Synergistic CDK control pathways maintain cell size homeostasis

To coordinate cell size with cell division, cell size must be computed by the cyclin-CDK control network to trigger division appropriately. Here we dissect determinants of cyclin-CDK activity using a novel high-throughput single-cell in vivo system. We show that inhibitory phosphorylation of CDK encodes cell size information and works synergistically with PP2A to prevent division in smaller cells. However, even in the absence of all canonical regulators of cyclin-CDK, small cells with high cyclin-CDK levels are restricted from dividing. We find that diploid cells of equivalent size to haploid cells exhibit lower CDK activity in response to equal cyclin-CDK enzyme concentrations, suggesting that CDK activity is reduced by DNA concentration. Thus, multiple pathways directly regulate cyclin-CDK activity to maintain robust cell size homeostasis.

of C-CDK enzyme, maximum C-CDK activity increases with cell size (Fig. 2h). This is 129 particularly noticeable when directly comparing the maximum C-CDK activity of cells with C-130 CDK level of ~750 AU in the 8 μm bin to the 14 μm bin in all backgrounds (Fig. 2h, dashed  131 lines). The single cell dose-response of CDK activity on C-CDK concentration in a wild-type 132 background is clearly bistable, with cells existing in either an 'on' or an 'off' state. The C-CDK 133 concentration required to switch cells "on" decreases with increasing cell size, and the 134 sharpness of the transition increases with size (Fig. 2h,j). This bistable behavior is heavily 135 dependent on CDK tyrosine phosphorylation (Fig. 2h,j,k). Removal of PP2A allows the 136 attainment of the "on" state at lower cell sizes (Fig. 2h), effectively shifting the C-CDK dose 137 response curve towards lower sizes without altering the shape of the response (Fig. 2j). In 138 addition, PP2A also adds switch like behavior to the C-CDK activity dose-response, as 139 bistable behavior present with C-CDK AF is not present with C-CDK AF PP2AΔ (Fig. 2h dashed  140 box, inset and 2k). 141 142 When looking across all size bins, maximum C-CDK activity increases with cell size in all 143 genetic backgrounds, but plateaus at about 12-13 μm in the absence of tyrosine 144 phosphorylation (Fig. 2i). However, it is clear that cell size is able to regulate C-CDK activity 145 even in the absence of both tyrosine phosphorylation and PP2A (Fig. 2h,i). These results are 146 consistent with our previous observations (Fig. 1), that although tyrosine phosphorylation 147 has a role in informing the cell cycle machinery of size, small cells are still restricted from 148 mitosis even in the absence of tyrosine phosphorylation. 149 150 PP2A and inhibitory tyrosine phosphorylation constitute two fundamentally different modes 151 of lowering CDK activity, however it is unknown if they act independently or synergistically 152 to do so. We therefore sought to calculate the individual contributions of PP2A and tyrosine 153 phosphorylation in restricting CDK activity in order to examine if their combined 154 contribution was greater than the sum of their parts. To calculate the individual 155 contributions of tyrosine phosphorylation and PP2A in restricting C-CDK activity, first we 156 measured the threshold C-CDK level required for 50% of cells to reach a C-CDK activity >5 in 157 different strain backgrounds within different size bins (Fig. 3a). This value was chosen as an 158 approximate value of the C-CDK concentration required in vivo to trigger mitotic entry in 159 wild-type cells (Fig. 1i). When this C-CDK threshold level was plotted across all size bins (Fig. 3b) the threshold was seen to be size dependent in all strain backgrounds, with wild-type 161 cells exhibiting the strongest capacity to raise the C-CDK level threshold for mitosis in 162 smaller cells. By subtracting the curves of cell length vs. mitotic C-CDK level (Fig. 3c) for 163 various backgrounds we were able to estimate the individual contribution of tyrosine 164 phosphorylation and PP2A in a given background. For example, C-CDK WT PP2AΔ -C-CDK AF 165 PP2AΔ, estimates the ability of tyrosine phosphorylation alone to restrict mitotic entry in a 166 background lacking PP2A. PP2A is able to restrict cells with 600 units of C-CDK from entering 167 mitosis at 8 μm cell length, but only 200 units of C-CDK at 10 μm (Fig. 3c, yellow). If the 168 different components of the CDK control network act separately, adding individual 169 threshold contributions together would generate a threshold curve similar to the wild-type 170 curve. However, when the individual contributions of tyrosine phosphorylation and PP2A, 171 were added to the C-CDK AF PP2AΔ curve, they did not recapitulate the wild-type curve (Fig.  172 3d). Thus, this analysis demonstrates that there is synergy between the tyrosine 173 phosphorylation network and PP2A activity, and that this synergy is important for 174 establishing the C-CDK level threshold for division. 175 176 We have shown that small cells are normally prevented from division by their low C-CDK 177 protein level (Fig. 1) along with PP2A and tyrosine phosphorylation working synergistically 178 to increase the level of C-CDK needed to trigger division in smaller cells (Fig. 3). Strikingly 179 however, in the absence of these canonical regulators, small cells are still able to restrict 180 division by lowering CDK activity as a result of some other factor related to cell size ( Fig.  181 2h,i,j). This unknown factor is able to lower CDK activity in small cells despite high C-CDK 182 levels, thus restricting them from division (Fig 2i). 183 184 Given the positive relationship between maximum C-CDK activity and increasing cell size in 185 the C-CDK AF PP2AΔ mutant (Fig. 2i), we hypothesized that a titration based model might be 186 operative, where cells dilute a CDK inhibitor as they grow 21 . Given that cell size is linked to 187 ploidy through an unknown mechanism, we tested whether DNA concentration could 188 influence CDK activity, and therefore constitute the unknown factor able to lower C-CDK 189 activity in small cells. We induced C-CDK AF in haploid and diploid variants of the C-CDK AF 190 PP2AΔ strain, thereby eliminating all major canonical CDK regulation at mitosis (Fig. 4a,b). 191 Strikingly, diploid cells exhibited lower C-CDK activity in response to the same C-CDK enzyme concentration as haploids (Fig. 4c). The EC50 of the diploid dose response curve was almost 193 double that of the haploid (Fig. 4d). Looking at single-cell, volume-resolved data, the 194 inhibition of C-CDK activity is most marked in smaller diploid cells, with larger diploid cells 195 having almost indistinguishable dose-response curves from their haploid equivalents (Fig.  196 4e). The effect of cell size on CDK activation is much less marked in these larger than normal 197 haploids (Fig. 4f). The diploids, which feature cells of physiological diploid size, still 198 experience DNA concentration dependent inhibition of their CDK activity. The effect of 199 equal C-CDK levels resulting in lower C-CDK activity in small diploids when compared to 200 equivalent haploids is readily seen from raw images (Fig. 4g). Therefore, in search of 201 additional C-CDK regulation we show that cells of different ploidies, but otherwise 202 equivalent volume, experience variable C-CDK activity in response to equal C-CDK level. This 203 suggests that even in the absence of all canonical CDK regulation, DNA itself is able to lower 204 CDK activity to prevent division in small cells. This regulation appears to operate in a 205 titration-based manner, as at higher volumes this inhibition of CDK activity disappears. Aldrich)) was made up in water at 1 g/L and used as 500x stock. Bortezomib was added to 235 cultures to inhibit the C-CDK degradation, as described previously 29 . SynCut3 was 236 constructed by Gibson assembly of a codon optimised fragment consisting of the first 528 237 amino acids of Cut3, a linker region, and a fluorescent protein (mCherry or mNeongreen). 238 YFP was tagged onto C-CDK at the C-terminus of the protein. Where the sfGFP labelled C-239 CDK was used, the sfGFP was present internally within the Cdc13 component 29 . Cut3-240 mCherry was generated by C-terminal tagging 30 and Cut3-GFP was developed previously 14 . 241 Details of the TetR promoter and linearised variants can be found in a previous publication 1 . 242

243
Imaging flow cytometry 244 Imaging flow cytometry was performed using an Imagestream Mark X two-camera system 245 (Amnis), using the 60x objective. Cells were concentrated by centrifugation (5000 rpm/30 246 seconds) and resuspended in ~25 μl of media before sonication in a sonicating water bath. exists that is greater than 1.5x the interquartile range from the top or bottom of the box, 294 this is shown as a red "+". 295

Statistical testing 297
Statistical testing was performed where appropriate using a two tailed two sample t-test. P 298 values below 0.05 were considered significant. Replicates are shown where appropriate by 299 N numbers. 300

Cell size measurement 301
Cell size was measured by three different metrics. In timelapse microscopy assays, cell size 302 was determined as the area of the 2D surface segmented by our segmentation algorithm. In 303 the high-throughput imagestream assays, cell size was measured as length of the cell. The 304 difference in metric choice between these two systems was due to improved ability of 305 measuring cell length in the high-throughput assay, where it was less affected by focal 306 dependent changes in cell volume. In the haploid vs. diploid experiments, a measure of cell 307 volume was used, where cells were assumed to behave as cylinders, and volume was 308 calculated from the measured radius and length. This was done as diploids are wider than 309 haploids and thus a simple length metric cannot be employed for size binning. 310  a Schematic of major components influencing C-CDK activity at mitosis, and in red the 392 pathways that do not influence C-CDK AF . 393 394 b Example cell lineage traces from timelapse microscopy. Cell size in pixels 2 is given in 395 orange, and C-CDK fluorescence intensity is given in purple. Steep decreases in cell size 396 traces correspond to cell division. 397 398 c Scatter plot of mean C-CDK level vs. cell size from timelapse microscopy data. C-CDK level 399 is a measure of C-CDK fluorescence intensity. Colours indicate density of data. Inset boxplot 400 is mean nuclear C-CDK concentration immediately prior to degradation at anaphase. Boxes 401 represent IQR, with whiskers delimiting 5 th to 95 th percentiles. C-CDK WT n=28, C-CDK AF n=44 402 full cycles. 403 404 d Plot of the probability of division at the next timepoint (P(Div)) vs cell length for CDK WT 405 and CDK AF . Cells were followed through timelapse microscopy with measurements taken 406 each frame. P(Div) defined as the proportion of cells that undergo C-CDK degradation at 407 anaphase by the next timepoint, given as rate per minute. Points represent cells binned by 408 size, with points plotted at bin centre. C-CDK WT n=685, C-CDK AF n=961 timepoints. 409 410 e Plot of P(Div) function vs C-CDK level for CDK WT and CDK AF . C-CDK WT n=685, C-CDK AF n=961 411 timepoints. C-CDK intensity measurements taken every frame from timelapse microscopy, 412 and binned by C-CDK level. 413 414 f Schematic of Cut3 as a CDK activity reporter. Mitotic CDK dependent phosphorylation of 415 Cut3 on T19 results in nuclear translocation of the protein.

417
g Experimental outline of block and release timelapse experiment for panels (h),(j)-(o). 418 Asynchronous cells possessing an analogue sensitive (as) CDK were blocked in G2 using 1 419 μM 1NM-PP1 for 5 hours, and then released into a range of 1NM-PP1 concentrations. Cells 420 were then followed and monitored for their Cut3-tdTomato nuclear/cytoplasmic (N/C) ratio 421 (C-CDK activity) and C-CDK-YFP level using fluorescence timelapse microscopy (see 422 methods i Timelapse quantification of CDK activity in asynchronous cells. Traces are aligned so that 0 432 minutes corresponds to peak Cut3-tdTomato N/C ratio. Curve smoothing could move Cut3 433 peak earlier/later than exactly 0 min. Trace colour indicates cell size. Red X indicates 434 automatically defined mitotic entry point. C-CDK WT n=23 and C-CDK AF n=14. 435