Fig 1.
Schematic diagram of cell-cycle regulatory interactions in budding yeast.
The icons represent the sixteen regulated proteins in our model of the budding yeast cell cycle. (The seventeenth component is a generic phosphatase, Hbf, that is synthesized and degraded constitutively but fluctuates nonetheless in the stochastic version of the model.) In this “influence diagram” the barbed arrows and blunt-headed lines represent positive and negative influences, respectively. Mechanistic details of the model are given in Figures A-F in S1 Text.
Table 1.
The growth rate and mass doubling time of yeast cells in different media.
Fig 2.
Deterministic and stochastic simulations of the model.
A (top panels). Deterministic simulation of the changing concentrations of a representative sample of the proteins in the model (left) and the changing numbers of mRNA molecules for some of the genes (right). Cell volume, V(t) (in fL, black line), increases exponentially during each cycle and drops by a factor of 2 at cell division (indicated by arrowheads in each panel). The cell-cycle regulated genes show oscillatory dynamics of mRNAs, whereas for unregulated genes (e.g. CLN3, CDH1, CDC14) the mRNA level stays constant throughout the cell cycle. B (bottom panels). Stochastic simulations, in the same format as the top panels. The numbers of protein molecules N in a cell of volume V (in fL) has been converted into concentration C (in nM) by the equation C = 1.67 N/V. Hence, a concentration of 100 nM in a cell of volume 50 fL corresponds to ~3000 molecules.
Fig 3.
Cell cycle noise and size control in daughter cells.
A. We plot the total number of cells in a “computational culture” of WT budding yeast as a function of time. The semilog plot clearly shows exponential increase of cell numbers. Lines of different colors represent repeat runs with the same initial conditions. The simulations were run with specific growth rate, μ = 0.007 min−1, representing glucose medium. Inset: scatter plot of the number doubling time of each computational culture. B and C. The average and CV (coefficient of variation) of some cell cycle properties for the computational cultures are correlated with experimental data [16]. D, E and F. Joint distributions of μTunbud with ln(Vbir) for three different growth media: μ = 0.007 min−1 (glucose), 0.00467 min−1 (galactose) and 0.00398 min−1 (glycerol-ethanol). Vbir is normalized by the average volume at budding (Vbud). Solid black circles are individual cells and colored circles are the average values of μTunbud over a small interval of ln(Vbir) (referred to as “binned data” points). Binned data points are fitted with straight lines, and the slopes of the fitted lines are given inside each plot. The slopes are characterized as large (red), intermediate (green), and small (blue), and they correspond to “strong”, “weak” and “no” size control, respectively.
Fig 4.
mRNA histograms for a population of budding yeast cells.
A. Simulations for μ = 0.007 min−1 mimicking growth in glucose medium. The average number of mRNA molecules, <N>, for each gene is reported on the histogram. B. Joint distributions of mRNAs in individual cells. C. Comparison of model-predicted joint distributions (bottom row) with experimentally measured joint distributions (top row). For details of the experimental measurements, see Materials and Methods.
Fig 5.
Model-predicted histograms of proteins for a population of budding yeast cells.
Simulations under different growth conditions: blue, μ = 0.007 min−1 (glucose); red, μ = 0.00467 min−1 (galactose); green, μ = 0.00398 min−1 (glycerol-ethanol). The average number of protein molecules per cell, <N>, is indicated in each panel for the glucose-medium simulation.
Fig 6.
Positive feedback in CLN2 activation and the coherence of entry into Start.
A and B. Joint distributions of the times from birth to the activation of the genes for RAD27 (Tbir,RAD27) and CLN2 (Tbir,CLN2) are plotted for WT and cln1Δcln2Δ cells from single-cycle simulations for an extant population of 500 mother (blue) and 500 daughter (red) cells in glucose (μ = 0.007 min−1). In (A1, B1) and (A2, B2) the full data for daughter cells and mother cells are plotted separately. Compare panels A and B to Fig 2e and 2f, respectively, of Skotheim et al [14]. C. As the rate constant for phosphorylation of Whi5 by Cln1,2 (i.e., the strength of the Cln1,2-mediated positive feedback loop) is progressively decreased (in panels C1-C5), the coherence of gene activation upon entry into Start decreases. The coherence of entry into Start cannot be restored by increasing the phosphorylation rate of Whi5 by Cln3 (panel C6; compare to Fig 2i of Skotheim et al). D. The correlation coefficients of Tbir,RAD27 and Tbir,CLN2 for daughter cells and mother cells decrease as the strength of the positive feedback loop decreases. The numbers on the abscissa refer to the data in panels C1-C6.
Fig 7.
Positive feedback in SIC1 degradation and CLB2 activation.
A and B. Temporal dynamics of total Sic1 are plotted for three WT and three clb5Δclb6Δ cells in glucose medium (μ = 0.007 min−1). The solid red lines fit the decay of Sic1 to a single exponential function to obtain the timescale of Sic1 degradation in individual cells. C. Half-lives of Sic1 in individual cells are clustered for WT and various mutant cells, showing that the deletion of S phase cyclin genes (CLB5 and CLB6 but not CLN1 and CLN2) increases the average half-life and the variability of Sic1 degradation, causing an increase in the delay time and the variability of the onset of DNA synthesis (Tg1) (inset). D and E. The durations of SG2M phase (Tsg2m = Tdiv−Tg1) from single-cycle simulations of an extant population of daughter and mother cells are plotted for WT cells, WT cells with decreased rate constant for the phosphorylation of Fkh2 by Clb2 (i.e., decreasing strength of the positive feedback for CLB2 activation), and WT cells with the weakest positive feedback loop and increased rate constants for phosphorylation of Fkh2 by Cln1,2,3 and Clb5. In each plot, the horizontal red line represents the median, the blue box represents 25th to 75th percentile of data, the horizontal black lines represent edges of data points and outliers are plotted as red dots. F and G. The average and CV of Tsg2m are plotted for the data in D and E.
Fig 8.
Mutant phenotypes in glucose medium.
A (daughter) and B (mother) cells. The average of six cell cycle properties obtained from ‘computational cell culture’ simulations of WT cells and nine different mutant strains in glucose medium (μ = 0.007 min−1). Cell volumes in fL and phase durations in min. C (daughter) and D (mother) cells. The color bars indicate the percentage change in CV, relative to WT cells, of selected cell cycle properties (bottom) for a variety of mutant strains (left side). E. The number doubling times of ‘computational cell cultures’ are clustered for WT and mutant strains, showing largest variability among cultures of cdh1Δ cells.
Fig 9.
Mutant phenotypes in galactose medium.
Same as Fig 8, but for computational cell cultures growing in galactose medium (μ = 0.00467 min−1).
Fig 10.
Variability in cell cycle time, and in cell size at birth, is closely correlated to variability in the duration of budded phase.
The coefficients of variation of Tdiv (top row) and Vbir (bottom row) are correlated with the coefficients of variation in Tbud (left column) and Tunbud (right column) for simulated populations of viable mutant strains (including wild-type) in glucose and galactose media. The computed correlation coefficients are given on each plot.