Cells display homeostatic behaviour in maintaining population cell size by controlling cell size at mitosis (Fantes et al., 1975; Ginzberg et al., 2015; Wood and Nurse, 2015; Lloyd, 2013). This homeostasis is driven by larger cells being more likely to divide than smaller cells, resulting in the correction at cell division of cell size deviances (Fantes et al., 1975; Fantes, 1977; Patterson et al., 2019). Cyclin-dependent kinase (CDK^Cdc2) is the master regulator of mitosis and cell division, and therefore the propensity for smaller cells not to divide must ultimately feed into the regulation of CDK activity (Coudreuse and Nurse, 2010).

CDK activity is subject to several mechanisms of control: cyclin synthesis and subsequent binding of cyclin to CDK, which drives CDK into a catalytically competent form Solomon et al., 1990; Wee1 kinase and Cdc25 phosphatase act to inhibit or activate CDK, respectively, through regulatory tyrosine phosphorylation (Nurse, 1975; Russell and Nurse, 1986; Gould and Nurse, 1989); and PP2A phosphatase works to remove phosphates deposited by CDK reducing its net activity (Kinoshita et al., 1990; Kinoshita et al., 1993; Gharbi-Ayachi et al., 2010; Mochida et al., 2009; Mochida et al., 2010; Mochida et al., 2016), and also controls the phosphorylation state of Wee1 and Cdc25 to regulate the level of CDK tyrosine phosphorylation (Lucena et al., 2017; Hutter et al., 2017; Rata et al., 2018; Kamenz et al., 2021). Finally, the CDK control network also co-ordinates cell division with cell growth through an unknown mechanism that responds to cell ploidy, with cell size generally doubling as ploidy doubles (Wood and Nurse, 2015).

It is likely that potential size control pathways will be integrated at the level of CDK activity control because CDK activity is the driver of mitosis. For example, in the fission yeast Schizosaccharomyces pombe, it has been proposed that size control was mediated by the DYRK kinase Pom1, which ultimately inhibits mitotic onset by causing the inhibitory tyrosine phosphorylation of CDK by signalling through the Wee1 kinase (Martin and Berthelot-Grosjean, 2009; Moseley et al., 2009). However, in both the absence of Pom1 itself or the absence of inhibitory tyrosine phosphorylation, cells are able to maintain cell size homeostasis (Coudreuse and Nurse, 2010; Wood and Nurse, 2013). Thus, there must exist alternative mechanisms by which fission yeast cells integrate cell size information into the CDK control network.

Much of our understanding of cyclin-CDK network regulation has been derived from in vitro studies, but these have limitations when considering cellular parameters such as cell size (Mochida et al., 2016; Pomerening et al., 2005; Pomerening et al., 2003; Sha et al., 2003). Here, therefore, we have studied in vivo regulation of cyclin-CDK activation at mitosis in the fission yeast. Using a novel CDK activity sensor, we have monitored cell size, CDK activity, and cyclin-CDK complex level simultaneously, whilst genetically varying regulators of the cyclin-CDK control system. We propose that CDK activity regulation through inhibitory tyrosine phosphorylation and PP2A work synergistically to communicate information about cell size to the CDK control network. Furthermore, we show that cyclin-CDK complex level scales with cell size, and this aids in the prevention of division in small cells. Finally, we show that in cells lacking PP2A and inhibitory tyrosine phosphorylation, haploid and diploid cells of equivalent size and similar cyclin-CDK concentration have differing cyclin-CDK activities, with diploid cells exhibiting a lower activity. This suggests that cyclin-CDK activity is increased in cells of lower ploidy. These experiments inform our understanding of the regulation of cyclin-CDK and illuminate how cell size is integrated into this regulatory network.

Given the complexity of the CDK regulatory network, we have used fission yeast cells containing a reduced CDK control system, with the cell cycle driven by a monomeric cyclin-CDK fusion-protein (C-CDK) (Coudreuse and Nurse, 2010). This simplifies the CDK control network by eliminating cyclin binding to CDK as a regulatory component and allows co-expression of both cyclin and CDK from a single promoter. This C-CDK fusion-protein is expressed under the Cyclin B^Cdc13 promoter, and therefore C-CDK expression mimics endogenous Cyclin B expression. Using this system, inhibitory Wee1-dependent phosphoregulation can also be removed using a non-phosphorylatable C-CDK^AF mutant (Coudreuse and Nurse, 2010; Wood and Nurse, 2013). These C-CDK^AF strains are healthy and viable, but have markedly distinct cell cycle profiles from C-CDK^WT expressing strains, as they spend a significantly longer period in G1 than C-CDK^WT cells (Coudreuse and Nurse, 2010). Nevertheless, C-CDK^AF cells co-ordinate cell division with cell growth and maintain cell size homeostasis (Figure 1a; Wood and Nurse, 2013).

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Figure 1—figure supplement 1

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To examine the relationship between cell size, C-CDK concentration, and mitosis, we performed quantitative fluorescence time-lapse microscopy on strains expressing C-CDK^WT and C-CDK^AF fluorescently tagged with YFP (Figure 1a–e, Figure 1—figure supplement 1, Figure 1—figure supplement 2a). This analysis showed clear oscillations of C-CDK^WT and C-CDK^AF, with degradation of C-CDK occurring just before cell division (Figure 1b). C-CDK^AF oscillations were more variable, and 5% of the C-CDK^AF cells trigger C-CDK degradation in the absence of division (Figure 1—figure supplement 2), similar to what has been observed in CDK1^AF expressing human cells (Pomerening et al., 2008). In both backgrounds, C-CDK concentration scaled with cell size, with C-CDK^WT exhibiting a higher amount of C-CDK at mitotic entry compared to C-CDK^AF (Figure 1c). On investigating the links between the probability of a given cell to divide, cell size, and C-CDK level, we found that for C-CDK^WT both cell size and C-CDK level reach sharp thresholds at which cell division rates increase (Figure 1d,e). In the absence of tyrosine phosphorylation, a sharp threshold for C-CDK^AF levels still is present (Figure 1e), but occurs at a lower level than C-CDK^WT. C-CDK^AF cells fail to generate a sharp threshold for cell size, but even without a clear size threshold, C-CDK^AF cells still restrict smaller cells from division (Figure 1d).

C-CDK level is not a direct measure of C-CDK activity because of the multiple regulatory networks affecting CDK (Pomerening et al., 2005). To investigate CDK activity, cell size, and C-CDK level at the same time, we developed an in vivo single-cell assay of CDK activity. We used Cut3, the Smc4 homolog, as a CDK activity biosensor, because it translocates from the cytoplasm into the nucleus upon CDK-dependent phosphorylation of a single site in its N-terminus (Figure 1f; Sutani et al., 1999). Thus, the Cut3 nuclear/cytoplasmic (N/C) ratio can be used to assess CDK activity, a method that has been applied to other protein kinases (Spencer et al., 2013; Araujo et al., 2016). As a test of this assay, we blocked cells expressing fluorescently tagged Cut3 in the background of a bulky ATP-analogue-sensitive C-CDK (Bishop et al., 2000) using 1NM-PP1, and tracked single cells following their release from G2 arrest into a range of 1NM-PP1 doses (Figure 1g, Figure 1—figure supplement 3). The response of the maximum nuclear Cut3 concentration to 1NM-PP1 was similar to the one measured in our previous phosphoproteomics study (Swaffer et al., 2016), confirming that the sensor reflects in vivo CDK activity (Figure 1h). Subsequently, we examined CDK activity in unperturbed cells measured by the Cut3 N/C ratio and showed that it both rises to a higher level in C-CDK^WT cells in comparison to C-CDK^AF cells and also that progress through mitosis in C-CDK^AF cells is slower and more variable (Figure 1i, Figure 1—figure supplement 4).

We next investigated the links between C-CDK protein levels, CDK activity, and cell size in C-CDK^WT and C-CDK^AF cells, which have been enlarged beyond their physiological cell size. During a G2/M block (Figure 1g), cell size and C-CDK enzyme concentration (as measured by C-CDK-YFP fluorescence intensity) scaled with each other in both backgrounds (Figure 1j,k). After the release from CDK inhibition, C-CDK^WT activity correlated well with both cell size and C-CDK protein level (Figure 1l,n). However, peak C-CDK^AF activity correlated better with protein level than with cell size (Figure 1m,o). The link between cell size and CDK activity was much clearer for C-CDK^WT than for C-CDK^AF in these low-throughput time-lapse assays (Figure 1m). Therefore, we repeated this experiment using a high-throughput assay based on imaging flow cytometry (Figure 1—figure supplements 5 and 6) and observed that peak CDK activity in both C-CDK^AF and C-CDK^WT was clearly size dependent (Figure 1—figure supplement 5e). Thus, CDK tyrosine phosphorylation helps to inform the cell division machinery of cell size (Figure 1d,l). However, in the absence of tyrosine phosphorylation, C-CDK^AF cells are still able to generate a threshold C-CDK level for division and prevent small cells from division (Figure 1e,o, Figure 1—figure supplement 5e).

A complication of the above assay is that cell size scales with C-CDK level (Patterson et al., 2019; Coudreuse and Nurse, 2010; Navarro and Nurse, 2012; Figure 1c,j,k). To uncouple cell size from C-CDK level, and study if small cells are prevented from entering mitosis due to low C-CDK level or for some other reason, we developed a more flexible single-cell CDK assay system. This assay was also based on Cut3 translocation into the nucleus (Figure 2a) but used a brighter synthetic C-CDK activity sensor, synCut3-mCherry to allow its co-detection with C-CDK in a high-throughput assay (Figure 2—figure supplement 1). This sensor was expressed in a strain where the endogenous CDK network can be switched off using a temperature-sensitive CDK1 allele, cdc2^TS. A tetracycline-inducible C-CDK tagged with superfolder GFP (sfGFP) was constructed and made non-degradable (Yamano et al., 1998) as well as sensitive to inhibition by 1NM-PP1. Induction of C-CDK at the cdc2^TS restrictive temperature allows the study of the activity of the inducible C-CDK without either wild-type CDK activity or C-CDK-sfGFP proteolysis during mitosis. Using this assay, we acquired hundreds of thousands of images of single cells, which allowed us to study the in vivo biochemistry of CDK activity in response to a wide range of C-CDK concentrations in physiologically sized cells. C-CDK level was uncoupled from cell size as induction of C-CDK was not dependent on cell size (Figure 2b,c). Results from this assay demonstrated that in vivo CDK activity was dependent on C-CDK level and was reduced when CDK activity was inhibited using 1NM-PP1 (Figure 2d, Figure 2—figure supplement 2).

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Combining this system with genetic backgrounds in which major C-CDK regulation was altered, we analysed how mechanisms of CDK regulation affected C-CDK activity in relation to cell size. We performed the assay in backgrounds lacking the major PP2A catalytic subunit (PP2A^ppa2Δ) (Kinoshita et al., 1990; Kinoshita et al., 1993), inhibitory CDK tyrosine phosphorylation, or both (Figure 2e). Following endogenous CDK1 inactivation after temperature shift, both PP2A⁺ and PP2AΔ cells arrest in an almost uniform G2 state, ensuring that downstream analysis is not confounded by cells arresting in different phases of the cell cycle (Figure 2f). C-CDK levels increased similarly upon induction in all mutant backgrounds (Figure 2g). Population mean C-CDK activity was comparable between all conditions (Figure 2h); however, C-CDK activity displayed differences at the single-cell level when activity was measured in cells of different sizes. In all genetic backgrounds at the same level of C-CDK enzyme, maximum C-CDK activity increases with cell size (Figure 2i). This is particularly noticeable when directly comparing the maximum C-CDK activity of cells with a C-CDK level of ~750 AU in the 8 μm bin to the 14 μm bin in all backgrounds (Figure 2i, dashed lines). The single-cell dose–response of CDK activity on C-CDK^WT concentration background is clearly bistable, with cells existing in either an ‘on’ or an ‘off’ state. The mean CDK activity is relevant directly for strains expressing C-CDK^AF, as these cells exhibit little bistability in CDK activation. In the C-CDK^WT expressing cells, there are two population distributions demonstrating bistability. We averaged the two population means as the gradient of this line shows the degree of bifurcation between the lower and the upper CDK activity populations. The C-CDK concentration required to switch cells ‘on’ decreases with increasing cell size, and the sharpness of the transition increases with size (Figure 2i,k). This bistable behaviour is heavily dependent on CDK tyrosine phosphorylation (Figure 2i,k,l). Removal of PP2A allows the attainment of the ‘on’ state at lower cell sizes (Figure 2i), effectively shifting the C-CDK dose–response curve towards lower sizes without altering the shape of the response (Figure 2k). In addition, PP2A also adds switch like behaviour to the C-CDK activity dose-response, as bistable behaviour with C-CDK^AF is not present with C-CDK^AF PP2AΔ (Figure 2i dashed box, inset and Figure 2l).

When looking across all size bins, maximum C-CDK activity increases with cell size in all genetic backgrounds, but plateaus at about 12–13 μm in the absence of tyrosine phosphorylation (Figure 2j). However, it is clear that cell size is able to regulate C-CDK activity even in the absence of both tyrosine phosphorylation and PP2A (Figure 2i,j). These results are consistent with our previous observations (Figure 1), that although tyrosine phosphorylation has a role in informing the cell cycle machinery of cell size, small cells are still restricted from mitosis when tyrosine phosphorylation is absent.

Inhibitory tyrosine phosphorylation directly results in a reduction of intrinsic CDK activity (Berry and Gould, 1996), whilst PP2A has a dual mechanism of CDK activity modulation: PP2A is able to regulate inhibitory tyrosine phosphorylation by controlling the phosphorylation state of Wee1 and Cdc25 (Lucena et al., 2017), and in addition can directly oppose the phosphorylation of CDK substrates (Godfrey et al., 2017). We therefore sought to calculate the contributions of tyrosine phosphorylation and PP2A in restricting CDK activity, both in contexts with and without tyrosine phosphorylation. This was carried out to examine if their combined contribution was greater than the sum of their parts. To calculate the individual contributions of tyrosine phosphorylation and PP2A in restricting C-CDK activity, first we measured the threshold C-CDK level required for 50% of cells to reach a C-CDK activity determined as being >5 in arbitrary units (see Figure 3 legend) in different strain backgrounds within different size bins (Figure 3a). This value was chosen as an approximate value of the C-CDK concentration required in vivo to trigger mitotic entry in wild-type cells (Figure 1i). When this C-CDK threshold level was plotted across all size bins (Figure 3b), the threshold was seen to be size dependent in all strain backgrounds, with wild-type cells exhibiting the strongest capacity to raise the C-CDK level threshold for mitosis in smaller cells. By subtracting the curves of cell length vs mitotic C-CDK level (Figure 3c) for various backgrounds, we were able to estimate the contributions of tyrosine phosphorylation and PP2A in a given background. For example, C-CDK^WT PP2AΔ–C-CDK^AF PP2AΔ estimates the ability of tyrosine phosphorylation alone to restrict mitotic entry in a background lacking PP2A. Inhibitory tyrosine phosphorylation is able to restrict cells with 600 units of C-CDK from entering mitosis at 8 μm cell length, but only 200 units of C-CDK at 10 μm (Figure 3c, yellow). If the different components of the CDK control network act separately, adding individual threshold contributions together would generate a threshold curve similar to the wild-type curve. However, when the contributions of tyrosine phosphorylation and PP2A were added to the C-CDK^AF PP2AΔ curve, they did not re-capitulate the wild-type curve (Figure 3d). Thus, this analysis suggests that there is synergy between the tyrosine phosphorylation network and PP2A activity and that this synergy is important for establishing the C-CDK level threshold for division.

Figure 3

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We have shown that small cells are normally prevented from division by their low C-CDK protein level (Figure 1), along with PP2A and tyrosine phosphorylation working synergistically to increase the level of C-CDK needed to trigger division in smaller cells (Figure 3). Strikingly however, in the absence of these major regulators, small cells are still able to restrict division by lowering CDK activity as a result of some other factor related to cell size (Figure 2h,i,j). This unknown factor is able to lower CDK activity in small cells despite high C-CDK levels, thus restricting them from division (Figure 2i).

Given the positive relationship between maximum C-CDK activity and increasing cell size in the C-CDK^AF PP2AΔ mutant (Figure 2i), we hypothesized that cells dilute a CDK inhibitor as they grow (Fantes et al., 1975), perhaps through a titration-based mechanism. Cell size is linked to ploidy through an unknown mechanism, and so we tested whether DNA concentration could influence CDK activity, and therefore be a candidate for the unknown factor able to lower C-CDK activity in small cells. We induced C-CDK^AF in haploid and diploid variants of the C-CDK^AF PP2AΔ strain, thereby eliminating all major CDK regulation at mitosis (Figure 4a). Both haploid and diplod cells were present almost uniformly in G2 after endogenous CDK1 inactivation, as cells with 2C and 4C DNA content respectively (Figure 4b), and expressed C-CDK^AF-sfGFP in a largely size-independent manner (Figure 4c). Strikingly, diploid cells exhibited lower C-CDK activity in response to the same C-CDK enzyme concentration as haploids (Figure 4d). The EC50 of the diploid dose–response curve was almost double that of the haploid (Figure 4e). Looking at single-cell, volume-resolved data, the inhibition of C-CDK activity is most marked in smaller diploid cells, with larger diploid cells having almost indistinguishable dose–response curves from their haploid equivalents (Figure 4f). The effect of cell size on CDK activation is much less marked in larger than normal haploids (Figure 4g). The diploids, which feature cells of physiological diploid size, still experience DNA concentration-dependent inhibition of their CDK activity. The effect of equal C-CDK levels resulting in lower C-CDK activity in small diploids when compared to equivalent sized haploids is readily seen from the raw images (Figure 4h). Therefore, cells of different ploidies, but otherwise equivalent volume, experience variable CDK activity in response to equal C-CDK level. This suggests that even in the absence of all major CDK regulation, DNA concentration is able to lower CDK activity and prevents division in small cells. At higher volumes, this inhibition of CDK activity disappears, and so the regulation may operate through titrating out an inhibitor.

Figure 4

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The cyclin-CDK complex, and its role in controlling mitotic onset, has been studied in many model eukaryotes from yeast (Nurse et al., 1976), through marine invertebrates (Evans et al., 1983), to mammalian cells (Santos et al., 2012). A number of regulatory components have been shown to be conserved across these model systems, including the CDK-activating cyclin B, inhibitory CDK tyrosine phosphorylation, and the CDK-counteracting PP2A phosphatase which both opposes CDK substrate phosphorylation and regulates CDK inhibitory phosphorylation through the Wee1/Cdc25 control loop. Despite extensive study, these studies have yet to reveal a fully satisfactory mechanism for cell size homeostasis at the onset of mitosis. To improve our understanding of this control system, we have focused on how CDK activity itself is directly regulated in the context of cell size. Our approach has demonstrated that three mechanisms inform the cell cycle control network of cell size through CDK activity control: C-CDK enzyme concentration scaling with cell size, synergistic PP2A and tyrosine-phosphorylation-dependent C-CDK threshold scaling, and DNA concentration-dependent inhibition of CDK activity. Our results demonstrate that C-CDK activity vs C-CDK level dose–response curves previously demonstrated in vitro operate in vivo, but in addition, we show that they are dependent on cell size in vivo (Pomerening et al., 2003). We also demonstrate a link between ploidy and CDK activity, with higher ploidy causing a reduction in CDK activity. We propose that CDK activity can be inhibited by a DNA-related mechanism in keeping with early work showing that increasing DNA content delays mitosis, with the removal of DNA by irradiation causing acceleration of the following mitosis (Devi et al., 1968; Sachsenmaier et al., 1970; Wilson, 1925). Our experiments show that DNA inhibits CDK activity more in smaller cells, potentially reducing CDK activity by a titration mechanism. This may be related to the mechanism by which cell size is linked to ploidy across cell types (Wilson, 1925; Amodeo and Skotheim, 2016; Prescott, 1956; Tzur et al., 2009). Finally, we show that tyrosine phosphorylation, PP2A activity, and DNA-dependent inhibition of CDK activity act together to restrict small cells from division, forming a mechanism to generate the robust cell size threshold behaviour observed in normal cells.

Our observations suggest that cell size control over the onset of mitosis involves several molecular mechanisms. If it is assumed that the accumulation of the C-CDK cyclin chimera driven by the cyclin promoter mimics the accumulation of cyclin, then one mechanism is the accumulation of cyclin through the cell cycle, which scales with the increase in cell size. A second is a synergistic interaction between the inhibitory CDK tyrosine phosphorylation pathway and the PP2A phosphatase, which acts on both the tyrosine phosphorylation pathway and dephosphorylation of CDK substrates. The third is a DNA-concentration-dependent inhibition of CDK activity. Given the conservation of all these molecular regulators, these mechanisms can be expected to have direct relevance in other eukaryotic cells.

Analysed data has been uploaded to Figshare with the handle 10779/crick.14633037.

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Author details

1. James Oliver Patterson

   1. Cell Cycle Laboratory, The Francis Crick Institute, London, United Kingdom
   2. College of Engineering, Swansea University, Swansea, United Kingdom

   Contribution

   Conceptualization, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing - original draft

   For correspondence

   jamesop@gmail.com

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-1993-4500

2. Souradeep Basu

   Cell Cycle Laboratory, The Francis Crick Institute, London, United Kingdom

   Contribution

   Investigation, Writing - original draft, Writing - review and editing

   For correspondence

   saz.basu@crick.ac.uk

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-4448-8688

3. Paul Rees

   1. College of Engineering, Swansea University, Swansea, United Kingdom
   2. Imaging Platform, Broad Institute of Harvard and MIT, Cambridge, United States

   Contribution

   Data curation, Formal analysis, Visualization, Methodology, Writing - review and editing

   Competing interests

   No competing interests declared

4. Paul Nurse

   1. Cell Cycle Laboratory, The Francis Crick Institute, London, United Kingdom
   2. Laboratory of Yeast Genetics and Cell Biology, Rockefeller University, New York, United States

   Contribution

   Conceptualization, Supervision, Funding acquisition, Project administration, Writing - review and editing

   Competing interests

   No competing interests declared

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