To obtain a precise assessment of cell size control during cell cycle progression, we sought a quantitative marker of the successive cell cycle phases in individual growing cells. Studies to date have relied on monitoring of bud emergence or of a fluorescent budneck marker, neither of which can distinguish between S, G2, and M phases. We reasoned that the burst of histone synthesis could serve as an accurate marker of S phase, thanks to the tight reciprocal coupling of DNA replication and histone synthesis, which has been characterized in detail (Baumbach et al., 1987; Heintz et al., 1983; Nelson et al., 2002; Sittman et al., 1983). Therefore, determining the onset and the end of the burst of histone expression would allow us to extract the duration of S-phase, but also deduce the duration of phases that precede (G1) and succeed DNA synthesis until anaphase onset. In budding yeast, metaphase is known to directly follow the end of replication, with no evidence of gap phase in between. However, we referred to this post-DNA synthesis interval as G2/M in the following for sake of simplicity and coherence with other organisms.

To this end, we took a strain carrying a fluorescent protein cassette fused to one of the histone 2B loci (HTB2, Figure 1A), which has been extensively used as a nuclear marker. We used a superfolder GFP (sfGFP) protein to ensure a fast maturation of the fluorophore, in order to prevent artifacts in measurements of histone dynamics, as described below. We monitored yeast cell growth in a microfluidic device which allowed us to track the successive divisions of individual cells forming bi-dimensional microcolonies (See Materials and methods and Figure 1 and Figure 1—figure supplement 1), as previously described (Goulev et al., 2017).

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Plotting total nuclear HTB2-sfGFP fluorescence as a function of time over one cell cycle (Figure 1B, see Figure 1—figure supplement 2A–D and Supporting Information for details of all quantifications), revealed a fluorescence plateau during the unbudded period of the cell cycle, followed by a linear ramp starting shortly before budding, and a plateau during the budded period of the cell cycle. This pattern was terminated by a sudden drop in fluorescence, corresponding to the onset of anaphase and nuclear division.

Quantification of fluorescence levels gave a consistent ~2-fold enrichment in histones before compared with after the histone synthesis phase (Figure 1—figure supplement 2E and F), as expected by the doubling of DNA content. Similarly, we verified that HTB2-sfGFP fluorescence was evenly partitioned between mother and daughter cells upon nuclear division (Daughter/Mother [D/M] asymmetry = 0.94 ± 0.01 Figure 1—figure supplement 2).

To further check that the measurement of total histone content over time is a reliable and physiological way to score cell cycle progression in individual cells, we performed a series of control experiments. First, we compared the division time (by measuring the anaphase to anaphase interval) of a strain carrying a constitutive NLS-GFP marker with a HTB2-GFP strain. We observed that the GFP-tag at the HTB2 locus only modestly affected cell division (Figure 1—figure supplement 3A–C). Of note, unlike the piecewise expression pattern observed with the HTB2-GFP strain (Figure 1—figure supplement 2A), the NLS-GFP strain yielded a continuous increase in total fluorescence throughout the cell cycle, as expected with a constitutive marker.

Next, we investigated how the maturation time of the fluorescent reporter affects the ability to accurately monitor the burst in histone level during S-phase. For this, we followed the expression of a second histone H2B marker, HTB2-mCherry, over time. Importantly, only a linear ramp followed by the anaphase drop could be discerned, in striking difference with the pattern observed with sfGFP (compare Figure 1—figure supplement 4A and B with Figure 1—figure supplement 4C and D). A numerical model confirmed that this effect could be quantitatively explained by the much longer maturation time of mCherry (~45 min [Charvin et al., 2008]) compared with sfGFP (~5 min [Pédelacq et al., 2006]), which blurs the apparent dynamics of histone synthesis (Figure 1—figure supplement 4E–H).

Although histone levels monitoring provides the timings of S phase and nuclear division, cytokinesis cannot be timed and, therefore, the duration of G1 cannot be deduced. To circumvent this problem, we used the septin subunit Cdc10-mCherry fusion as an additional cytokinesis marker (Figure 1—figure supplement 5A–C). We measured that cytokinesis (the sudden drop in Cdc10-mCherry fluorescence) and nuclear division were tightly correlated (Pearson coefficient 0.94), with a median offset of 5.6 ± 0.4 min between both events (Figure 1—figure supplement 5D and Figure 1—figure supplement 5E). Therefore, for the sake of simplicity, we chose to ignore cell-to-cell variability in this part of the cycle and, in the rest of the paper, we arbitrarily defined cell cytokinesis as an event occurring 5.6 min after the end of anaphase. We could not exclude the possibility that this procedure would introduce artefacts regarding measurements of G1 duration in mutants with cytokinesis defects. Yet, none of the reported mutants reported below, with the exception cdh1(Tully et al., 2009), have been described to affect cell cytokinesis.

Similarly, we used the Whi5-mCherry fusion protein to assess the coordination between cell cycle Start (as defined by nuclear exit of the transcriptional repressor Whi5) and the onset of histone synthesis (Fig. Figure 1—figure supplement 5F–H). Start consistently occurred before the onset of histone synthesis (Fig. Figure 1—figure supplement 5I–J), which was expected because HTB2 expression is controlled by the G1/S-specific transcription factors SBF/MBF. Taken together, these results confirmed the tight coordination between cell cycle progression and our measurements of the dynamics of histone expression.

To extend this preliminary analysis, we developed custom MATLAB software Autotrack to automate the processes of cell and nucleus contour segmentation, cell tracking, histone content measurement, and mother/daughter parentage determination (Figure 1—figure supplement 6 and Supporting Information). We then used a piecewise linear model to identify the histone synthesis plateaus and ramp in the raw data, which allowed us to extract four intervals per cell cycle (Figure 1B–C and Figure 1—video 1): G1 (plateau), S (linear ramp), G2/M (plateau preceding anaphase), and the interval between anaphase onset and cytokinesis (referred to as ‘Ana’), taking into account our hypothesis that the period between the end of anaphase and cytokinesis was constant, as mentioned above.

Using this method, we extracted the duration of cell cycle phases for up to ~500 cells in each of the eight cavities in each independent chamber. By pooling 17 replicate experiments, we collected ~26,900 cell cycles for WT cells (Figure 1C) of which 63% passed our quality control procedure aimed at discarding cells with segmentation/tracking or data fitting issues (see Supporting Information and Figure 1—figure supplement 7). To decrease the rate of cell rejection due to noise in histone level signals, we tested multi-z-stack acquisition for HTB2-sfGFP fluorescence. However, this only marginally improved the signal to noise ratio (Figure 1—figure supplement 8A–C) while greatly affecting the cell cycle duration likely due to photo-damage (p<0.001, Figure 1—figure supplement 8D). Therefore, we retained the single plane acquisition method.

Using this analysis, we found that the cell cycle durations for WT cells were in good agreement with data obtained using other markers or methodologies. Thus, the durations for mothers and daughters, respectively, were: G1 (19.0 ± 0.1 and 45.5 ± 0.3 min) (Di Talia et al., 2007), S (29.5 ± 0.1 and 36.7 ± 0.2 min) (Magiera et al., 2014), G2/M (15.7 ± 0.1 and 14.7 ± 0.1 min), and Ana (11.4 ± 0.1 and 12.2 ± 0.1 min), Figure 1D and supplementary file 2. Importantly, the large sample size allowed us to identify statistically significant differences in these intervals. For instance, the S phase was 7.2 min longer in daughters compared with young mother cells (p<0.001; Figure 1D). In addition, this interval converged toward an asymptotic value over several divisions following cell birth (Figure 1—figure supplement 9). This contrasts with G1 duration, which decreased abruptly when daughters (replicative age 0, Figure 1—figure supplement 9) became mother cells (replicative age >0, Figure 1—figure supplement 9) in their subsequent division, and G2/M, the duration of which is quite independent of the replicative age of the cells. This phenomenon explains the previously reported (Cookson et al., 2005) progressive shortening of the cell cycle duration with the replicative age of the cell (see also Figure 1—figure supplement 9). Also, our result recapitulate the systematic shorter S/G2/M interval in mother cells compared to daughters that was recently measured(Mayhew et al., 2017). Over, these findings illustrate the power of our technique to quantitatively measure the temporal distribution of cell cycle intervals.

Because our methodology allowed us to detect even minor differences in cell cycle duration, we sought to validate its robustness by measuring the timing of cell cycle phases following perturbation by diverse environmental and genetic perturbations approaches that have been extensively studied using other techniques.

First, we asked whether our methodology could capture the lengthening of the S phase induced by hydroxyurea (HU), which inhibits DNA replication. As expected, we observed a progressive HU concentration-dependent increase in S phase duration in both mother and daughter cells, from an average of 27.1 ± 0.4 min and 35.1 ± 0.8 min at 0 mM to 48.0 ± 1.4 and 43.9 ± 1.4 min at 50 mM HU, respectively (p<0.001, Figure 2A). This prolongation of S phase was accompanied by a parallel doubling in G2/M duration (from ~15 min to ~30 min in both mothers and daughters, p<0.001, Figure 2A), which is likely due to the activation of the checkpoint that follows DNA damage(Weinert et al., 1994). Interestingly, mothers, but not daughters, exposed to HU experienced a dose-dependent slowing of the entire cell cycle, due to an apparent compensatory decline in G1 duration in the daughters (Figure 2A).

Figure 2

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We next measured the duration of cell cycle phases in cells carrying mutations in important regulators of G1, S, or G2/M phases (Figure 2B–D and supplementary file 2). First, we confirmed that sic1 and whi5 (G1/S transition repressors) daughter cells underwent premature entry into S phase (i.e., shorter G1 duration) compared with WT cells (Soifer and Barkai, 2014), which was accompanied by a compensatory increase in G2/M duration (Figure 2B) (Soifer and Barkai, 2014). Conversely, mutation of G1/S transition activator BCK2 (Soifer and Barkai, 2014), but not CLN3, caused a small delay in G1 of daughter cells. A slight decrease in G2/M duration was also observed in both BCK2 and CLN3 mutants compared with WT cells (Figure 2B and and supplementary file 2).

Next, we monitored the effect of mutations in genes involved in several biochemical pathways related to S-phase (Mrc1, Clb5, Dpb3, Rad27, Dia2). These mutations had previously been shown to induce an abnormally long S-phase interval using a cytometry assay (Koren et al., 2010). Our results confirmed this observation in all mutants, and, with the exception of dia2, the ordering of mutants according to S-phase duration was similar to Koren et al. (Figure 2C)(Koren et al., 2010). In addition, most of these mutants also displayed a longer G2/M phase, similar to the effect of HU treatment, with the exception of dpb3 cells (Figure 2A and C). This result suggests that the increased G2/M duration observed following HU treatment and in most S phase mutants is likely to be biological in origin rather than an artefact of our methodology. In this regard, a similar delay in G2/M progression was previously reported in dia2, mrc1, and rad27 mutants, but not in dpb3 mutants (Koren et al., 2010).

Lastly, we measured the cell cycle duration in mutants of G2/M progression. We found that deletion of SWE1, a kinase that inhibits Cyclin B/Cdk activity and therefore prevents a premature onset of anaphase, did barely affect G2/M duration, yet induced a slight increase in G1 duration of daughter cells, as previously observed (Harvey and Kellogg, 2003). However, mutants defective in Hcm1, a forkhead transcription factor that regulates late S phase genes, or Clb2, one of the main mitotic cyclins, both displayed longer G2/M phases (Figure 2D), in agreement with previous measurements (Pramila et al., 2006; Surana et al., 1991).

Collectively, these results obtained in various mutant backgrounds further establish proof-of-principle for our methodology, in which a single fluorescent marker enables simultaneous measurements of key events associated with cell cycle progression. In total, we monitored the dynamics of cell cycle progression of 22 mutants. The raw cell cycle data are available on a dedicated server (Tassy and Charvin, 2018) that allows detailed data exploration and on-the-fly statistical analyses (see Appendix 1).

Our ability to measure the duration of specific cell cycle phases provides a unique opportunity to investigate in detail the coordination of growth and division during each phase of the cell cycle. We extracted 15 variables (e.g., phase durations, bud/cell volumes and growth rates during unbudded and budded period; see Supporting Information) describing cell cycle progression in both mother and daughter cells. Cell volumes were computed from segmented cell contours assuming an ellipsoid model.

Using this dataset, we sought to identify novel compensatory effects reflecting the existence of size control mechanisms. For this, we systematically measured the Pearson correlation coefficient for all measured distributions of variables in mothers and daughters (Figure 3A and B). This analysis successfully confirmed classical results, such as the negative correlation between size at birth (V_birth) and the duration of G1 (T_G1) in daughter cells (yellow star in Figure 3B) (Di Talia et al., 2007), which is indicative of a G1 compensatory mechanism in small daughter cells, as well as the positive correlation between the growth rate in unbudded cells (μ_unb.) and the cell volume the end of G1 (V_G1) in daughters cells (green star in Figure 3B)(Ferrezuelo et al., 2012).

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However, this analysis also revealed that the duration of G2/M (T_G2/M) varies inversely with the volume of the bud at the end of S phase (Vb_S) in both mother and daughter cells, see magenta stars in Figure 3B. This suggest that, after reaching the end of S phase, cells experience a bud size–dependent delay before entering anaphase. However, G2/M and S phase durations also appear negatively correlated, therefore, an alternative explanation would be that a longer S-phase provides more time for the cells to accumulate B-type cyclin, thus leading to a quicker anaphase onset and a reduction of the measured G2/M interval. In this case, the negative correlation between T_G2/M and Vb_S may result from the longer S phase that leads to a larger bud size by the end of S phase, as indeed observed (see the positive correlation between Vb_S and T_S on Figure 3A). To discriminate between the direct versus indirect link between these two variables, we first checked that the Pearson correlation coefficient ρ was more pronounced for T_G2/M and Vb_S than for T_G2/M and T_S (ρ = −0.43 and ρ = −0.29, respectively), thus arguing in favor of a direct size-dependent modulation of G2/M duration. Second, we used a Bayesian statistics approach to determine which model (direct versus indirect link) fits better the data (Meilă and Jaakkola, 2006). This analysis confirmed the causative link between Vb_S and T_G2/M (see supplemental information for details).

Interestingly, this phenomenon is in agreement with the bud morphogenesis checkpoint model, which proposed that bud growth perturbations lead to a cell cycle arrest that prevents a potentially deleterious premature onset of anaphase (Harvey and Kellogg, 2003). It also matches the conclusions of a recent theoretical model of cell cycle control, in which bud size control appears to play an important role for the overall cell size homeostasis (Spiesser et al., 2015), as well as a recent statistical analysis of the duration of the budded period versus cell size (Mayhew et al., 2017).

However, another study provided evidence that this control mechanism does not operate as a bud size controller during an unperturbed cell cycle (McNulty and Lew, 2005). Therefore, to characterize this potential G2 bud size control further, we sought to determine the magnitude of compensatory growth effects during this phase of the cell cycle, and to compare it to the one of other phases. To this end, we monitored variation in cell volume ΔV during G1, G2/M, and the complete cell cycle as a function of initial cell volume (Figure 3C and D), according to a methodology widely used in previous studies (Jun and Taheri-Araghi, 2015): for an ideal Sizer, the variation in cell volume is such that the final volume V_f is constant, independently of the initial one V_i. In this case, since ΔV = V_f Vi, plotting ΔV versus V_i yields a linear relationship with a slope −1. For an ideal Timer (in which the duration of the phase is constant), the slope becomes +1, assuming an exponential growth model, and a doubling of cell size during the considered interval(Jun and Taheri-Araghi, 2015). Last, an Adder is such that the amount of added volume is independent of the initial volume; in this case, the slope is 0. Therefore, measuring the slopes s of ΔV vs. V_i plots provide a quantitative assessment of the magnitude of size compensation effects, as well as their deviation from theoretically ideal behaviors (i.e. Sizer, Adder and Timer).

The analysis captured the well-characterized daughter-specific Sizer in G1 (Figure 3D: slope s_G1 is negative in daughters, −0.30 ± 0.01, but approaches zero in mothers, −0.02 ± 0.01) (Di Talia et al., 2007). It also confirmed that the daughter and the mother cells behave as a weak Sizer and Adder, respectively, over the entire cell cycle (s_tot = −0.22 ± 0.02 for daughters and 0.09 ± 0.01 for mothers) – in previous studies, the low absolute values of s_tot showed that the budding yeast cell cycle behaves as an Adder, as observed in other unicellular organisms (Jun and Taheri-Araghi, 2015; Soifer et al., 2016).

In addition, the data clearly indicated the existence of a bud-specific size-compensatory growth in G2/M in both daughter and mother cells (s_G2/M = −0.39 ± 0.01 and −0.49 ± 0.01 in daughters and mothers, respectively, Figure 3D). Importantly, we found that the magnitude of the Sizer was strongly reduced when considering the total cell volume (rather than only the bud, see Figure 3—figure supplement 1B), or when measuring the magnitude of size compensation during the whole budded period of the cell cycle (Figure 3—figure supplement 1C). This very likely explains why G2/M size control has been largely ignored in budding yeast and has been considered as ‘cryptic’. Instead, our measurements revealed that the G2/M bud size control is of comparable magnitude to the long-known size control in G1. Therefore, these results suggest that at least two mechanisms may act coordinately to ensure size homeostasis throughout the cell cycle (Soifer and Barkai, 2014).

To better characterize the molecular basis of size compensation effects throughout the cell cycle, we measured the magnitude of compensatory growth for daughter cells (using ΔV vs. V plots, as in Figure 3C) in a subgroup of the cell cycle progression mutants examined earlier (Figure 2). We found that deletion of the repressor of G1/S cyclin Whi5 decreased the magnitude of G1 control (s_G1 = −0.17 ± 0.02) but compensated with a slight increase in G2/M control (s_G2/M = −0.46 ± 0.02, Figure 4). However, these changes were relatively modest, and the overall size-compensation slope was similar in whi5 and in WT cells (s_tot = −0.26 ± 0.03 and s_tot = −0.22 ± 0.02, respectively; Figure 4). Deletion of other G1/S regulators (cln1, cln2, cln3, swi4) lead to similar conclusions. However, G1 size compensation was slightly improved by deletion of the activator of G1/S transition BCK2 (s_G1 = −0.34 ± 0.04), and the overall compensatory growth was stronger than in WT cells (s_tot = −0.46 ± 0.06).

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In striking contrast to these G1/S regulators, deletion of other cell cycle control genes related to the control of B-type cyclin function, such as sic1, swe1, clb5, and clb2, induced a much larger decrease in size compensation in both G1 and (with the exception of clb2) G2/M phases, as well as the overall compensatory growth (Figure 4). For instance, loss of Swe1, which inhibits Cyclin B-Cdk activity and regulates the onset of anaphase, leads to a slightly Timer-like behavior (s_tot = 0.15 ± 0.05), in which both G1 (s_G1 = −0.12 ± 0.03) (Soifer and Barkai, 2014) and G2/M (s_G2/M = −0.15 ± 0.04) size compensation were largely abolished. Taken together, these data indicate that the compensatory mechanisms ensuring the control of cell size were strongly affected in mutants linked to the regulation cyclin B-Cdk activity but, unexpectedly, only marginally impaired in mutants of the G1/S control network.

To determine how size G1 and G2/M compensation effects actually impact size homeostasis, we quantified cell size variability during cell cycle progression. We measured the coefficient of variation (CV) of the distributions of cell/bud volumes at various points in the cell cycle from bud emergence to the next division of the resulting daughter cell (Figure 5A). We found that the CV gradually decreased as a function of cell cycle progression and cell size, roughly following a square-root dependency: CV = F^1/2 / <V>^1/2, where F is a constant and <V > is the mean cell/and or bud volume at a given point in the cell cycle. This scaling relationship between CV and cell size is to be expected, according to the Central Limit Theorem, assuming that cell growth is the sum of elementary stochastic processes: growth fluctuations tend to average out in larger cell compartments compared to smaller ones. Therefore, to characterize the intrinsic variability in cell size during cell cycle progression and to facilitate comparison among mutants of diverse sizes, we evaluated F (known as the Fano factor [Fano, 1947]), rather than the CV, because F provides a size-independent measurement of noise in cell size during the cell cycle (F is sometimes referred to as noise strength [Raser and O'Shea, 2004]).

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As expected, the Fano factor was much more stable than the CV during cell cycle progression of WT cells (Figure 5A). Still, it displayed some notable variations around the mean at different points in the cell cycle: specifically, F decreased during G2/M and G1 phases, but increased during the rest of the cell cycle, especially during S phase (Figure 5A). The Fano factor associated with cell size was much higher than the noise due to segmentation errors (see Material and methods for detail), thus ruling out the possibility that measurements of cell size variability might be dominated by experimental noise. Instead, our results support the hypothesis that cell size noise is clearly modulated during cell cycle progression. To check this further, we asked whether the magnitude of the decrease in Fano factor at specific cell cycle phases was consistent with that of the compensatory growth. For this, we plotted the fold-change in Fano during G1 (Figure 5B) and G2/M (Figure 5C) for each of the cell cycle mutants. Importantly, we observed that mutants with strong size compensation effects (i.e. with a negative slope) displayed larger reductions in Fano factor in both G1 and G2/M phases. Of interest, the reduction in Fano factor was larger in G2/M (fold-change ~0.65) than in G1 (~0.9) in WT cells (Figure 5B and C), confirming the importance of cell size control during G2/M. Also, this analysis clearly demonstrated that the magnitude of size compensation mechanisms directly influences size homeostasis in a cell cycle phase-specific manner.

Following the analysis of compensatory growth during G1 and G2/M, we wondered how the overall (i.e., during a full cell cycle) daughter cell size homeostasis was dependent on the overall size control (s_tot) in the cell cycle mutants. To explain the quantitative relationship between the magnitude of size control due to compensatory growth and actual variability in cell size, we turned to a noisy linear map of the cell cycle, which provides a simple model to couple phenomenological parameters that describe cell growth and division (Tanouchi et al., 2015). Under this assumption, the evolution of daughter cell volume V_n at the beginning of the cell cycle n can be given by (see Supporting Information for detail):

with p =$ra$, where a characterizes the efficiency of size control (which is directly related to the magnitude of size compensation, represented by the slope s_tot measured in Figure 3B: a = s_tot +1, see Supporting Information), r is the fraction of volume going to the daughter cell at division (asymmetry factor, 0 < r < 1/2), V_eq is the volume of a daughter cell at equilibrium (Fig. 6A), and η represents a Langevin noise, such that <η> = 0 and <η²> = constant. Under these assumptions, we demonstrated that the Fano factor is given by (see Supporting Information for detail):

This equation indicates that the variability in cell size depends on a, size-independent, intrinsic noise constant ${\displaystyle \frac{<{\eta }^2>}{V_{eq}}}$, which reflects the stochasticity of the growth process, and an effective size control parameter p (with 0 < p < 1). Notably, this model predicts a non-linearity in size variability as a function of size control parameters, and has two interesting limit cases: for a perfect Sizer (s_tot = −1), p equals 0, therefore the Fano factor equals the intrinsic noise associated with the growth process, given by <η²>/V_eq,. In contrast, for a perfect Timer (s_tot = 1), and assuming symmetrical division of mother and daughters (r= ½), p equals 1 and thus there is a divergence in Fano factor, leading to a complete loss of size homeostasis. In the case of budding yeast, which divides asymmetrically (r< ½), such extreme case is impossible. In other words, even with a perfect Timer, asymmetrical division is sufficient to limit cell size variability.

To check the validity of this description, we computed the average Fano factor during the cell cycle and calculated p by robust linear regression of single-cell data in WT and mutants (Figure 6A). We observed large variations in Fano factor among the mutants, which appeared to be correlated with the size control parameter p (Pearson correlation coefficient = 0.60, Figure 6B): overall, Sizers (i.e. with low values of p) tend to have less cell size noise than Timers (i.e. high values of p). Interestingly, mutants related to the G1/S network (bck2, swi4, whi5, cln1, with the exception of cln2 and cln3) generally displayed a noise level comparable to WT and lower than did the mutants associated with the regulation of B-type cyclin function (clb5, swe1, clb2, cdh1; Figure 6B).

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Fitting the model prediction to the experimental data (using a single parameter fit <η²>/V_eq) yielded reasonable agreement, despite a large spread in the experimental data and the existence of an outlier, the dia2 mutant, which failed to fit the model (Figure 6B). Therefore, this analysis revealed that the degree of size variability observed in this cohort of cell cycle mutants, associated with diverse roles in cell cycle progression, can be reasonably accounted for by a simple model in which there is a universal noise parameter that characterizes the stochasticity of the growth process, as well as a mutant-specific parameter associated with size control. The deviation of experimental data from the predictions of the model are likely to originate, in part, from the simplistic assumption that size control is a homogenous process throughout the cell cycle, thus ignoring the contributions of size compensation mechanisms in specific phases. In addition, whereas the hypothesis of a linear map was correct for some strains (e.g. WT in Figure 6A), some deviations were observed in others (i.e. multiple slopes may be needed to describe the behavior of bck2 in Figure 6A).

Interestingly, the parameter p is related to the rate λ of convergence of the linear map, which sets the time it takes for a chain of daughter cells to return to equilibrium following a fluctuation in cell size:

where < T_div > is the average generation time of a specific mutant. By computing λ from p and <T_div > , we identified a large spread in convergence rates, ranging from 1.9 × 10⁻³ min⁻¹ to 5.7 × 10⁻³ min⁻¹ (Figure 6C). By selecting the fraction of daughter cells that deviated significantly (larger or smaller) from the equilibrium size at birth and tracking the average size of consecutive daughters, we confirmed that convergence to equilibrium was impaired in the swe1 mutant but slightly improved in the bck2 mutant (yet only for large cells, presumably because the slope p seems different for small versus large bck2 cells on Figure 6A, see above) compared with WT cells (Figure 6D). Therefore, this analysis revealed that mutations of cell cycle regulators not only modify the average duration of specific phases but also control the timescale of size fluctuations and hence the robustness of the cell cycle orbit.

All strains were congenic to S288C unless specified otherwise and were constructed following standard genetic techniques. A detailed list of strains is provided as a supplementary file 1. HTB2-sfGFP fusion protein was generated by classical PCR-mediated genome editing. Mutant strains were obtained from the deletion collection of non-essential genes. In the list of constructed strains, we noticed that the cdh1Δ HTB2-sfGFP strains were quite unstable and yielded a large fraction of dead cells as well as large multinucleated cells that retained a fast division time and eventually outgrew the rest of the population. Indeed, the cdh1Δ mutation has previously been described to induce genomic instabilities (e.g. chromosome loss, etc..)(Ross and Cohen-Fix, 2003). We hypothesize that introducing the histone marker in this background exacerbates this phenotype. To circumvent this issue, we used freshly thawed cells from frozen stock.

Microfluidic chips were designed and made using standard techniques as previously described (Goulev et al., 2017). The microfluidic devices, which feature eight independent channels, each consisting of 8 chambers, allow parallel monitoring of 8 genetic backgrounds in the same time-lapse assay. The microfluidic master was made using a standard SU-8 lithography process at the ST-NANO facility of the IPCMS (Strasbourg, France). CAD files and detailed dimensions of the chip are available on the metafluidics open repository: https://metafluidics.org/devices/yeast-high-throughput-culture-device-with-8-independent-flow-chambers/. The micro-channels were cast by curing PDMS (Sylgard 184, 10:1 mixing ratio) and then covalently bound to a 24 × 50 mm coverslip using plasma surface activation (Diener, Germany). Chips were then baked for 1 hr at 70°C to improve the sealing between PDMS and glass. Microfluidic chips were connected using Tygon tubing and media flows were driven by a peristaltic pump (Ismatec, Switzerland) with a 30 μL/min flow rate.

Strains were cultured overnight in synthetic complete medium with glucose and all amino acids. The next morning, the cultures were diluted and allowed to grow until optical density at 660 nm reached 0.2–0.5. Each strain was then loaded into independent chambers chosen at random to avoid potential systematic bias in measurements. For each strain, at least two fields of view were recorded during the time-lapse acquisition interval. Each assay included a WT strain as a control. Mutants were analyzed in at least three independent assays. In total, we collected at least 2000 cell cycles per mutant ~25,000 cell cycles for the WT strain.

Cells were imaged every 3 min using an automated inverted microscope (Nikon TI, Nikon, Japan) with a 60 × phase contrast objective and a sCMOS camera (Hamamatsu Orca Flash 4.0, Japan) driven by Nikon Software (NIS). Constant focus was maintained using a Perfect Focus system. Fluorophore excitation was performed using LED light (Lumencor X1) and appropriate filter sets. The cells were allowed to grow for up to 10 hr in the device, yielding about 500 cells per field of view by the end of the assay.

Raw proprietary Nikon files (.nd2 format) were converted using Bio-format and bftools packages into MATLAB-compatible lossless jpeg files. We developed custom software (Autotrack; see Fig. Figure 1—figure supplement 2 and Supplemental Information for details) to: (1) segment and track individual cells in yeast microcolonies, (2) quantify HTB2-sfGFP (or mCherry) levels in individual cells and extract individual cell cycles, (3) determine the duration of individual cell cycle phases, and (4) discard outliers based on specific criteria (detailed in Supplemental Information). Cell volumes were calculated from segmented cell contours assuming an ellipsoid model.

Linear regression was performed with a robust regression procedure (robustfit) function in Matlab) using a weighting function to limit the impact of potential outliers (Error estimates correspond to a 95% confidence interval). Volume measurement errors reported in Figure 5A were estimated by comparing the volume obtained from automated cell segmentation to a manual ground truth segmentation performed over more than 500 cells of various sizes.

All variables extracted during image processing were stored in a mutant-specific database designed to allow straightforward analysis using custom MATLAB software, as described in the Supporting Information. We developed a web application, Yeast Cycle Dynamics, that allows custom statistical analysis of extracted cell cycle data for all mutants in this study. In addition, raw data showing histone levels and cell size as a function of time for all cells can be monitored (Tassy and Charvin, 2018). See Supplemental Information for details.

Autotrack is software developed during this study to automate the processing of time-lapse datasets. It is based on the project architecture of PhyloCell, which is frontend software previously developed by our group to process time-lapse images. Both programs are available for download at github: https://github.com/gcharvin.

The software allows parallel segmentation, tracking, and quantification of individual cells in yeast microcolonies. Information on both the cell and nucleus is used to ensure a reliable determination of cellular parentage (mother/bud relationships), which is mandatory for assessing cell growth during a complete cell cycle (see Figure 1—figure supplement 6 for an overview of the pipeline). Finally, a specific routine is used to extract the duration of individual phases for each cell cycle, and a quality control routine is run to discard outliers. The steps are described in detail below.

Yeast Cycle Dynamics (YCD) is a tool accessible online (http://charvin.igbmc.science/yeastcycledynamics/index.php) to compare and analyze the data acquired during this study for both mutant and wild type strains.

Different mutants can be compared thanks to our dynamic graph system. This tool uses R to compute several analyses involving a selection of mutants and features. Mutant lines are selected using a dedicated interface that allows to display a short movie of the growing cells with a representation of their main characteristics. This makes it possible to visually estimate and compare the consequences of a mutation on the growing yeasts and their cell cycle. The analysis tool then allows to study the distribution of a mixture of variables for both mother and daughter cells on every selected lines. The results can be visualize as a distribution or a whiskers box plot.

This tool offers the possibility to study the correlation existing among these variables and see if they are conserved in the selected mutants. Here again, two graphs, a histogram and a correlogram, are available to depict these features.

The distance segregating mutants can be computed for all or every combination of variables. This way, it is possible to see which lines behave similarly for a given set of parameters. This tool uses the Mahalanobis distance which minimize the influence of the noisiest datasets for this measure.

Also, a principal component analysis module has been developed to better identify the variables that are the most discriminant among the mutants. Variables are represented as vectors which direction and length show their relative influence in the observed behaviors.

Last, it is possible to select specific yeasts from the database based on the volume of their body, bud and nucleus as well as the time duration for every phase of the cell cycle. The characteristics of the resulting cells can be further explored using their individual file. Each page shows the cell identity, its genotype, the number of reported divisions and a summary of all the variables recorded during the procedure. The system also generates an interactive graph showing the evolution of the fluorescence signal as well as the volume of the cell and its bud over time. When yeasts have been tracked during several divisions, the user can display these features for every step to see how they evolve in time.

YCD is developed in PHP v.5 and JavaScript. The graphs are generated using R v.3 and the Rgraph library. Data are stored and accessed from a PostgreSQL v.9 database. The gene descriptions used in the system have been downloaded from the Saccharomyces Genome Database.

The whole dataset, including single cell data for each mutant, is available upon request.

A key result of this work is to show that there is a negative correlation between bud size at the end of $S$ phase ($V{b}_S)$ and G2/M duration ($T_{G2/M})$ which suggest the existence of a G2/M size control mechanism. However, the data also show that the duration of $S$ phase ${(T}_S)$ correlates both with $V{b}_S$ and $T_{G2/M}$ which could be untimely the underlying cause of an indirect correlation between $V{b}_S$ and $T_{G2/M}$, hence the proposed underlying size control mechanism would be artefactual. These two scenarios can be depicted with the two simple tree belief networks shown below:

and:

which link conditional dependencies between variables. In Equation 11, the dependency between the variables $T_{G2/M}$ and $V{b}_S$, and $V{b}_S$ and $T_S$ are direct which induces an indirect correlation between the $T_{G2/M}$ and $T_S$. In contrast, the dependency between $T_{G2/M}$ and $T_S$ is direct in Equation 12.

The question is then whether it is possible to elucidate which of these two alternative models is correct. A first clue can already be obtained by having a closer look at the correlation coefficients between the three variables: ${\mathrm{\rho }(T}_S,V{b}_S\mathrm{})=0.33$, ${\mathrm{\rho }(T}_S,T_{G2/M}\mathrm{})=-0.29$ and $\rho (V{b}_S,\mathrm{}{T}_{G2/M})=-0.43$ (after removing cell cycles in which Vb_S=0). The fact that the correlation between $V{b}_S$ and $T_{G2/M}$ is stronger than the correlation between $T_S$ and $T_{G2/M}$ suggest that the conditional dependency $T_S\to V{b}_S\to T_{G2/M}$ agrees better with the data.

To further support this statement, we use a Bayesian statistical approach that allows us to evaluate which tree belief network (Equation 11 versus Equation 12) fits better the data(4). To do so we first discretize the three-dimensional space formed by the three cell-cycle variables considered here ($T_{G2/M},{V{b}_S,T}_S$) into voxels by splitting their domains into b bins. We then and count the number of cells $n_{xyz}$that lay inside each voxel labeled by the three discrete indexes $x,y,z$ (where the identities$x=T_{G2/M}$, $y=V{b}_S$ and ${z=T}_S$were introduced to simplify the notation). We then assume that there is a join discrete probability distribution $p_{xyz}$ that stands for how likely is to find a cell in the bin $x,y,z$. The two belief network models represent a specific factorization of the join distribution as a product of conditional probabilities. that is $p_{xyz}=p_{x|y}{p}_{y|z}{p}_z$ or $p_{xyz}=p_{x|z}{p}_{y|z}{p}_z$. Using a Dirichlet distribution with concentration parameters (or pseudocounts) $\mathit{\alpha }=(\alpha ,\dots ,\alpha )$ as a prior, we can integrate out all the discrete distributions. The likelihood of the data $D\equiv \left\{n_{xyz}\right\}$ given the first belief network is:

where the sums over indexes are indicated by removing them, for example: $n_{xy}\equiv \sum _z{n}_{xyz}$. Alternatively, given the second belief network we obtain:

And finally, the ratio of the two probabilities leads to:

Notice that the ratio depends only on the counts $n_{yz}$ and $n_{xz}$ which are the ones related to the links of the networks that are different between the two models. that is $V{b}_S\to T_{G2/M}$ and $T_S\to T_{G2/M}$. Then, applying the Bayesian theorem, we obtain that the probability of model $T_S\to V{b}_S\to T_{G2/M}$ given the data is:

where we assume that the prior probabilities of each model are equal, that is $P\left(T_S\to V{b}_S\to T_{G2/M}\right)=P\left(V{b}_S\leftarrow T_S\to T_{G2/M}\right)=1/2$.

Finally, substituting the data in the previous equation, that is the discrete counts $\left\{n_{xyz}\right\}$that indicate the number of cells that showed values for the variables $T_{G2/M}$, $V{b}_S$ and $T_S$ within the voxel $xyz$, we obtain $P\left(T_S\to V{b}_S\to T_{G2/M}|D\right)=1$ for different number of bins (10, 50 and 100) and pseudocounts (${10}^{-6}$,0.5 and 1). Namely, the conditional dependency structure $T_S\to V{b}_S\to T_{G2/M}$ is consistently supported by the data indicating that the correlation between S and G2/M durations is indirect and the negative correlation between bud size at the end of S phase and G2/M duration is direct. It is important to note that this approach allows us to evaluate only conditional dependencies and not causation. Indeed, it is not possible to distinguish the models (Equation 11 and Equation 12) from similar ones where the direction of the arrows are flipped. However, the fact that there is a temporal ordering of our variables (i.e. the size of the bud after S phase is determined before the duration of the G2/M phase is realized) allows to state that the link $V{b}_S\to T_{G2/M}$must be causative.

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

We are very grateful to Damien Coudreuse for extensive discussion and feedbacks on the manuscript, Manuel Mendoza and Etienne Schwob for insightful discussions, as well as Sophie Quintin and the Charvin lab for careful reading of the manuscript. We are very grateful to Felix Jonas for pointing an experimental error in the preprint version of this manuscript. We thank Sandrine Morlot for help with microscopy. We thank Michaël Knop for sharing plasmids and Joseph Schacherer for the gift of the cell cycle mutants. This work was supported by the ATIP-Avenir program (GC), a grant from the Fondation pour la Recherche Médicale (GC), and by grant ANR-10-LABX-0030-INRT, a French State fund managed by the Agence Nationale de la Recherche under the frame program Investissements d’Avenir ANR-10-IDEX-0002–02.

1. Received: December 2, 2017
2. Accepted: July 1, 2018
3. Accepted Manuscript published: July 4, 2018 (version 1)
4. Version of Record published: August 9, 2018 (version 2)
5. Version of Record updated: September 24, 2019 (version 3)

© 2018, Garmendia-Torres et al.

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