Fig 1.
Simple illustration of the cell cycle.
The four phases of the cell cycle (G1, S, G2, and M), the non-cycling G0 state, and three well-known checkpoints (dashed lines) are shown. The exact location and nature of the G1 checkpoint is controversial, indicated by ‘← ? →’. The number and location of other checkpoints within the G1, S, and G2 phases is also a topic of current research.
Fig 2.
Schematic representations of stochastic cell cycle checkpoint models.
(A) The DDT model random variable is depicted as a ball stochastically traversing a staircase. The ball can move both up and down the staircase (diffusion) but the probability of taking a step up is greater than taking a step down (drift; thick arrow vs. thin arrow). Checkpoint passage occurs immediately upon the ball reaching the top of the staircase (threshold), emulating a bistable switch. (B) The EMPF model is depicted as a staircase connected to a basin. Once the ball reaches the top of the staircase it falls into the basin, from which time to escape is exponentially distributed. In contrast to the DDT model, here the ball can only move up the staircase (single arrow). The transition-probability model of Smith and Martin [15] corresponds to the special case in which the time to traverse each step is constant (delayed exponential). The EMG [38, 39] relaxes this assumption, so that the total time to traverse the staircase is Gaussian distributed. See S1 File for a detailed mathematical comparison of the two models.
Fig 3.
Illustration of a two-checkpoint drift-diffusion+threshold model of the cell cycle.
Simulation was performed by numerically solving Eq 1, twice in sequence, using the Euler-Maruyama algorithm [56] with a fixed time step Δt = 0.01. Drift and diffusion constants are μ1 = μ2 = 0.2 and σ1 = σ2 = 0.1, respectively.
Fig 4.
A two-checkpoint drift-diffusion+threshold (DDT2) model best describes IMT variability under numerous conditions.
(A), (B), and (C) correspond to independent experiments (with slightly different culture conditions; see “Cell culture”). Note that in most cases the DDT3 curve is obscured by the DDT2 curve. n: number of experimental IMT measurements.
Fig 5.
A highly-variable cell cycle phase is preserved between multi-checkpoint DDT models.
Relative variability in checkpoint passage times, as quantified by the coefficient of variation (CV), is shown for each phase of the DDT2 and DDT3 models for all experimental conditions considered. Note that the phase numbers are arbitrary (ordered from largest to smallest CV) and do not reflect their actual order in the cell cycle (see “Stochastic checkpoint models”). Hereafter, the high-variability phase is referred to as “H” and the low-variability phase(s) as “L” (L1 and L2 for DDT3).
Fig 6.
Parameter estimates under growth factor perturbation suggest that the highly-variable (H) phase is growth factor sensitive.
(A) MCF10A cells in DMSO control vs. treatment with the EGFR inhibitor erlotinib; (B) MCF10A wild-type (WT) cells vs. MCF10AT1 cells (indicated by V12-Ras). p-values were calculated using a two-sample bootstrapping scheme (see “Parameter estimation and model selection”). Blue signifies unperturbed; red signifies perturbed.
Fig 7.
Model-predicted H and L phases correlate with experimental G1 and S-G2-M times.
Experimental results and model predictions for untreated A375 cells: (A) IMT data (n = 266) overlaid by the best-fit DDT2 model; (B) histograms of times spent in G1 (left) and combined S, G2, and M (right) cell cycle phases were compared to DDT2 model-predicted H and L phases. The H phase most closely correlates with G1, while the L phase correlates with S-G2-M. Dashed lines indicate distributions shifted (∼3.5 h, indicated by arrows) to best describe the G1 data.
Fig 8.
Hypothetical models of G1 checkpoint activity.
(A) The H phase begins Δ h after the M/G1 phase boundary and ends at the G1/S phase boundary. Cells can enter G0 at any point within the first Δ h of G1, and return at the same position, but not after. This model is consistent with Refs. [22, 27]. (B) The H phase begins at the M/G1 phase boundary and ends Δ h before the G1/S phase boundary. Some cells enter into the cell cycle in G0 and reside there for some time before stochastically emerging into G1, which is the source of variability in this phase. This model is consistent with Refs. [23, 24, 26, 33]. Note that Δ ≈ 3.5 h for A375 cells (Fig 7).