Introduction

Cell size is intrinsically linked to cellular function. For example, red blood cells must be small enough to efficiently move through capillaries, while macrophages need to be large enough to engulf pathogens. As cells grow larger, the concentration of biochemical components changes to alter the internal biochemistry of cells. If cells become excessively large, they grow poorly and exhibit features of senescence (Crozier et al., 2023; Foy et al., 2023; Khurana et al., 2023; Lanz et al., 2022, 2024; Manohar et al., 2023; Miettinen & Björklund, 2016; Tzur et al., 2009; Zatulovskiy et al., 2022). To avoid such a detrimental outcome, organisms have evolved robust regulatory circuits that sense and control cell volume across successive divisions, ensuring that biomolecular concentrations remain within functional limits. These size-control mechanisms have been extensively reviewed, providing insight into how cells link their growth and division cycles to preserve homeostasis in diverse contexts (Ginzberg et al., 2015; Lloyd, 2013; Xie et al., 2022).

One way eukaryotic cells actively control their size is by linking cell growth to specific cell cycle transitions. For example, in fission yeast a sharp cell size threshold governs entry into mitosis (Fantes, 1977; Sveiczer et al., 1996). In contrast, budding yeast shows its strongest size control at the G1/S transition in its smaller daughter cells (Di Talia et al., 2007, 2009; Johnston et al., 1977). The strength of a size control mechanism can be quantified by plotting the amount of cell growth during a given phase against the size the cell was when it entered that phase. A strong negative correlation (slope near –1) indicates that initial size differences are nearly fully corrected within one division cycle as is the case for both fission yeast and mouse epidermal stem cells (Fantes, 1977; Sveiczer et al., 1996; Xie et al., 2024; Xie & Skotheim, 2020). The corresponding slope for budding yeast at the G1/S transition is lower but still appreciable (Di Talia et al., 2007). Many bacteria employ a weaker form of size control called an “adder,” in which each cell adds a nearly constant volume from birth until division (slope near 0), regardless of its initial size (Amir, 2014; Eun et al., 2018; Jun et al., 2018; Westfall & Levin, 2017; Willis & Huang, 2017). In symmetrically dividing species, this adder mechanism gradually pushes cells towards a target size over multiple generations.

While measuring the correlations between size and growth can be used to assess size control in specific cell cycle phases, a more holistic way to assess cell size control is to consider the entire distribution of cell sizes. In this view, mutations affecting size control are defined as those that alter the coefficient of variation (CV), which is the ratio of the standard deviation to the mean (CV = σ/μ). Because this metric is normalized, it reveals how tightly cell sizes cluster irrespective of the average cell size, making it possible to compare cells across different conditions or even different organisms. Surprisingly, recent work demonstrated that budding yeast mutations with large effects on cell size only modestly or even imperceptibly affect the CV (Barber et al., 2020; Chen et al., 2020). In other words, while the average cell size changes in response to these mutations, the shape of its distribution does not. This observation raises the question of whether we have fundamentally misunderstood cell size control. Specifically, what connection should we anticipate between mutations and population-wide size variability, and is our current understanding of how growth is linked to specific cell cycle transitions compatible with these unexpected findings?

Here, we use both experimental and theoretical approaches to investigate how cell size control mutations influence population size variability. We employ an established computational model for the budding yeast cell cycle featuring a size-dependent G1/S transition in daughter cells, followed by more weakly regulated S/G2/M phases (Chandler-Brown et al., 2017). Through parameter sensitivity analysis, we find that the primary driver of changes in the CV is the division mechanism itself. Namely, the CV is primarily controlled by the difference in cell sizes at division between the larger mother and smaller daughter cells. Altering mother–daughter asymmetry proportionally shifts the CV as predicted by our computational model. In addition, G1/S size control mutations typically modulate the CV by 10–20%, consistent with the measured effects of size control mutations affecting G1/S control. Our findings show how the current framework for yeast growth and division can reconcile the paradox of why size control mutations have a limited impact on CV.

Results

Recent work showed that mutations affecting budding yeast cell size only modestly or even imperceptibly affect the CV of the population (Chen et al., 2020). A typical change in the CV was about 10% even when average cell size increased as much as 50% (Fig. 1). This raised the question as to how sensitive we should expect the population CV to be to mutations that affect cell size? To determine how sensitive the CV is to mutations to parameter values, we turned to a mathematical model of the growth and division of budding yeast cells that was previously validated experimentally (Chandler-Brown et al., 2017). While various molecular models have been proposed to explain the size-dependence of the budding yeast cell cycle (Barber et al., 2020; Schmoller et al., 2015), the Chandler-Brown model is agnostic to this debate and coarse-grains the molecular machinery into the physiological dependencies of the different cell cycle transitions. In this model, each cell cycle transition is determined by a stochastic rate that depends on physiological parameters such as cell size or growth rate. While this model is simple enough to comprehensively analyze, it is complex enough to accurately describe progression through the budding yeast cell cycle in both the larger mother and smaller daughter cells following cell division (Fig. 2A). The model is described in the Materials and Methods section. This model has 21 independent parameters that were originally fit to WT data and strikes a good balance between phenomenology and descriptiveness (Chandler-Brown et al., 2017). Notably, G1 phase is broken up into a pre-Start and a post-Start phase, where the Start transition marks the point of commitment to the cell cycle with respect to exposure to mating pheromone, which coincides with the export of the cell cycle inhibitor Whi5 from the nucleus (Hartwell et al 1974; Skotheim et al 2008; Charvin Siggia Cross 2010; Doncic Skotheim 2011). Cell size control is implemented at Start in daughter cells mainly via a linear size-dependent rate of cell cycle progression. In this way, cell size control in this model is stochastic and thus imperfect. In addition, mother cells accumulate size over successive generations because they have a non-zero growth phase in G1 and cannot lose this accumulated mass because the daughter cell is only made from the mass accumulated in the S/G2/M phases of the cell cycle. Because growth is close to exponential during most of the cell cycle, a bigger cell will accumulate mass faster than a smaller cell. This has an important consequence which will become relevant later on, namely, that a bud grown on an older cell (2nd generation or older) will become a larger daughter cell than if its progenitor was a 1st generation cell (Fig. 2A).

Figure 1:

Figure 2:

The population CV responds moderately to the drastic perturbations of Start

To begin our analysis of the sensitivity of the CV of cell size distributions, we first set out to perturb the cell size control mechanism at Start and then see how this affected the CV of the population cell size distribution at steady state. We chose this metric of variability because it is the most basic measurement of a complex population of mother and daughter cells at all phases of the cell cycle. Moreover, the distribution and population CV are easily accessible experimentally using either a Coulter counter or flow cytometer (Berenson et al., 2019), which is why it is commonly used in publications analyzing the effects of cell size control (Barber et al., 2020; Chen et al., 2020).

The implementation of the size control mechanism in the Chandler-Brown model is an imperfect sizer where the rate of going through the Start checkpoint increases linearly with cell size at a slope α and offset V₀ (Fig. 2B). One drastic change of this mechanism could be to turn it into a perfect sizer mechanism, in which the Start checkpoint becomes a deterministic transition once cell size reaches a threshold size. This can be implemented easily in the model by setting the slope α to ∞. We then fixed the free parameter V₀ such that the average size of the resulting steady-state distribution would be identical to that of WT, thus avoiding any potential change to CV solely due to a change in average size. With a perfect sizer mechanism operating at the Start transition, we measure a relative change in CV of -8% (Fig. 2C). Conversely, we can abolish the size-sensing mechanism by setting the slope α to 0. Specifically, by setting the rate of progression through Start to a constant rate independent of size, we can turn the pre-Start G1 into a stochastic timer where cells spend on average the same time in pre-Start G1 irrespective of their initial size at birth. If we set this constant rate of progression through Start such that the average size of the resulting steady-state distribution remains unchanged from WT, we find that the CV increases by 25% (Fig. 2D).

So far, our analysis suggests that even drastic perturbations to cell size control at Start in S. cerevisiae, where parameters are either set to 0 or ∞, only yield relative changes in CV up to 25%. In this light, the changes to the CV of the mutants shown in Fig. 1 lie within an expected small range (0-20%) of what one might expect from a significant perturbation to size control at Start. In other words, we should not expect to see any 50% to 100% changes to the CV from any perturbations affecting the cell cycle in G1.

Live cell analysis of Start mutants is consistent with moderate changes to the CV

Next, we sought to experimentally test our new intuition for how the population CV should respond to mutations of genes known to regulate Start. Namely, we predict that the effect on CV should be modest and below 20%. We chose to analyze two of the most well-known mutants of the Start checkpoint, cln3Δ and cln3Δwhi5Δ (Bruin et al., 2004; Costanzo et al., 2004; Cross, 1988; Nash et al., 1988). Cln3 is an activator while Whi5 is an inhibitor of Start and both proteins have been linked to specific size control mechanisms (Qu et al., 2019; Schmoller et al., 2015, 2022; Wang et al., 2009).

To identify the effect of mutations to known Start regulators on the population CV, we imaged unperturbed cells growing and dividing asynchronously in the same conditions as used by (Chandler-Brown et al., 2017). The cells were grown in a synthetic complete medium using glycerol and ethanol as the carbon source. In these conditions, cells have a longer G1 phase and exhibit stronger size control at Start in daughter cells compared to growth in glucose medium (Di Talia et al., 2007). Cells were then segmented and tracked using the Cell-ACDC software (see Methods) (Padovani et al., 2022). This allowed us to measure the cell size of 377 cln3Δ cells and 504 cln3Δwhi5Δ cells at steady state (Fig. 3C, E). The CV increased ∼9% for cln3Δ mutant cells and ∼27% for cln3Δwhi5Δ double mutant cells. It is notable that removing the size-sensing inhibitor Whi5 along with the activator Cln3 yields cells with an average size similar to WT cells, yet with a CV of 27% bigger than the WT. This is approximately the magnitude of change we expected from turning the WT size control mechanism into a stochastic timer (Fig. 2D).

Figure 3:

Next, we set out to investigate whether size was still the best predictor of the Start transition in the cln3Δ and cln3Δwhi5Δ mutants as had previously been found for WT cells (Chandler-Brown et al., 2017). To test this, we performed a series of logistic regressions using individual and combinations of statistical predictors to describe the Start transition. Following Chandler Brown et al. (2017), we chose cell size, age, and added size since birth as the individual predictors of the timing of the transition. We also combined predictors together to perform 2- and 3-variable logistic regressions. We then examined the deviance of the prediction for each logistic regression to identify the best predictors of the transition. The deviance can be interpreted as a measure of goodness of fit: the lower the deviance, the more accurate the logistic regression is at predicting the Start transition. The resulting deviance measurements for the WT data of the original publication are shown in Fig. 3B with cell size being the best individual predictor of Start in this case. In both the cln3Δ (Fig. 3C-D) and cln3Δwhi5Δ (Fig. 3E-F) mutants, we see cell size become less important as an individual predictor in favor of cell age. This is particularly interesting given the expected magnitude of change of CV for a pure stochastic timer in pre-Start G1 and the resulting change in CV for this mutant (Fig. 2D). Indeed, a stochastic timer is a good description of the pre-Start G1 phase of cln3Δwhi5Δ mutant daughter cells.

Parameter sensitivity analysis identifies division mother-daughter asymmetry as a major determinant of cell size variability

After finding that mutations affecting the cell size control mechanism at the Start checkpoint had only a limited impact on the CV of the steady-state size distribution, we next sought to identify which (other) cell cycle parameters exert a more significant influence. To do this, we went back to theory and performed a local parameter sensitivity analysis of the Chandler-Brown model by computing the numerical gradient of the CV in the 21-dimensional parameter space of the model (Fig. 4A, see details in Materials and Methods). This gradient is a 21-dimensional vector that quantifies the local contribution of each parameter to the CV, enabling direct comparisons between them. Because parameters have different units and scales, we need to rescale them properly for comparison. To do this, we followed a standard strategy and computed the numerical gradient with respect to the logarithm of each parameter which can be interpreted as transforming every parameter into a free-energy equivalent (Gutenkunst et al., 2007). Additionally, we examined both the CV of the steady-state distribution (CV_SS) and that of the daughter size distribution at the Start checkpoint (CV_Start). While CV_Start is less readily accessible experimentally because it requires live-cell tracking, it is particularly relevant to the previously studied cell size control mechanisms operating at the Start transition in daughter cells. Since the resulting 21-dimensional gradient vectors for both CVs are difficult to interpret at first glance, we sought to gain an intuition for how these perturbations affect cell size control by perturbing parameters along the gradient direction and observing the resulting effects on cell cycle dynamics. Specifically, we explored the gradient’s influence by modifying the value of each individual parameter in the direction of the gradient. The i^th parameter θ_i becomes , where ê_i is a unit vector whose sole component is in the direction of parameter θ_i, and where ε = 0.5 is a scaling factor. Since the gradient identifies the direction in parameter space where the magnitude of the CV changes the most, we define positive ε as the direction yielding an increase in CV.

Figure 4:

From our computation (Fig. 4A), we see that the dominating directions in parameter space driving changes to the steady state size distribution, identified by the , can be explained to be the combination of two main effects: decreasing the growth rate and lengthening the post-Start G1 timer for the mothers. Slow growth decreases the size of the bud, resulting in a decreased size at birth for new daughter cells. While slowing down the growth rate creates smaller cells in general, this effect is less in mother cells because they also lengthen their post-Start G1 phase. Altogether, this parameter direction corresponds to a regime where mothers are bigger and daughters are smaller, which is thus expected to amplify the asymmetry between these two types of cells to widen the overall cell size distribution with an increase of CV of more than 40% in our simulations for ε = 0.5 (Fig. 4B). Our gradient analysis further confirms the modest effect of Start size control parameters on CV relative to the first two vector components shown in Figure 4A. Importantly, modifying parameters along the gradient direction has a greater effect on CV than altering the G1 size control mechanism to a pure sizer or timer, or randomly perturbing the parameter space with the same magnitude (Fig. 4C). This is noteworthy because shifting the control mechanism requires extreme parameter modifications, such as setting a parameter to zero or infinity, whereas perturbations along the gradient direction are comparatively subtle, yet more effective in modulating the CV.

Having identified daughter-mother asymmetry as crucially important for driving changes to the CV_SS of the population size distribution, we next sought to better quantify this asymmetry. To do this, we use the Jensen-Shannon divergence D_JS(D, M), where the arguments D and M indicate the probability distributions for daughter and mother sizes respectively. This measure is a symmetrized version of the Kullback-Leibler divergence that allows us to measure the level of overlap or similarity between two probability distributions (Lin, 1991). The closer D_JS is to 0, the more they overlap, and the closer it is to 1, the more separated they are. We then proceeded to look at how CV_SS correlated with such Jensen-Shannon divergence in multiple conditions, including random parameter perturbations of equivalent magnitude (Fig. 4D). As expected, the maximum CV_SS variations are found in the direction of the gradient, but, remarkably, scatter plots of the CV_SS as a function of the asymmetry between subpopulations show them to be strongly correlated in general. The trend is also consistent with the experimental values for the cln3Δ and cln3Δwhi5Δ mutant cells we examined earlier. This suggests that the differences in size between the mother and daughter populations is the dominating mode driving CV_SS variation. There are only a few outliers to this general trend, including the G1 timer that leads to lower asymmetry with higher CV_SS. However, removing all G1 size control so that the transition to S phase is governed by a timer is an extreme perturbation that is not a modulation of the model parameters. Overall, these results suggest changing the level of size asymmetry between daughters and mothers is the most efficient way to modulate the CV_SS.

Parameter sensitivity analysis identifies subpopulations resulting from division asymmetry as a major determinant of cell size variability at Start

After analyzing the determinants of the CV_SS of the population size distribution, we conducted a similar analysis to identify which parameters influence cell size variability at Start. This is particularly relevant because size control at Start could be thought to ensure that cells reach a critical size before initiating DNA replication, rather than merely reducing CV across the population. We therefore examined the parameter gradient having the largest effect on the CV of the daughter size distribution at Start, CV_Start. The parameter gradient is dominated by a single leading component, the division rate of mother cells, and 7 other significant components that alter the cell cycle in subtle ways (Fig. 4A). Perturbing the model along the parameter gradient directly affects the size asymmetry at Start and has a much larger effect on CV_Start than random parameter perturbations (Fig. 4E-F). Perturbations along the gradient increase the size asymmetry between daughters born from first-generation cells and those born from second-generation or later cells (Fig. 4E). As previously noted, due to the exponential accumulation of size, daughters born from larger mother cells are themselves larger than those born from first-generation cells. For WT cells, this difference in size is present but much smaller. However, perturbing the model along the gradient direction accentuates the effect and greatly changes CV_Start. While significant, perturbations along the gradient have smaller effects on the CV than a pure deterministic sizer, which forces all cells below the critical size to pass through Start at the same threshold to sharply narrow CV_Start. After performing the gradient analysis, we sought to determine if there was a general connection between the subpopulation structure and CV_Start. To do this, we again used the Jensen-Shannon divergence, but this time to measure the differences between the size distributions of the daughters born from 1st generation cells and the daughters born from 2nd generation or later cells, D_JS(D₁, D₂₊) (Fig. 4G). This revealed a clear correlation between CV_Start and the daughter cell population structure. Outliers of the trend correspond to drastic parameter changes, such as specifying a deterministic sizer or timer mechanism.

It is important to note that our parameter sensitivity analysis assumes all 21 parameters of the model are independent from each other. In live cells however, there is coordination between cell cycle events meaning that there probably exist correlations between some of our 21 parameters that might be revealed by a larger scale mutational analysis. Thus, when we define a pure sizer or timer in pre-Start G1 (Fig. 2C,D) the parameters regulating the rest of the cell cycle remain unchanged. This could explain the discrepancy between the observed asymmetry of the cln3Δwhi5Δ mutant and the pre-Start G1 timer models as shown in Fig. 4D. Both models display a similar CV, but the asymmetry between the daughter and the mother sub-distributions is decreased rather than increased, as our analysis would predict.

Mother-daughter asymmetry is highly correlated with population CV in S. cerevisae cells growing on different carbon sources

Our computational analysis suggests that mother-daughter asymmetry is a key determinant of the CV of cell size. However, testing this hypothesis experimentally was not straightforward because the mutations we have previously studied primarily affect the Start transition and do not directly alter mother-daughter asymmetry. To address this, we need to find a way to increase mother-daughter asymmetry while minimally impacting other cell-cycle aspects. We thus examined WT cells growing under different conditions. This is a ‘natural’ perturbation, minimally perturbating cell homeostasis, where we further expected that changes of growth rates would give rise to variations in mother-daughter size-asymmetry. This expectation is based on multiple findings. First, the duration of the budded phase, when cell growth is directed into the daughter, remains relatively constant across different growth rates (Hartwell & Unger, 1977). Because the daughter-to-mother size ratio at division is determined by the length of the budded phase relative to the time required to double a cell’s biomass, slower growth should increase mother-daughter asymmetry. Second, the growth rate is one of the dominant parameters of the CV_ss gradient direction as identified by our parameter sensitivity analysis (Fig. 4A). Thus, by analyzing yeast cells in different growth conditions, we could experimentally test our hypothesis that mother-daughter asymmetry is a primary determinant of the CV of cell size.

To generate different cell size distributions, we examined S. cerevisiae cells growing in synthetic complete media with 12 different carbon sources using a Coulter counter to measure cell size (see Materials and Methods; Fig. 5A). These distributions exhibited a range of cell size CVs from 0.4 to 0.62 (CV_WT = 0.41), which largely, but not completely, correlated with the population growth rate (R²=0.6; Fig. 5B). This is consistent with the fact that growth rate indeed is a major determinant of CV_ss.

Figure 5:

Next, we sought to measure the asymmetry at division in several different growth conditions exhibiting a range of CVs. To do this, we examined MYO1-mKate cells that express a fluorescent Myo1-mKate fusion protein from its endogenous locus. This myosin protein disappears from the bud neck following cytokinesis to allow an accurate determination of the time of division (Bi et al., 1998), and the corresponding daughter-to-mother size ratio (Fig. 5C). Consistent with our hypothesis, we find a strong correlation (R²=0.86) between the daughter-to-mother size ratio and the population CV (Fig. 5D). This confirms the model prediction that daughter-to-mother size ratio is a major mechanism that drives CV_ss variation.

Discussion

Our study analyzes the determinants of cell size variability in S. cerevisiae to identify mother-daughter asymmetry as a primary driver of the coefficient of variation (CV) of cell size within a population. While previous research has largely focused on size control mechanisms at Start, we find that even the strongest possible perturbations to the G1/S transition have a limited impact on CV, typically in the range of 10-25%. Instead, the degree of size asymmetry at division plays a dominant role in shaping population-wide size variability. This conclusion is supported by both computational modeling and experimental measurements, which reveal a strong correlation between mother-daughter size asymmetry and CV across different genetic and environmental conditions. These findings challenge the prevailing view that G1 size control alone is sufficient to regulate population size variability and instead suggest that asymmetric division is integral to cell size homeostasis. Indeed, division asymmetry poses a significant barrier to maintaining a narrow cell size distribution.

Our computational parameter sensitivity analysis further refines this understanding by identifying two distinct types of asymmetry that influence CV: (1) the size difference between mother and daughter cells, and (2) the differential size of daughters born from first-generation and later-generation mothers. These asymmetries emerge from the growth dynamics of larger mother cells producing larger daughters, due to exponential biomass accumulation, and mother cells growing larger with each cell division cycle. Experimentally, we validate these predictions by growing yeast in different nutrient conditions and observing that variations in growth rate correlate with shifts in mother-daughter size asymmetry and, consequently, in CV. These results underscore that size asymmetry is not merely a byproduct of the asymmetric cell division cycle of budding yeast but is the key feature controlling cell size heterogeneity.

More broadly, our findings suggest that population-level size control in budding yeast arises from the interplay between asymmetric division and size control at Start, rather than size control alone. While deterministic sizer mechanisms at Start can narrow the size distribution, they do not significantly alter the underlying size asymmetry between subpopulations and therefore have limited effect on the population CV. However, sizer mechanisms at Start do have a crucial effect on the cell size at the time of DNA replication and to ensure a certain minimal size before attempting cell division. Ultimately, while we do not currently know the evolutionary pressures that shape the asymmetric division cycle of budding yeast and other species, we can certainly say that it poses a significant problem for maintaining a narrow distribution of cell sizes.

Finally, that mother-daugher asymmetry is strongly correlated with CV is in line with the existence of a small number of ‘soft-modes’ (or in machine learning/data science term, low dimensional reduction) observed in multiple biological systems (Russo et al., 2025). It has been proposed that such soft-modes naturally evolve to allow for homeostatic control. It is much ‘easier’ biologically speaking to control a few canalized modes than to independently buffer the potentially infinite number of possible perturbations. Our simulations and experiments are consistent with the existence of a soft-mode in cell size distributions for two reasons. First, random perturbations (both in models and experimentally) appear to move the system along a dominating direction of increased mother-daughter asymmetry strongly correlated with CV_SS. Second, most random mutations nevertheless have a limited effect on CV_SS (Chen et al., 2020). This can further be seen and explained with the Chandler-Brown model. Namely, most random mutations barely change CV_SS (10% or less for most perturbations, compared to up to 40% for directed perturbations of equivalent magnitude), precisely because a random parameter change in a high-dimension parameter space has very little chance to be significantly aligned with the dominating direction of variation (the soft-mode). Taken together, our analysis shows how combining modelling and experiments to identify gradients of variations of phenotypes can uncover controllable and interpretable soft-modes, such as mother-daughter division asymmetry.

Materials and Methods

Mathematical Model

The Chandler-Brown (Chandler-Brown et al., 2017) model simulates a population of cell volumes growing exponentially with time. We note here that we use volume interchangeably with the total protein content, which was found to accumulate exponentially. Geometric volume exhibited slightly different dynamics, possibly due to systematic error in measurement of the complex geometric dynamics that characterize the budding yeast cell cycle and possibly due to modest changes in protein density. After birth, there are separate cell cycles for the smaller daughter and larger mother cells (Fig. 2A). The daughter cells begin their cell cycle at birth in pre-Start G1. Then, at each time step, the cell has a chance of progressing through the Start checkpoint with a rate k_Start which is a function of the current cell size. In the original study, the authors performed logistic regressions on various predictors to identify the best statistical predictor for the Start transition, which led them to identify cell size as the single best predictor. For this reason, the authors chose to model this size-dependent rate of going through the Start checkpoint by a linear function which has two parameters, the slope α and the offset V₀ (Fig. 2B). That the rate of progression through Start increases with cell size V is the model’s implementation of G1 cell size control in daughter cells. This results in the time spent in G1 being inversely correlated with cell size at birth, as previously observed (Di Talia et al., 2007). After Start, daughter cells enter a short post-Start G1 timer period where cells spend roughly the same amount of time in this phase regardless of their size at the Start transition. This behavior is implemented through the very weak size dependence of the stochastic rate of progression to the next phase of the cycle (see Fig. 2D for a different but similar example). Next, cells enter the final S/G2/M phase of the cell cycle in which all cell growth is directed into the bud that will become the next daughter cell at division. At each time step during S/G2/M, cells have a chance of dividing proportional to the stochastic rate k_Div, which is a linear function of the current cell size and the cell size at Start. Importantly, just like for the post-Start G1 transition rate, k_Div is only weakly dependent on cell size and S/G2/M is close to a timer as well. After division, the bud compartment and the main compartment are separated, and the bud begins a new cell cycle as a daughter cell, while the mother begins its separate cell cycle as a second-generation mother cell. As mother cells are born bigger and display little to no amount of cell size control, they are modelled as beginning their cell cycle already at the Start transition. Mother cells spend a short amount of time in post-Start G1 before entering an S/G2/M characterized by a stochastic rate k_Div. Daughter and mother cell cycles are molecularly different, as there are several daughter specific proteins including Ace2 and Ash1 that impact the cell cycle (Colman-Lerner et al., 2001; Di Talia et al., 2009). This is implemented in the model by daughter cells and mother cells having independent and different parameter values for their cell cycle progression rates but having the same functional forms.

The model simulates an exponentially growing population of thousands of cells independently going through their cell cycles, but does not include cell death. For numerical purposes, we allow a maximal number of cells in the population such that when this number is reached, cells are randomly dropped out of the population. Over time, this allows us to reach a steady state in the growth of the population and allows us to look at the cell size distribution at various points of the cell cycle.

To generate the model predictions of Figures 2 and 4, we simulated the cell cycles of a maximum of 10⁴ cells for 2000 time-steps corresponding to an equivalent number of minutes for cell growth and cell cycle progression. In all simulations, we ensured the population reached steady state before performing the analysis. We refer the reader to the original publication of the model for more details on the implementation (Chandler-Brown et al., 2017).

Parameter sensitivity analysis

To compute derivatives of any function f(θ) with respect to the logarithm of the parameters, we simply perform a change of variable to find that Using this equality, we can simply use numerical differentiation to approximate the gradient along the parameter direction θ with the following formula , where τ is the differentiation step. We can take τ to be proportional to the value of θ such that τ = hθ, where h is a small relative perturbation (we choose h = 0.05). Thus, we get the final equation for the component of the gradient along parameter direction θ with respect to the logarithm of the parameter:

Each gradient component computation requires running the model twice. First, we run the model with the corresponding parameter component altered to θ(1 + h), and then a second time with θ(1 − h). For each of these runs, we let the population reach steady-state and compute the size distributions from which we extract mean, standard deviation and CV. These measures are then used in the equation above to approximate the gradient component. We then repeat this computation for all 21 independent parameter directions.

Experimental strains and growth conditions

The XG04 strain was used to measure the coefficient of variation of cell size distributions in different growth conditions. The MYO1-mKate strain (MS358) was used to determine daughter and mother cell size upon division by microscopy. Yeast cells were cultured in synthetic complete media (SC) with 2% different carbon sources. For the microscopy experiments, SC + 2% glucose, SC + 2% glycerol + 1% ethanol, SC + 2% trehalose were used. For the coefficient of variation measurements, SC media with 2% different carbon sources (fructose, glucose, sucrose, mannose, acetate, galactose, lactate, ethanol, pyruvate, glycerol, trehalose, and melibiose) were used.

Cell growth rate measurements

To measure the growth rate of cells in a specific carbon source, cells were first cultured for more than 10 doubling times to ensure they were in the steady state of the exponential phase. Cells were then diluted into a pre-heated flask with 50 ml of fresh media (OD600=0.01). Cells were incubated at 30°C and OD600 was measured every 1-2 hours. To determine the specific growth rate, the slope of log (OD600) versus time was calculated using a linear fit. There were at least two biological replicates for each condition.

Coefficient of variation measurements

Cells were first cultured for more than 10 doubling times to ensure they were in the steady state of the exponential phase. Cells growing at an OD600 of 0.1–0.2 were then sonicated and diluted 100 times in 10 mL of Isoton II diluent (Beckman Coulter #8546719) prior to measurement. The coefficient of variation was determined using a Beckman Coulter Z2 counter. Cell volumes below 10 femtoliters (fL) or above 300 fL were excluded from the analysis. There were at least two biological replicates for each condition.

Mother-to-daughter cell size ratio measurements

Cells expressing a Myo1-mKate myosin fusion protein were used to determine the cell size of mother and daughter cells at division. Yeast cells were grown in SC media supplemented with the indicated carbon sources to exponential phase (OD = 0.1–0.2). 80 µl cell culture and 200 µl fresh medium were loaded into the corresponding wells of a microfluidic plate (CellASIC #Y04C-02-5PK). The microfluidic plate was then connected to the CellASIC ONIX2 Microfluidic System to control the media flow rates. Media was initially perfused into the chamber for 2 minutes at 8 psi, followed by cell loading for 10 s at 2 psi. Continuous perfusion of fresh medium at 2 psi was maintained until imaging was completed. A Tempcontrol 37-2 digital system ensured cell growth at 30°C. Cells were imaged on a wide-field epifluorescence Zeiss AXIO Observer.Z1 microscope (63X/1.4NA oil immersion objective and a Colibri LED module). mKate was imaged in the red channel (555 nm LED module; 25% intensity; 1 second exposure) and phase contrast images were taken to give cell boundaries. Cells in glucose and glycerol/ethanol were imaged for 8 hours at 5 min intervals, while cells in trehalose were imaged for 15 hours at 10 min intervals. Cell boundaries were automatically segmented in Cell-ACDC (Padovani et al., 2022) using the software’s default settings, followed by manual correction of segmentation errors. For S/G2/M phase cells, the disappearance of the MYO1-mKate signal at the bud neck marked the time of the cell division. At division, mother and daughter cell sizes were then obtained using Cell-ACDC’s volume algorithm.

Yeast strains

MS358

W303 WHI5pr-WHI5-mCitrine::ura; whi5Δ::cgTRP; MYO1-3xmKate2::kanMX6; ADE2 MATa

Source Swaffer et al., 2023

XG04

W303 PUS1-EGFP:KanM*6; pdr5Δ:leu2; RPS9A-Halotag:HygB; ADE2 MATa

Source This study

Data availability

We have generated very big movies (several TB of data ) which are not easy to share or to deposit. We will share movies with interested parts upon publication.