ABSTRACT
The longer cells stay in particular phases of the cell cycle, the longer it will take these cell populations to increase. However, the above qualitative description has very little predictive value, unless it can be codified mathematically. A quantitative relation that defines the population doubling time (Td) as a function of the time eukaryotic cells spend in specific cell cycle phases would be instrumental for estimating rates of cell proliferation and for evaluating introduced perturbations. Here, we show that in human cells the length of the G1 phase (TG1) regressed on Td with a slope of ≈0.75, while in the yeast Saccharomyces cerevisiae the slope was slightly smaller, at ≈0.60. On the other hand, cell size was not strongly associated with Td or TG1 in cell cultures that were proliferating at different rates. Furthermore, we show that levels of the yeast G1 cyclin Cln3p were positively associated with rates of cell proliferation over a broad range, at least in part through translational control mediated by a short uORF in the CLN3 transcript. Cln3p was also necessary for the proper scaling between TG1 and Td. In contrast, yeast lacking the Whi5p transcriptional repressor maintained the scaling between TG1 and Td. These data reveal fundamental scaling relations between the duration of eukaryotic cell cycle phases and rates of cell proliferation, point to the necessary role of Cln3p in these relations in yeast and provide a mechanistic basis linking Cln3p levels to proliferation rates and the scaling of G1 with doubling time.
INTRODUCTION
Recurring shapes and patterns in nature are sometimes described with mathematical relationships. As a result, these natural processes can be predicted and understood better. Regarding patterns of eukaryotic cell division, one could ask: How are the lengths of eukaryotic cell cycle phases related to each other and to the total doubling time of the population? Can such relations be described mathematically, in the form of a scaling formula? If so, what are the molecular mechanisms that govern the scaling? A scaling relation that describes eukaryotic cell division would be a significant advance. For example, it could serve as a point of reference against which the effects of genetic or other perturbations can be evaluated.
The ‘textbook’ view in the coordination of growth and division in the eukaryotic cell cycle (e.g., see Fig. 10-26 in (MORGAN 2007)) is that expansion of the G1 phase of the eukaryotic cell cycle accounts for most, if not all, of the lengthening of the cell cycle in slower proliferating cells, in budding yeast (JOHNSTONet al. 1977; BRAUERet al. 2008) or humans (BASERGA 1985; FISHER 2016). However, there is no report in the literature of a quantitative relation that defines the doubling time (Td) as a function of the time yeast or human cells spend in the G1 phase (TG1). Here, based on all the available data for budding yeast and human cell populations, we derived for the first time in the field scaling relations between TG1 and Td. These scaling relations also allowed us to critically evaluate the role of cell cycle regulators in yeast cells proliferating at different rates.
Two key regulators of the length of the G1 phase in S. cerevisiae are the Cln3p and Whi5p proteins. The G1 cyclin Cln3p promotes initiation of DNA replication (CROSS 1988; NASHet al. 1988). In contrast, the transcriptional repressor Whi5p acts analogously to the retinoblastoma gene product in animals, to inhibit the G1/S transition (COSTANZOet al. 2004; DE BRUINet al. 2004; PALUMBOet al. 2016). It has been reported that while synthesis of Cln3p parallels cell size, the synthesis of Whi5p is independent of cell size (SCHMOLLERet al. 2015), arguing that dilution of Whi5p as cells get bigger in G1 governs the length of the G1 phase (SCHMOLLER AND SKOTHEIM 2015; SCHMOLLERet al. 2015).
Here, we obtained the first measurements of Cln3p and Whi5p levels as a function of proliferation rates in steady-state cultures. The levels of Cln3p varied over a broad range, due to a uORF affecting translation of CLN3. Our data also show that loss of Whi5p does not significantly affect the scaling relation between Td and TG1. Instead, we provide strong evidence for the functional and molecular basis for the necessary role of Cln3p in this process.
MATERIALS AND METHODS
Strains
Unless stated otherwise, S. cerevisiae wild-type, cln3Δ and whi5Δ strains were in the BY4741 background (NCBI Taxon 559292; MATa, his3Δ1, leu2Δ0, ura3Δ0, met15Δ0) and they have been described previously (SOMAet al. 2014). For protein surveillance, we constructed an otherwise wild type strain that carried epitope-tagged WHI5 and CLN3 alleles at their endogenous chromosome locations. First, a commercially available WHI5-TAP::HIS3 strain (BY4741 otherwise; GE Healthcare) was backcrossed three times into the W303 background (NCBI Taxon 580240; MATa leu2-3,112 trp1-1 can1-100 ura3-1 ade2-1 his3-11,15). Then, it was crossed with an otherwise wild-type strain carrying a CLN3-13MYC allele (W303 background) described elsewhere (THORBURNet al. 2013), and kindly provided by Dr. A. Amon (MIT and HHMI). The resulting diploid was sporulated and dissected, to obtain MATa haploid segregants carrying both the epitope-tagged WHI5 and CLN3 alleles (strains HB94/97; MATa CLN3-13MYC::TRP WHI5-TAP::HIS leu2 ura3 met15), which were used in the experiments shown in Figure 4. We verified expression of Whi5p-TAP and Cln3p-(Myc)13 in this strain (see Supplementary File 1), and their absence in whi5Δ or cln3Δ strains, respectively. We also generated a derivative of this strain, which lacks the uORF in the 5’-leader of the CLN3 mRNA. To this end, we used plasmid A-315T-pMT10 we had described previously (POLYMENIS AND SCHMIDT 1997), as a template in a PCR reaction with forward (5’-CAAGAACTACCATTCGACAGG-3’) and reverse primers (5’-CGTACAGAAAGCGTATCAAA-3’) to generate a product that carries in the 5’-leader of CLN3 the URA3-marked A-315T mutation that inactivates the uORF. We then used this PCR product to transform strain HB94 (WHI5-TAP, CLN3-13MYC). Genomic DNA of transformants was sequenced to verify the presence of the A-315T mutation. Confirmed A-315T mutants were then backcrossed with wild type (W303) to segregate away possible secondary mutations at other loci. The resulting heterozygote was sporulated and dissected to isolate a WHI5-TAP, A-315T-CLN3-13MYC segregant (HB104), which was used in the experiments shown in Figure 4.
Datasets for population-based cell cycle parameters
All the obtained variables we report here represent population averages. They do not resolve intergenerational differences in cell cycle progression of the same cells in successive cell cycles. In the context of this study, population averages hold significant advantages: First, they are easily obtained; Second, they are ubiquitously used and reported in the literature; Third, they allow straightforward comparisons between different systems, for example between yeast and human cells (see Figure 1).
For yeast, the data we collected (Table S1) were from wild type strains from various backgrounds, except in the few cases where they carried temperature-sensitive alleles, such as cdc mutations (JAGADISH AND CARTER 1977), to estimate the length of the G1 phase upon transfer to the non-permissive temperature. The methods used to calculate the fraction of G1 cells included: measurements of the DNA content of the cells by flow cytometry (SLATERet al. 1977; JOHNSTONet al. 1980; GUOet al. 2004; BRAUERet al. 2008; HENRYet al. 2010); budding (TYSONet al. 1979; RIVIN AND FANGMAN 1980); sensitivity to cell cycle arrest before DNA replication by pheromone (HARTWELL AND UNGER 1977; JAGADISH AND CARTER 1977), or cdc (JAGADISH AND CARTER 1977) mutations. In this study, to obtain the fraction of G1 cells (e.g., see Figures 3, 4), we used DNA content measurements by flow cytometry, as described previously (HOOSEet al. 2012; HOOSEet al. 2013).
For human cells, earlier studies employed 3H-thymidine pulses or division waves after thymidine block (BASERGA 1985). The doubling times of the NCI-60 human cancer cell lines we included in Table S2 are known (ROSSet al. 2000; SCHERFet al. 2000; POLYMENIS 2017), but there was no quantitative cell cycle data for most of the cell lines. However, images of DNA content profiles for the NCI-60 panel, albeit with no quantification, have been published (GARNER AND EASTMAN 2011). We requested and obtained high-resolution files of these images from Dr. Alan Eastman (Geisel School of Medicine - Dartmouth College).
From the entire DNA content histogram, to quantify the fraction of cells in G1, we used imaging software to measure the area on the left side of the G1 peak (from peak to valley) and multiplied this area by two, as has been described previously (JOHNSTONet al. 1980). This approach avoids complications from heavy right side tails due to S phase cells and yields an acceptable estimate of the relative G1 length as a fraction of total cell cycle time. We then combined these values with all others available from human cells, cancerous and normal (SISKEN AND KINOSITA 1961; DEFENDI AND MANSON 1963; LENNARTZ AND MAURER 1964; AOKI AND MOORE 1970; BASERGA 1985; KUMEIet al. 1989; BRONSet al. 1992; LUCIANIet al. 2001; HAHNet al. 2009), to compile a dataset of 96 values for G1 length (TG1) and doubling time (Td) for human cells, shown in Table S2.
Estimates of G1 length
The values we show in Tables S1 and S2 were obtained from studies reporting on the relative duration of the G1 phase. To estimate the absolute length of the G1 phase, TG1, we multiplied the relative G1 length by Td (Tables S1, S2). This simple equation is the appropriate one to use with chemostat data when as many cells are removed as are being produced in the culture (HOFFMAN 1949). Subtracting TG1 from Td yields the duration of the rest of the cell cycle phases (TnonG1). For non-chemostat data, other more elaborate equations could be used, especially for the asymmetric patterns of division of budding yeast (HARTWELL AND UNGER 1977; JOHNSTONet al. 1980). However, for simplicity and ease of comparison across systems, we uniformly applied the simple equation mentioned above. Furthermore, inaccuracies in the absolute values of TG1 may only affect the intercept of the linear relation between Td and TG1, but not the slope that describes the fundamental scaling between Td and TG1, or any of our conclusions. Indeed, when we plotted in the same manner as in Figure 1 only the chemostat values in Table S1 (94 data points), the slope of LnTd ∝ LnTG1 was 0.6107. For the remaining, non-chemostat values (55 data points), the slope of LnTd ∝ LnTG1 was 0.6074.
Lastly, a limitation of the non-chemostat data in yeast and all the data from human cells is that it is assumed that cell death contributes negligibly to the doubling time of the population. This assumption is reasonable in yeast because young cells vastly outnumber older ones approaching senescence. However, it may be of concern in mammalian culture systems. Hence, our data with human cells should be interpreted with caution, because the fraction of growing cells in the culture may be significantly lower than one. Also, although we are looking at trends that seemingly hold across a multitude of human cell types, the data were overwhelmingly derived from cancer cell lines, which in many cases have altered cell cycles.
Chemostat cultures
The experiments were done using a New Brunswick BioFlo (BF-110) reactor with a working volume of 880 mL. The reactor was run at room temperature, as described earlier (HENRYet al. 2010). In each experiment and at each dilution rate the reactor was sampled several times to measure protein levels by immunoblots, the DNA content with flow cytometry, and the cell size and cell density of the culture using a Beckman Z2 channelyzer (HENRYet al. 2010; HOOSEet al. 2012), as indicated. We measured the cell density at every sampling, to ensure that we never reached ‘wash-out’ conditions at the high dilution rates. In every experiment the cell density remained >1E+07 cells/ml and did not vary more than 3-fold between the lowest and highest dilution rates.
Protein surveillance
Proteins were resolved onto 4-12% Tris-Glycine gels (Thermo Scientific, Cat#: XP04125BOX). Cln3p-(Myc)13 was detected with an anti-Myc antibody (Abcam, Cat #: ab13836). All other procedures for TAP-tagged protein detection, extract preparation for immunoblots and their analysis have been described elsewhere (BLANKet al. 2017).
Statistical analysis
Data were analyzed and displayed with R language packages. All R functions, the corresponding packages, and their use are listed in Table S3. To build the linear models we described using the values for the yeast (Table S1) and human (Table S2) datasets, we first examined if the assumptions for building simple, linear parametric models were satisfied. The diagnostic residual plots evaluating whether the errors were independent of each other, normally distributed around a mean of zero and equal variance, are shown in Figure S2. In both the yeast and human datasets, the existence of a few outlier points appeared to violate the necessary assumptions (Figure S2; p<0.05 for assessment of the assumptions using the global test on four degrees-of-freedom (PENA AND SLATE 2006)). Hence, we opted for non-parametric, robust linear regression models based on Siegel repeated medians (Table 1). For the meta-analysis of cell size data (see Figure 2) we used the metafor R language package (VIECHTBAUER 2010). Briefly, the correlation coefficients from each study were transformed using Fisher’s z transformation. An unbiased random-effects analysis, as opposed to a fixed-effects one, was then performed using this index, and the summary values were converted back to correlations and displayed as such with forest plots (Figure 2, Table S3).
Data availability
Strains and plasmids are available upon request. The authors affirm that all data necessary for confirming the conclusions of the article are present within the article, figures, and tables. Figure S1 shows goodness-of-fit plots for lognormal distribution of yeast and human TG1 values. Figure S2 shows diagnostic plots of simple linear regression models for Td and TG1 values of yeast and human cells. Figure S3 shows additional chemostat experiments with whi5Δ and cln3Δ cells. Table S1 lists all the cell cycle values for yeast cells from the literature. Table S2 lists all the cell cycle values for human cells from the literature. Table S3 lists all R functions, the corresponding packages, and their use. File S1 contains all raw immunoblot images generated and used in this study. All supplementary figures, tables and files can be found at (10.6084/m9.figshare.7011275).
RESULTS
Rationale
The rationale for the experiments we describe was the following: First, use all the available values from the literature to derive a quantitative relationship of the population doubling time (Td) as a function of the time eukaryotic cells spend in the G1 phase of the cell cycle (TG1) (Figure 1). Second, based on the same datasets and analyses, examine if cell size is also related to Td or TG1, because cell size is often used as a proxy for the control of cell division by nutrients (Figure 2). Third, use the linear relation linking Td and TG1 as a metric to evaluate the contributions of Whi5p and Cln3p, two proteins that govern the G1/S transition in budding yeast (Figure 3). Fourth, if Cln3p or Whip5p impinges on the relation between Td and TG1, then provide a mechanistic understanding of its role (Figure 4).
TG1 values are distributed lognormally, consistent with exponential patterns of growth
We compiled the available values for Td and TG1 from the literature for budding yeast (Table S1) and human (Table S2) cells (see Materials and Methods). With the dataset of TG1 values at hand, we next examined their distribution. Knowing how the TG1 values are distributed will inform how to better model TG1 against Td and offer some insight into the processes that determine G1 length. We found that TG1 values were not normally distributed for yeast (p = 4.434E-14, Shapiro-Wilk test) or human cells (p = 1.039E-07, Shapiro-Wilk test). Instead, TG1 values fit better a lognormal distribution. For example, for yeast TG1 values, the Anderson-Darling statistic was the lowest for the lognormal distribution (0.347), compared to other distributions (Weibull: 1.693; gamma: 1.521; exponential: 2.462). As expected for lognormal distributions, log-transformed values of TG1 were normally distributed for yeast (Figure S1A-D, p = 0.1871, Shapiro-Wilk test) and human cells (Figure S1E-H, p = 0.3099, Shapiro-Wilk test). The apparent lognormal distribution of TG1 values is consistent with a multiplicative process of many, positive, independent random variables that determine the G1 length (KOCH 1966). Lognormal distributions are very common in biological growth processes (MOSIMANN 1988). In cell proliferation, lognormality has been proposed to reflect exponential patterns of growth in mass. Despite fluctuations in the growth rate constant, the growth of the overwhelming majority of cellular components is influenced similarly, leading to lognormality (KOCH AND SCHAECHTER 1962; KOCH 1966). In budding yeast and other cell types there is evidence for exponential patterns of protein synthesis (ELLIOTT AND MCLAUGHLIN 1978; DI TALIAet al. 2007; TZURet al. 2009) and increase in mass in the cell cycle (BRYANet al. 2012; SONet al. 2012). Such considerations accommodate the lognormality of TG1 values we describe here.
Strong association between TG1 and Td, but non-G1 phases also expand in lower proliferation rates
To test for association between TG1 and Td we used the distribution-free Spearman’s and Kendall’s tests for independence based on ranks. We used these non-parametric, distribution-free tests because of the existence of outliers even in log-transformed TG1 values (e.g., see Figure S1). The high values (> 0.75) of the rank correlation coefficients (τ for Kendall’s and r for Spearman’s; see Table 1) show a strong positive association between TG1 and Td, for both yeast (Figure 1A) and human (Figure 1C) cells. Interestingly, however, the duration of the non-G1 phases (TnonG1) of the cell cycle were also positively correlated with Td (Figures 1B, D; and Table 1) in both organisms, albeit less so in yeast (τ=0.398; Figure 1B) than in human cells (τ=0.579; Figure 1D). Overall, our data document the strong association between TG1 and Td (Figures 1A, C). Additionally, they suggest that growth requirements for cell division are not registered exclusively in G1, but also later in the cell cycle (see Figures 1B, D), in agreement with observations from other groups (ANASTASIAet al. 2012; FERREZUELOet al. 2012; DOWLINGet al. 2014; SOIFER AND BARKAI 2014; CERULUSet al. 2016; MAYHEWet al. 2017; GARMENDIA-TORRES et al. 2018).
A scaling relation between TG1 and Td
To estimate a predictive and quantitative relation between TG1 and Td we derived non-parametric, robust linear regression models using the Siegel repeated median estimates (SIEGEL 1982), (Figure 1 and Table 1; see also Materials and Methods). The intercepts of the linear TG1 vs. Td plots reflect the apparent minimum duration of the S+G2+M phases in yeast (1.4 h; Table 1) and human (7.6 h; Table 1) cells. The slopes in the linear relations indicate how much Td is affected by TG1, or TnonG1. For example, if non-G1 phases were not expanding in slower proliferating cells, then one would expect a vertical line parallel to the y-axis in TnonG1 vs. Td plots. We noticed that the slope of the regression of TG1 on Td appeared to slightly differ between the yeast and human datasets (Figure 1 and Table 1). Applying the non-parametric Sen-Adichie test for parallelism confirmed that the difference in the slopes of the regression lines of TG1 on Td between yeast and human cells was statistically significant (V statistic = 7.324, p-value = 0.007). Although the TG1 distributions themselves are lognormal, log-transformation is not necessary for any of our conclusions, since we used a non-parametric, ordinal-based analysis in all our statistical tests. Nonetheless, we display regression plots using log-transformed data to improve visualization, because data points appear more evenly on these graphs. Furthermore, log-transformed values are often incorporated in scaling relations between the measured variables in the literature (CHAN AND MARSHALL 2010). The quantitative relations we identified linking TG1 with Td are significant because they provide a framework to interpret experimental perturbations in cell cycle progression and cell proliferation, as we will describe for yeast cells.
Nutrient-specific, but not growth rate-dependent association between cell size and TG1, or Td
Control of cell size has frequently been used synonymously with growth control of G1 transit in the cell cycle, especially in budding yeast. Daughter cells of S. cerevisiae are born smaller than their mother is, and they will not initiate a new round of cell division until they reach a size characteristic of the culture medium. The rate at which daughter cells increase in volume has been reported to contribute to the size at which they will initiate a new round of cell division (FERREZUELOet al. 2012). Note that unless indicated otherwise, here we use the term ‘growth rate’ to describe the rate at which cells proliferate, and not the rate at which they increase in size in a given cell cycle. As the cell cycle is prolonged in poor nutrients, it is also widely assumed that the cells get smaller (e.g., see Fig. 10-26 in (MORGAN 2007)). To test the strength of the association between cell size and TG1 or Td, we combined the available data from previous studies ((TYSONet al. 1979; GUOet al. 2004; BRAUERet al. 2008); see Table S1). From such an unbiased but unweighted analysis (Figure 2A, D), it appeared that the size of yeast cells was not significantly associated with Td (p-value= 0.171, based on Kendall’s test; Figure 2A) or TG1 (p-value= 0.2449, based on Kendall’s test; Figure 2D).
Unlike the strong association of TG1 with Td, which was consistent across studies (see Figure 1 and Materials and Methods), the association between cell size and TG1 or Td appeared to vary among the relevant studies. Given the different number of samples analyzed in each study and their associated variance, we calculated the effect sizes from each study separately, based on the non-parametric Spearman’s and Kendall’s correlation coefficients. These study-specific correlation coefficients then served as the effect size index, to standardize the different studies and arrive at a summary correlation (BORENSTEIN 2009). The results were visualized in typical ‘forest’ plots (Figures 2B, C, E, F). A negative association between size and rates of cell proliferation, with cells getting smaller with larger Td values, was only evident at a moderate level in batch cultures (τ = −0.52, r = −0.64; see Figures 2E, F), where different nutrients were used to achieve different doubling times (TYSONet al. 1979). In contrast, in other studies (GUOet al. 2004; BRAUERet al. 2008), which employed chemostats to alter the population doubling time independently of the limiting nutrient, there was no correlation between cell size and Td or TG1 (Figure 2). Importantly, within these chemostat studies, cell size measurements were internally calibrated. Hence, the lack of any correlation between cell size and Td or TG1 cannot be attributed to experimental variabilities of different studies incorporated in our meta-analysis of the literature. Lastly, the lack of a significant association between TG1 and cell size agrees with a genome-wide survey of single gene deletions (HOOSEet al. 2012), which found no pattern of correlation between cell size and the relative duration of the G1 phase. Hence, although cell size can be modulated by changes in nutrient composition in yeast ((TYSONet al. 1979; SOMAet al. 2014); and others), our data suggest that it is more likely that these are nutrient-specific effects, not causally linked to changes in cell proliferation rates.
Cln3p, but not Whi5p, is required for the strong association between TG1 and Td
To understand how the relation between the length of the G1 phase and doubling time is established in budding yeast, we next examined the role of the Cln3p and Whi5p proteins, which regulate the G1/S transition in this organism. It has been proposed that dilution of Whi5p as cells get bigger in G1 is the key event controlling the timing of the G1/S transition (SCHMOLLER AND SKOTHEIM 2015; SCHMOLLERet al. 2015). Since in cells proliferating at different rates there is not a significant correlation with cell size (Figure 2, Table S1), it is not clear how the inhibitor dilution model would apply to the conditions we examine in this study. To our knowledge, the kinetics of cell cycle progression in cells lacking Cln3p or Whi5p have not been examined previously in steady-state cultures proliferating at different rates. To test the role of Cln3p and Whi5p in the relation between TG1 and Td, we examined the cell cycle profile of cln3Δ or whi5Δ cells in continuous, steady-state chemostat cultures. We measured TG1 in cln3Δ or whi5Δ cells from the DNA content of the cultures under glucose (0.08% W/v) limitation and at different dilution rates (0.038 h-1 to 0.348 h-1; corresponding to Td values between 18 h and 2 h, respectively). As expected, cells lacking Whi5p were very small (≈18 fL), and their size did not change significantly as a function of Td (Figures 3E and S3D). Furthermore, the intercept of the linear fit between the log-transformed Td and TG1 values of whi5Δ cells was significantly higher than the intercept of the linear fit of these parameters in wild-type cells (1.17 vs. 0.92; see Table 1), consistent with the shortened G1 phase of whi5Δ cells. The slope of the linear relation between Td and TG1 in whi5Δ cells (Figure 3B) was similar to what we observed in the aggregate analysis of wild-type cells (Figure 1A, and Table 1; Sen-Adichie V statistic = 1.775, p-value = 0.183), albeit slightly smaller than the slope of wild type cells from a separate, independent experiment performed in this study (0.6723 in wild type (Fig. 3A) vs. 0.6166 in whi5Δ cells (Fig. 3B)). These data suggest that in different physiological states, and despite their shortened G1 phase and small size, whi5Δ cells nonetheless remain responsive to different environments, displaying minimal changes in their scaling of the expected proportional changes between Td and TG1.
In contrast, cells lacking Cln3p had an abnormal behavior. In three independent experiments (Figures 3C, and S3B,C), TG1 did not even have a straightforward linear relation with Td in cultures of cln3Δ cells. At shorter division times (Td < 5 h), the Td and TG1 values of cln3Δ cultures were related linearly, albeit with a higher slope (e.g., Figure S3C; slope = 0.7685). More importantly, in all three independent experiments, the linear relation breaks down at slower proliferating cln3Δ cultures (Figures 3C, and S3B,C). Even when combining all data points from the individual experiments for each strain, we found that at all doubling times tested the linear relation between Td and TG1 remains strong for whi5Δ cells (τ > 0.8, based on Kendall’s non-parametric test). The same is true for cln3Δ cells at values of LnTd < 1.5 (corresponding to Td values < 4.5 h). In contrast, the linear relation between Td and TG1 is significantly weaker (τ < 0.5) for slower proliferating cln3Δ cells (LnTd > 1.5). These data suggest that Cln3p is more important than Whi5p for imposing the proper scaling relation of Td ∝ TG1 in wild type cells.
Cln3p levels are strongly and positively associated with cell proliferation rates
Given the important role of Cln3p in establishing the proper relation between Td and TG1 (Figures 3 and S3), we sought to measure the levels of Cln3p and Whi5p as a function of Td. There are no reports of the steady-state levels of Cln3p or Whi5p in cell populations proliferating at different rates in chemostats.
To measure Whi5p and Cln3p levels from the same cells, we generated a strain that carries WHI5-TAP and CLN3-13MYC alleles, providing the only source of these gene products in the cells, expressed from their endogenous chromosomal locations (Figure 4A, see Materials and Methods). The expressed proteins were epitope-tagged, but otherwise un-mutated, wild type Whi5p-TAP and Cln3p-(Myc)13. These cells were then cultured in continuous, steady-state chemostat cultures under glucose (0.08% w/v) or leucine (0.0015% w/v) limitation. Although the CLN3-13MYC allele provides the means for reliable detection of otherwise wild type Cln3p, it is known to be slightly hypermorphic, stabilizing the Cln3p protein somewhat and shortening the G1 phase of the cell cycle (THORBURNet al. 2013). Indeed, the intercept of the linear fit between the log-transformed Td and TG1 values of this strain (HB94; WHI5-TAP, CLN3-13MYC) was slightly higher than the intercept of the linear fit of these parameters in wild-type cells (0.97 vs. 0.92; see Table 1), consistent with a shortened G1 phase. The slope of the linear relation between the log-transformed values of Td and TG1 was increased somewhat for these cells compared to the aggregate analysis of wild-type cells (0.68 vs. 0.6; see Table 1). Importantly, these cells still displayed a strong, linear, positive association between Td and TG1 (τ=0.77; r=0.92; see Table 1), at all dilution rates we tested. Hence, we concluded that the relation between Td and TG1 was only minimally affected in this strain, and we proceeded to quantify the levels of both Whi5p-TAP and Cln3p-(Myc)13, from separate chemostat experiments under glucose or leucine limitation, each run at ≥5 dilution rates (Figure 4; see Materials and Methods).
The levels of Whi5p-TAP were not increased in slower proliferating cells (Figure 4A, B). Previously, (LIUet al. 2015) reported that Whi5p abundance increases ≈3-fold in cells growing in poorer carbon sources, although this was not seen in a more recent study by (DORSEYet al. 2018). In any case, several variables were different between the (LIUet al. 2015) study and ours, which could account for the disagreement in the findings: First, different epitope-tagged alleles were used (WHI5-tdTomato vs. WHI5-TAP). Second, different detection methods were applied (fluorescence live cell imaging vs. immunoblots). Third, (LIUet al. 2015) use cells in the W303 background, which are larger than cells of the BY background we use here, possibly leading to differences in cell size regulation. Fourth, and most significantly, nutrient-specific effects could not be separated from growth rate-specific ones in (LIUet al. 2015). As we discussed earlier (see Figure 2), chemostats provide the only experimental approach for properly studying how rates of cell proliferation may affect a given output, separately from any effects unique to particular nutrients.
We observed a significant and disproportionate reduction of Cln3p-(Myc)13 levels in slower-proliferating cells (Figure 4A, B). With Cln3p-(Myc)13 levels normalized against the total cellular protein content, the fastest proliferating populations had >10-fold higher levels of Cln3p-(Myc)13 compared to the slowest proliferating cells (Figure 4A, B). Furthermore, because these estimates rely on the hypermorphic CLN3-13MYC allele that produces a slightly stabilized Cln3p protein (THORBURNet al. 2013), the dynamic range of Cln3p levels as a function of doubling time is likely even broader.
A uORF in CLN3 adjusts the levels of Cln3p at different cell proliferation rates
What is the mechanism that underpins the growth-dependent control of Cln3p abundance? We had predicted that a uORF in CLN3 could inhibit its translational efficiency in poor media disproportionately (POLYMENIS AND SCHMIDT 1997). However, predictions of a growth-dependent role of the uORF had not been accompanied with measurements of Cln3p levels. A kinetic model of protein synthesis (LODISH 1974) forecasts that removing the uORF would de-repress synthesis of Cln3p in slowly dividing cells when the ribosome content of the cell is low. In contrast, removing the CLN3 uORF would have minimal effects in cells that proliferate fast, when the ribosome content is high. To test this model, we introduced an A-315T substitution that mutates the start codon of the uORF in CLN3 without affecting CLN3 mRNA levels (POLYMENIS AND SCHMIDT 1997), in the strain that expresses otherwise wild type Whi5p-TAP and Cln3p-(Myc)13 (see Materials and Methods). Note also that in chemostat conditions very similar to the ones we used here, the levels of wild type CLN3 mRNA do not change significantly as a function of growth rate (BRAUERet al. 2008).
The effects of the uORF were evident in slower proliferating cultures (Td > 4h), where the dynamic range of Cln3p levels was much narrower (3-4 fold) in A-315T cells, and very different from the range of Cln3p levels (10-fold) in their wild type counterparts at these longer doubling times (p = 0.03648, based on the non-parametric Kolmogorov-Smirnov test), and indistinguishable from the range of Whi5p levels (Figure 4A, B and File S1). We note that although the range of Cln3p levels is narrower in slower proliferating CLN3 uORF mutant cells (Figure 4), it is not flattened, arguing for additional mechanisms that could adjust the levels of Cln3p at different growth rates. Nonetheless, an independent piece of functional evidence further strengthened a growth-dependent role of the CLN3 uORF. A hallmark phenotypic readout of gain-of-function CLN3 alleles is a reduction in cell size (NASHet al. 1988). Cells that lack the CLN3 uORF were smaller than their wild type counterparts were, and this effect was Td-dependent (see Figure 4C, D). Especially in leucine-limited cells, which displayed pronounced enlargement as they proliferated slower, removing the CLN3 uORF reduced their size substantially (Figure 4D). These results are consistent with a de-repression of Cln3p synthesis upon removal of the CLN3 uORF.
These data argue that translational control contributes to the disproportionate reduction of Cln3p levels as a function of Td. Note also that loss of Cln3p severely perturbs the linear relation between Td and TG1 (Figures 3 and S3). In summary, our results underscore the critical role of the G1 cyclin Cln3p in the physiological coupling between growth and division.
DISCUSSION
The scaling relations between G1 length and population time in yeast and human cells we report are significant for several reasons. First, if the duration of G1 is estimated, they allow predictions of proliferation rates, which could be useful in diverse settings, such as in tissues at an organismal level. Second, they serve as benchmarks against which the effects of genetic or other perturbations can be evaluated, as we demonstrated for Whi5p and Cln3p, two cell cycle regulators in yeast. Third, scaling relations of cellular physiology may ultimately point to general, physical mechanisms that organize life at the cellular level. In the next paragraphs, we discuss our findings in relation to current models of how cell division is controlled by cellular biosynthetic capacity, with emphasis on the roles of Whi5p and Cln3p.
What is the context of this study in relation to others?
Our results pertain to cell cycle kinetics of steady-state cultures that proliferate at different rates, not to cell cycle adjustments immediately after nutrient shifts (TOKIWAet al. 1994; LEITAO AND KELLOGG 2017). We also did not examine G1 progression in a particular cell cycle, where small daughter cells will not initiate a new round of cell division until they reach a size characteristic of the culture medium (HARTWELL AND UNGER 1977; JOHNSTONet al. 1977). Hence the scaling of G1 duration between populations with different doubling times may not necessarily be controlled by the same mechanism that controls how G1 duration is regulated to maintain size homeostasis within a population of cells that proliferates at a given rate. This interpretation is consistent with the findings that cell size is not associated with rates of cell proliferation (Figure 2), at least in experimental settings of steady-state chemostat cultures, which separate nutrient-specific effects from the impact of different rates of cell proliferation. For example, note the very different sizes of cells in glucose vs. leucine-limited cultures at the same dilution rate (compare Figures 4C and 4D), offering yet another demonstration of how particular nutrients may affect cell size independently of any changes in rates of cell proliferation. Furthermore, in leucine-limited cultures, the cells were not only bigger than cells in glucose-limited chemostats at all dilution rates tested, but they also got even bigger as they divided slower (Figure 4). These observations argue against the widely-held assumptions that cells get smaller the slower they proliferate. Instead, they support the notion that nutrient effects on cell size may be particular to specific nutrients, and not associated with changes in rates of cell proliferation.
How do our results mesh with models of G1 control?
As we noted above, our data were from cells dividing at different rates, which was not addressed in the Whi5p dilution model of (SCHMOLLERet al. 2015). Hence, the two studies are not directly comparable. The Whi5p dilution model, however, was constructed on the basis that while Whi5p levels were disproportionately lower than expected from cell growth, Cln3p levels were roughly constant and proportional to the increase in size from birth to START (SCHMOLLERet al. 2015). Given the disproportionate dependency of Cln3p levels on cell proliferation rates that we reported here and had predicted earlier (POLYMENIS AND SCHMIDT 1997), could the uORF-mediated translational control of CLN3 affect Cln3p synthesis in the G1 phase from birth to START? We think this is unlikely because the uORF-mediated translational control we described operates when the concentration of active ribosomes in the cell changes (LODISH 1974), for example in poor vs. rich nutrients. Hence, while such translational control mechanisms provide excellent conduits to disproportionately alter gene expression and communicate growth-related inputs to downstream mRNA targets, to our knowledge, there is no report of cell cycle-dependent changes in ribosome content. Other mechanisms, not due to changes in the translational efficiency of CLN3, may contribute to significant, periodic changes in Cln3p abundance in G1, within a given cell cycle.
There are conflicting reports in the literature about whether Cln3p ‘cycles’ in the cell cycle. Cln3p is of such low abundance that cannot be properly measured in the single-cell microscopy methods of (SCHMOLLERet al. 2015), because mutant CLN3 alleles had to be used, producing extremely stabilized and dysfunctional Cln3p protein that accumulates at very high, but non-physiological levels, so that it can be visible with microscopy. The initial report claiming that Cln3p-HA levels were constant in the cell cycle did not interrogate the early G1 phase (TYERSet al. 1993). In that report, although early G1, small (25 fL), elutriated daughter cells were collected, Cln3p levels were not measured until much later in G1 (at 35 fL, when by 40 fL 25% of the cells were already budded in that experiment; see Fig. 4 in (TYERSet al. 1993)). Based on that result, it had been assumed for decades that Cln3p levels were constant in the cell cycle. Recently, however, two independent studies by the Amon (THORBURNet al. 2013) and Kellogg (ZAPATAet al. 2014) labs, assayed elutriated synchronous cells carrying epitope-tagged, but otherwise wild type CLN3 alleles. Both studies showed that Cln3p levels change >10-fold in G1. Cln3p is absent in early G1 cells, while it rises dramatically before START. We also used the same CLN3-13MYC allele to monitor Cln3p levels at different rates of cell proliferation (see Figure 4). The CLN3-13MYC allele is known to produce a slightly stabilized Cln3p protein (THORBURNet al. 2013). Note that, on the face of the slight stabilization of the Cln3p-(Myc)13, the dynamic range of Cln3p levels as a function of growth rate we report is likely even broader, not narrower. Hence, our conclusions are strengthened, not weakened by the slight stabilization of the Cln3-Myc we used. For the same reasons, the changes in Cln3p levels in G1 observed previously (THORBURNet al. 2013; ZAPATAet al. 2014) are likely even greater than indicated in these reports.
Overall, although a 2-fold dilution of Whi5p is observed in G1 (SCHMOLLERet al. 2015), the changes in Cln3p levels are likely more pronounced (THORBURNet al. 2013; ZAPATAet al. 2014), through transcriptional (ZAPATAet al. 2014), or other mechanisms. In this context, it is perhaps unsurprising that we found Cln3p to be more important than Whi5p in the relation between Td and TG1. It is important to stress, however, that any changes of Cln3p levels in G1 do not affect the key aspect of the inhibitor dilution model, namely that Whi5p levels are reduced by cell growth. Hence, we may be dealing with a more complex, ‘mixed’ model of inhibitor dilution and activator accumulation. It is possible that the levels of additional proteins may behave analogously to Cln3p and Whi5p, contributing to a broader network of factors whose antagonistic relations control the timing of initiation of cell division. Regardless of the identity of those proteins, in yeast and other models, the fundamental relation between TG1 and Td we describe in this report will serve as a useful metric to evaluate the role of these protein(s) in the control of cell division by growth inputs.
ACKNOWLEDGEMENTS
Author Contributions
Methodology, H.M.B., M.P.; Formal Analysis, H.M.B., M.P.; Investigation, H.M.B., M.C., I.P.E.P., A.O.P., M.P.; Resources, M.P.; Data Curation, H.M.B., M.P.; Writing – Original Draft, M.P., Writing – Review and Editing, H.M.B., M.P.; Visualization, H.M.B., M.P.; Supervision, H.M.B., M.P., Funding Acquisition, M.P.
This work was supported from the NIH (grant GM123139 to M.P.). M.C. was supported by a National Science Foundation REU award (DBI-1358941). The authors declare no conflicts of interest.