Quantifying intrinsic and extrinsic control of single-cell fates in cancer and stem/progenitor cell pedigrees with competing risks analysis

Abstract

The molecular control of cell fate and behaviour is a central theme in biology. Inherent heterogeneity within cell populations requires that control of cell fate is studied at the single-cell level. Time-lapse imaging and single-cell tracking are powerful technologies for acquiring cell lifetime data, allowing quantification of how cell-intrinsic and extrinsic factors control single-cell fates over time. However, cell lifetime data contain complex features. Competing cell fates, censoring, and the possible inter-dependence of competing fates, currently present challenges to modelling cell lifetime data. Thus far such features are largely ignored, resulting in loss of data and introducing a source of bias. Here we show that competing risks and concordance statistics, previously applied to clinical data and the study of genetic influences on life events in twins, respectively, can be used to quantify intrinsic and extrinsic control of single-cell fates. Using these statistics we demonstrate that 1) breast cancer cell fate after chemotherapy is dependent on p53 genotype; 2) granulocyte macrophage progenitors and their differentiated progeny have concordant fates; and 3) cytokines promote self-renewal of cardiac mesenchymal stem cells by symmetric divisions. Therefore, competing risks and concordance statistics provide a robust and unbiased approach for evaluating hypotheses at the single-cell level.

Figure 1. Single-cell tracking generates cell lifetime data that are visualized as single-cell pedigrees.

(a) Stylised cartoon of a single cell pedigree showing the fate and time of fate for each cell (right censored, lost, division, death, differentiation, etc.), kinship relationships, and generation numbers. Measurements of a cell’s internal molecular state, morphological appearance, as well as other lifetime events such as cell-cell contact may be recorded within a single cell pedigree. Establishment of kinship relationships within a single cell pedigree provides unique access to study the influence of inheritance on cell fate outcomes. (b) Cell lifetime data from the pedigree shown in (a), depicted in table format. Note: only sibling cell clusters are shown in the table. (c) Example of heterogeneous fate outcomes and right censoring that is inherent within single cell pedigrees. The green and red boxes demarcate observed and right censored fates. Lost cells are also considered to be right censored because their final fate is not observed. The two pedigrees on the left of the grey dotted line exemplify symmetric fate outcomes in siblings, i.e. the pair of daughter cells produced by the first division in each pedigree divide at the same time. The two pedigrees on the right of the grey dotted line exemplify asymmetric fate outcomes in siblings, i.e. the pair of daughter cells produced by the first division in each pedigree have discordant fates as a result of right censoring and competing fate outcomes. Importantly, if censored lifetimes and discordant fates are discarded from cell lifetime analysis (i.e. only pedigrees on the left of the grey dotted line would be included) then conclusions are biased towards symmetric fates and shorter cell lifetimes.

Figure 2. Bivariate plots and histograms demonstrating that pre-competition probability distributions (bivariate plots) cannot be identified from post-competition distributions for division and death (histograms).

In (a,b) pre-competition distributions show varying degrees of correlation (rho = 0.39 and rho = 0.96, respectively) while observed division and death distributions remain unaffected. (c) Competing risks analysis of time to division and death for the distributions shown in (a,b). Dotted lines represent 95% confidence intervals. Note that there is no dependence on the correlation coefficient (rho). (d) Kaplan-Meier analysis of time to division and death for the distributions shown in (a,b). Note that the probability of death and division is over estimated, and there appears to be dependence on the value of the correlation coefficient.

Figure 3. Effect of chemotherapy on division and death of WT (pooled BT474 and MCF7 cell lines) and MUT (pooled MDA-MB231 and T47D cell lines) BC cells treated with Dox or Nut.

(a) Pie-charts showing the distribution of fate outcomes (division, death, right censored) in control and dox treated WT and MUT BC cells. (b) Mean cycle time in control and dox treated WT and MUT BC cells. Right censored lifetimes are not included in calculation of mean cycle time. **Indicates p < 0.001 and n.s. is not significant. (c) Non-parametric (dashed lines) and semi-parametric (solid lines) CIF for division probability in WT (green), MUT (black), MUT + Nut (light pink), WT + Dox (blue), WT + Nut (red), and MUT + dox (pink). (b) Non-parametric (dashed lines) and semi-parametric (solid lines) CIF for death probability in WT (green), MUT (black), MUT + Nut (light pink), WT + Dox (blue), WT + Nut (red), and MUT + Dox (pink). (d) The estimated coefficients for semi-parametric models are shown in Supplementary Table S3. All data analysed are from pooled observations from replicate wells for each condition (N = 853 cells).

Figure 4. CR regression and concordance analysis of division, death, and differentiation in GMPs treated with hematopoietic cytokines.

(a) Simulated CIFs for division for GFP- cells (black) treated with MCSF or GCSF, GFP+ cells treated with MCSF (green), and GFP+ cells treated with GCSF (red). Dashed lines show standard error (SE). (b) Simulated CIF for death for GFP- cells (black), treated with MCSF or GCSF, GFP+ cells treated with MCSF (green), and GFP+ cells treated with GCSF (red). Dashed lines show SE. (c) Division concordance probability for GFP- siblings (black), parent-child (green), 1^st cousins (red), and 2^nd cousins (blue). Dashed lines are 95% confidence intervals (CI). (d) Division concordance probability for GFP+ siblings (black), parent-child (green), 1^st cousins (red), and 2^nd cousins (blue). (e) Histogram showing the number of cells that transition from GFP- to GFP+ in each generation (MCSF and GCSF pooled data). (f) Concordance probability for onset of GFP expression after MCSF treatment for siblings (black), 1^st cousins (red), and 2^nd cousins (blue). Dashed lines are 95% CI. (g) Histograms showing the proportion of concordant, discordant, and censored fate outcomes in mother-daughter (MD), sibling (S), 1^st cousin (C1), and 2^nd cousin (C2) kinship clusters. (h) The percentage of cell lifetime data used by statistical tests for quantifying association in cell fate (averaged over all kinship clusters). CRR models and COR are shown in Table 2.

Figure 5. The effect of cytokines and PDGFRα expression on probability of division, death, and self-renewal of cCFU-F.

(a) Overlaid phase contrast and fluorescence (GFP) image of Pdgfra-GFP cCFU-F showing heterogeneity in morphology and GFP expression. *and **indicate GFP⁺ and GFP⁻ spindle-shaped cells, respectively. ***Indicates a GFP⁻ cell with a myofibroblast morphology. (b) CIF (solid lines) for division (generation 0) given TGFβ1 (green), bFGF (blue), PDGF(red), all three factors (black), or no factors (grey). Dashed lines show standard errors (SE). (c) Histogram showing variation in Pdgfra-GFP intensity, and threshold limit used to classify GFP⁺ and GFP⁻ cells. (d) Simulated CIF (solid lines) for division (generation > 0) of GFP⁺ cells with PDGF (green), GFP⁺ without PDGF (blue), GFP⁻ cells with PDGF (red), and GFP⁻ cells without PDGF (black). Dashed lines show SE. (e) Pie-charts showing the frequency of observed fate outcomes for GFP⁺ and GFP⁻ cells. (f) Simulated CIF (solid lines) for GFP⁺ divisions (green) vs GFP⁻ divisions (black). Dashed green and red lines are 95% confidence intervals (CI). (g) Pie-chart showing inheritance of GFP. GFP⁺ mothers give rise to a majority of GFP⁺ and a minority of GFP⁻ daughter cells, while GFP⁻ mothers equally give rise to GFP⁻ and GFP⁺ cells. (h) Simulated CIF (solid line) showing that GFP⁺ mothers give rise to a majority of GFP⁺ and a minority of GFP⁻ daughters. Dashed lines are 95% CI. All data analysed are from pooled observations from replicate wells for each condition (N = 1316 cells).

Figure 6. Symmetry in cCFU-F sibling cell fate outcomes.

(a) Illustration of symmetric GFP⁺ division. (b) Relative proportion of discordant, concordant, and right-censored fates for cCFU-F sibling pairs. Q is Yule’s Q estimate of association in fate. ICC is the intraclass correlation coefficient, numbers in brackets are 95% CI. (c) PCC in sibling cell divisions, GFP⁺ pairs (green), GFP⁻ pairs (blue). r is Pearson’s correlation coefficient and numbers in brackets are 95% CI. For all cells N = 84 pairs, and for GFP⁺ cells N = 51 pairs. (d) Distribution of the mean difference between 10,000 random permutations of cell pairs for all cells (left) and GFP⁺ pairs (right). μ and SD represent the mean and standard deviation of the randomly generated distributions, respectively. The observed mean difference in cell cycle for all siblings was 8.59 hr. The observed mean difference in cell cycle for GFP⁺ pairs was 7.17 hr. In both groups the observed mean difference was significantly shorter than the mean difference between randomly sampled cell pairs. (e) Probandwise concordance (black), showing the conditional probability of a GFP⁺ division for sibling 1 given a GFP⁺ division for sibling 2 had occurred (black dashed line, 95% CI). The unconditional probability of a GFP⁺ division (red solid line) is much lower. +/− indicates SD. All data analysed are from pooled observations from replicate wells for each condition (N = 1316 cells).