Fig 1.
Family relations among cells observed in vitro.
(A)Time-lapse microscopy permits the tracking of individual cells, identifying division moments, family relations, cell cycle and cell-cycle phase duration, and protein concentration at the time of each observation. Introduced notations and colors indicate cell cycle (CC, blue), G1 phase (G1, red) and S/G2/M phases (green). Corresponding simulation data are represented by the gray color. (B) Correlations between family members based on experimental and simulation data. Estimation of standard deviations from experimental data is described in detail in Supporting Information (S1 Text, Methods). Simulation results for the autoregression bifurcation model are described in detail in Methods.
Fig 2.
Analysis of protein dynamics based on experimental and simulation data.
(A) Schematics of the model. In the population, each cell is characterized by seven parameters. At division, the parent-cell mass (Cend, Gend) is randomly split between the two progeny cells, according to the expression in which β is the random variable. Cell-cycle phase durations (
) for progeny cells (i is progeny number) are calculated using autoregression bifurcating models.
—production rate of Cdt1 and Geminin proteins, are calculated using linear regression models,
—cell cycle duration, TG1,TSG2M—G1 or S/G2/M phases length of the parent cell, μG1,μSG2M–mean G1 or S/G2/M cell cycle phases length, θG1,θSG2M–relation between parent and progeny G1 or S/G2/M cell cycle phases length,
– random variables from bivariate lognormal distributions (common mean zero, common variances and correlation coefficients). We abandoned the originally assumed bivariate normal distribution to lognormal because of the positive skewness of the distributions of cell-cycle duration. (B) Comparison of linear relationships between the total division time and the duration of phases for experimental and simulation data. Solid black lines show the fitted linear relations of the form y = (slope) × x. (C) Comparison of distributions of the cell cycle and the cell-cycle phase duration for experimental data and modelling results. (D) Looking for probable regulatory mechanisms. Data-derived and simulation-based correlations between pairs of variables characterizing the protein trajectories. (E) Data-derived and simulation-based correlations between production parameters of family members.
Fig 3.
Results of long term simulations.
(A) Dynamics of the time series of the Cdt1 and Geminin protein contents in a randomly chosen lineage of descendants of the ancestor cell. (B) Phase portrait of experimental and simulation data. Ten trajectories of cell cycle were randomly selected from the experiment (left) and simulation (right) data. In both cases, fluorescence levels were normalized to maximum values.
Fig 4.
Comparison of simulation results obtained by proposed model and Wright-Fisher model.
(A) Main assumptions of Wright-Fisher model and our model are presented in separate boxes. The most important difference concerns population size, constant in Wright-Fisher and variable in our model. Series of in silico experiments were performed with different initial population sizes of 3, 25, and 100 cells drawn from previously generated populations. Each cell was characterized by different cell-cycle time and at the time 0 cells were not synchronized (i.e. cells were spread over different cell-cycle phases). (B–D) Example of performed simulations for initial population with N = 3. B) Descendants of ancestor cells are identified and counted. Total population size is marked by black dashed line. C) The fractions of the progeny in population were calculated. We analyzed the fraction of progeny in the population at time 300, but the level is determined after t = 200. Simulations were repeated until required sample size was obtained. D) Cumulative distribution functions for simulation data and Wright-Fisher model. (E) Comparison of simulation data and Wright-Fisher model for three different values of initial cell count N. Histograms of simulation datasets (left) and random numbers drawn from estimated binomial distribution with K (right) represent the fractions of progeny in population after 300 h of simulations. Cumulative distribution functions for both cases are also presented to compare the tails of distributions.
Table 1.
Comparison of data-estimated and Wright-Fisher model-predicted parameter values, variances, and correlation coefficients, based on simulated genealogies of proliferating cells.
Table 2.
Comparison of data-estimated and Wright-Fisher model-predicted parameter values, variances, and correlation coefficients, based on simulated genealogies of proliferating cells obtained by model which does not include family relations; the cell-cycle length for each cell is a random variable, drawn from lognormal distribution.
Fig 5.
Effect of epigenetic drift on population development.
The effective population sizes K were estimated for different values of parent-progeny and sibling correlation coefficients.