcodes were used for lineage tracing. A potential source for such heterogeneity is that dominant clones derive from cancer stem cells with an unlimited self-renewal capacity. Furthermore, ongoing evolution and selection within the growing population may also induce clonal dominance. To understand how clonal dominance developed in the iterated growth and passage experiments, we built a computational model that accurately simulates these experiments. The model simulations reproduced the clonal dominance that developed in <i>in vitro</i> iterated growth and passage experiments when the division rates vary between cells, due to a combination of initial variation and of ongoing mutational processes. In contrast, the experimental results can neither be reproduced with a model that considers random growth and passage, nor with a model based on cancer stem cells. Altogether, our model suggests that <i>in vitro</i> clonal dominance develops due to selection of fast-dividing clones.</p></div

Parameters of the stochastic growth and passage models.

<p>Parameters of the stochastic growth and passage models.</p

ABM simulations match the limited clonal dominance development for the monoclonal K562 cell line.

<p><b>A</b>–<b>B</b> Maximum Likelihood estimator (<i>ℓ</i>) based on clone loss (<b>A</b>) or Gini coefficient (<b>B</b>), for a range of initial division rate SDs () and mutation SDs (). <b>C</b>–<b>D</b> Clone loss (<b>C</b>) and clonal dominance (<b>D</b>) in simulations, with the parameters from the red rectangle in <b>B</b>, and in the experiments with monoclonal K562 cells. All simulation results are the mean of 10 runs and the results for the monoclonal K562 cells are the mean of 3 replicates, with the error bars representing the SD.</p

ABM simulations describing evolution of division rate variability match results for polyclonal K562 cell line.

<p><b>A</b>–<b>B</b> Maximum Likelihood estimator (<i>ℓ</i>) based on the percentage of clones lost (<b>A</b>), on the Gini coefficient (<b>B</b>), and on both metrics (<b>C</b>) for a range of initial division rate SDs () and mutation SDs (). Note that we plot −<i>ℓ</i> in these plots and thus its minimum value is sought. <b>D</b>–<b>E</b> comparison of clone loss (<b>D</b>) and clonal dominance (<b>E</b>) observed in simulations with the best fitting parameter values for the Gini coefficient (red rectangle in <b>B</b>) and in the experiments with polyclonal K562 cells. <b>F</b> Comparison of the number of major clones, i.e. clones representing more than 1% of the population, developing in simulations with the parameter set highlighted by the red rectangle in <b>B</b> and in the experiments with polyclonal K562 cells. <b>G</b> Evolution of the mean division rate with the best fitting parameter values for the Gini coefficient. All simulation results are the mean of 10 simulations and the results for the polyclonal K562 cells are the mean of 3 replicates, with the error bars or colored areas representing the SD.</p

The ABM that describes evolution of division rate variability induces clone loss and clonal dominance.

<p><b>A</b>–<b>B</b> Clone loss (<b>A</b>) and Gini coefficient (<b>B</b>) for a range of initial division rate SDs () and mutation SDs (), with all other parameters as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005954#pcbi.1005954.t001" target="_blank">Table 1</a> and all data points representing the mean for 10 simulations.</p

Simulations with CSC model result in massive clone loss and no development of clonal dominance.

<p><b>A</b> Scheme illustrating the divisions and cell death in the CSC growth model. <b>B</b> Heatmap showing the difference between <i>in vitro</i> and simulated population doubling time (19 hours) depending on the maximum number of DC divisions (<i>M</i>) and DC division rates (<i>r</i>_DC) in the CSC growth model. The white cross denotes the default model settings and the black crosses depict several alternative parameter sets that result in a similar population doubling time. <b>C</b>–<b>D</b> Clone loss (<b>C</b>) and Gini coefficient (<b>D</b>) for the parameter sets highlighted in <b>B</b> and all other parameters as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005954#pcbi.1005954.t001" target="_blank">Table 1</a>. <b>E</b>–<b>F</b> Effect of symmetric CSC division probability (<i>p₁</i>) and initial CSC percentage (CSC₀) on clone loss (<b>E</b>) and Gini coefficient (<b>F</b>), with all other parameters as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005954#pcbi.1005954.t001" target="_blank">Table 1</a>. All values are the mean of 10 simulation replicates with the error bars depicting the SD.</p

Clonal dominance does not develop during passaging of cells that divide at a fixed rate.

<p><b>A</b>–<b>B</b> Clone loss (<b>A</b>) and Gini coefficient (<b>B</b>) during iterated growth and passage with either deterministic or stochastic growth and initialized either with a uniform clone size distribution or the initial distribution for polyclonal K562 cells. All values are the mean of 10 simulations and the error bars represent the SD. <b>C</b> histogram of the initial clone sizes of polyclonal K562 cells.</p

Setup and results of the <i>in vitro</i> iterated growth and passage experiment previously described by Porter <i>et al</i>. [13].

<p><b>A</b> Experimental setup. <b>B</b>–<b>E</b> Development of the clone size distribution of polyclonal K562 cells, as obtained from our own analysis of the FASTQ files published by Porter <i>et al</i>. [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005954#pcbi.1005954.ref013" target="_blank">13</a>]. Shown are the percentage of clones that remain after each passage (<b>B</b>), the percentage of clones versus the percentage of the population taken up by those clones (<b>C</b>, mean ± SD and 3 biological replicates shown) and the Gini coefficient (<b>E</b>; ratio of areas X and Y in <b>D</b>). <b>F</b> Clone loss (left) and Gini coefficient (right) for the <i>in vitro</i> experiments with the monoclonal K562 cell line. <b>G</b> Clone loss (left) and Gini coefficient (right) for the <i>in vitro</i> experiments with HeLa cells. All error bars depict the SD of the 3 replicates.</p

Effects of reducing tip cell chemoattractant sensitivity for varying NICD thresholds.

<p>Morphospace of the final morphologies (10 000 MCS) with varying tip cell chemoattractant sensitivities (<i>χ</i>(tip)) and NICD thresholds (Θ_NICD).</p

Comparison of networks formed with mixed cells and cells with average properties.

<p><b>A</b>, <b>F</b>, and <b>K</b> morphologies for mixed tip (red) and stalk (gray) cells (<i>F</i>_tip = 0.5). <b>B</b>, <b>G</b>, and <b>L</b> morphologies for averaged cells (<i>F</i>_tip = 0.5). <b>C</b>-<b>E</b>, <b>H</b>-<b>J</b>, and <b>M</b>-<b>O</b> morphometrics for a range of tip cell fractions for both the control and mixed model. The morphometrics were calculated for 50 simulations at 10 000 MCS (error bars represent the standard deviation). p-values were obtained with a Welch’s t-test for the null hypothesis that the mean of mixed model and the control model are identical.</p