Evidence that the human cell cycle is a series of uncoupled, memoryless phases

Abstract

The cell cycle is canonically described as a series of four consecutive phases: G1, S, G2, and M. In single cells, the duration of each phase varies, but the quantitative laws that govern phase durations are not well understood. Using time-lapse microscopy, we found that each phase duration follows an Erlang distribution and is statistically independent from other phases. We challenged this observation by perturbing phase durations through oncogene activation, inhibition of DNA synthesis, reduced temperature, and DNA damage. Despite large changes in durations in cell populations, phase durations remained uncoupled in individual cells. These results suggested that the independence of phase durations may arise from a large number of molecular factors that each exerts a minor influence on the rate of cell cycle progression. We tested this model by experimentally forcing phase coupling through inhibition of cyclin-dependent kinase 2 (CDK2) or overexpression of cyclin D. Our work provides an explanation for the historical observation that phase durations are both inherited and independent and suggests how cell cycle progression may be altered in disease states.

Keywords: Erlang model; cell cycle; cell‐to‐cell variability; computational systems biology; single‐cell dynamics.

Figure 1. Variation and lack of correlation among cell cycle phase durations in single human cells

1. Diagram of the cell cycle composed of G1, S, G2, and M phases (not to scale). Phase durations were quantified by time‐lapse fluorescence microscopy using a PCNA‐mCherry reporter to identify four discrete events during the lifetime of an individual cell (see main text and Materials and Methods). Images were acquired every 10 min.

2. Mean phase durations in RPE, U2OS, and H9 cell lines. Error bars represent standard deviations.

3. Coefficient of variation (CV) of phase durations.

4. Percentage of the total variation in cell cycle duration contributed by individual phases.

5. Correlations between individual cell cycle phase durations.

Data information: Sample sizes were adequate to detect correlations (see Materials and Methods). n = 125 (RPE), 130 (U2OS), 113 (H9). R ², square of Pearson correlation coefficient.Source data are available online for this figure.

Figure 2. Erlang model of cell cycle progression

1. Distributions of cell cycle phase durations for RPE, U2OS, and H9 cells using single‐cell measurements of phase duration reported in Fig 1. Black curves represent fits to Erlang distribution.

2. Erlang model of cell cycle progression. Each phase consists of a distinct number of steps, k. Each step is a Poisson process with rate parameter, λ. After fitting each phase to the Erlang distribution, we were able to accurately simulate all phase durations except for M phase (2‐sided Kolmogorov–Smirnov test for difference between measured and simulated distributions, Appendix Fig S7B and C).

3. Fitted shape parameter, k, representing the number of steps for each phase. Error bars represent std from 1,000 bootstraps.

4. Normalized shape parameter, k, for G1, S, and G2 phases in RPE, U2OS, and H9 cells. Bar height represents the fraction of total cell cycle steps spent in each phase. Error bars represent std from 1,000 bootstraps.

5. Fitted rate parameter, λ, representing the progression rate of each step within a cell cycle phase. Error bars represent std from 1,000 bootstraps.

6. Rate parameter λ for each phase, shown by cell type.

Figure 3. Lack of coupling among cell cycle phases under perturbation

1. Schematic of shortening G1 by myc overexpression. RPE cells infected with retrovirus harboring a tamoxifen‐inducible myc overexpression construct.

2. Shift in phase durations of RPE cells overexpressing Myc.

3. Pairwise correlation between cell cycle phase durations of RPE cells overexpressing Myc.

4. Schematic of prolonging S phase by replication stress using aphidicolin. Asynchronously proliferating RPE cells were treated with 50 ng/ml aphidicolin for 8 h, washed with PBS, and then replenished with fresh media. Only cells whose S phase overlapped with the 8‐h treatment window for at least 1.8 h were analyzed.

5. Shift in phase durations of RPE cells treated with 50 ng/ml aphidicolin.

6. Pairwise correlation between cell cycle phase durations under aphidicolin treatment.

7. Schematic of prolonging all phases by incubating cells at 34°C.

8. Shift in phase durations of RPE cells incubated at 34°C.

9. Pairwise correlation between phase durations for cells incubated at 34°C.

10. Schematic of prolonging G1 by DNA damage using NCS. Asynchronously proliferating RPE mother cells were treated with 25 ng/ml NCS, and their daughter cells were analyzed for a full cell cycle.

11. Shift in phase durations of RPE cells treated with NCS.

12. Pairwise correlation between phase durations for cells treated with NCS.

Data information: In panels (B, E, H, and K), boxplots representing the distributions of phase durations in untreated cells are underlaid for comparison. Horizontal lines: median; box ranges: 25^th to 75^th percentiles; error bars: 1.5 interquartile away from the box range. *P < 1 × 10⁻⁵; **P < 1 × 10⁻¹⁰; ***P < 1 × 10⁻²⁰, 2‐sided Kolmogorov–Smirnov test. Number of cells: Myc, n = 116; aphidicolin, n = 115; 34°C, n = 122; NCS, n = 119.Source data are available online for this figure.

Figure 4. A model for heritable factors governing the rate of cell cycle phase progression

1. Alternative models for inheritance of molecular factors governing the durations of cell cycle phases.

2. Simulation of the “strength of coupling” as a function of the number of unique phase‐coupling molecule types under the many‐for‐all model. Each simulation generated 200 cells for which an R ² value was calculated. R ² values were averaged across 200 simulations. The shaded area represents the standard deviation of R ² across the simulations.

3. Simulation of coupling strength as a function of the number of unique phase‐coupling and phase‐specific factors. Phase‐coupling factors have shared control over a pair of cell cycle phases, whereas phase‐specific factors affect only one cell cycle phase. Strength of coupling is represented by mean R ² value as in panel (B).

4. Same as in (B), but simulating the effect of perturbing a single phase‐coupling factor by significantly increasing its abundance or activity. Perturbation was simulated by increasing the abundance of a phase‐coupling factor by 10‐fold.

5. Same as in (C), but simulating the effect of increasing a phase‐coupling factor by 10‐fold (see Materials and Methods).

6. Schematic of prolonging all phases by adding CDK2 inhibitor. RPE cells were treated with 2 μM CVT‐313 and the durations of each phase were quantified for a full cell cycle.

7. Shifts in phase durations for RPE cells treated with 2 μM CVT‐313. A boxplot representing the distributions of durations in untreated cells is underlaid for comparison. Horizontal lines: median; box ranges: 25^th to 75^th percentiles; error bars: 1.5 interquartile away from the box range. *P < 1 × 10⁻⁵, 2‐sided Kolmogorov–Smirnov test. (n = 117 cells).

8. Pairwise correlation between cell cycle phase durations upon treatment with CVT‐313. P indicates P‐value from Student's t‐test for Pearson correlation coefficient.

9. Schematic of shortening phases by overexpression of cyclin D. Cyclin D was overexpressed in RPE cells and the durations of each phase were quantified for a full cell cycle.

10. Shifts in phase durations for RPE cells overexpressing cyclin D. A boxplot representing the distributions of durations in untreated cells is underlaid for comparison. Horizontal lines: median; box ranges: 25^th to 75^th percentiles; error bars: 1.5 interquartile away from the box range. *P < 1 × 10⁻⁵, 2‐sided Kolmogorov–Smirnov test. (n = 113 cells).

11. Pairwise correlation between cell cycle phase durations upon overexpression of cyclin D. P indicates P‐value from Student's t‐test for Pearson correlation coefficient.

Source data are available online for this figure.

Figure 5. Stress‐induced coupling of cell cycle phases in a cancer cell line

1. Schematic of prolonging G1 by DNA damage using NCS. Asynchronously proliferating U2OS mother cells were treated with 100 ng/ml NCS, and their daughter cells were analyzed for a full cell cycle.

2. Shift in phase durations of U2OS cells treated with NCS.

3. Pairwise correlation between phase durations for U2OS cells treated with NCS. P indicates P‐value from Student's t‐test for Pearson correlation coefficient.

4. Schematic of prolonging S phase by replication stress using aphidicolin. Asynchronously proliferating U2OS cells were treated with 50 ng/ml aphidicolin for 8 h, washed with PBS, and then replenished with fresh media. Only cells whose S phase overlapped with the 8‐h treatment window were analyzed.

5. Shift in phase durations of U2OS cells treated with 50 ng/ml aphidicolin.

6. Pairwise correlation between cell cycle phase durations under aphidicolin treatment. P indicates P‐value from Student's t‐test for Pearson correlation coefficient.

Data information: In panels (B and E), boxplots representing the distributions of phase durations in untreated cells are underlaid for comparison. Horizontal lines: median; box ranges: 25^th to 75^th percentiles; error bars: 1.5 interquartile away from the box range. *P < 1 × 10⁻⁵; ***P < 1 × 10⁻²⁰, 2‐sided Kolmogorov–Smirnov test. Number of cells: NCS, n = 114; aphidicolin, n = 153.Source data are available online for this figure.