Cell size sensing in animal cells coordinates anabolic growth rates with cell cycle progression to maintain uniformity of cell size

The uniformity of cell size in healthy tissues suggests that control mechanisms might coordinate cell growth and division. We derived a method to assay whether growth rates of individual cells depend on cell size, by combining time-lapse microscopy and immunofluorescence to monitor how variance in cell size changes as cells grow. This analysis revealed two periods in the cell cycle when cell size variance decreases in a manner incompatible with unregulated growth, suggesting that cells sense their own size and adjust their growth rate to correct aberrations. Monitoring nuclear growth in live cells confirmed that these decreases in variance reflect a process that selectively inhibits the growth of large cells while accelerating growth of small cells. We also detected cell-size-dependent adjustments of G1 length, which further reduce variability. Combining our assays with chemical and genetic perturbations confirmed that cells employ two strategies, adjusting both cell cycle length and growth rate, to maintain the appropriate size.

the intriguing question of whether there are dedicated mechanisms that restrict cell size to a specific range. Is size uniformity the product of cellular processes that monitor cell size and  cerevisiae (4,5). In contrast, studies of animal cell size have remained inconclusive as to whether animal cells employ any form of size sensing (1, 3). As early as 1965, A. Zetterberg published 6 evidence consistent with the existence of a cell size checkpoint in human fibroblasts (6,7). Later literature, however, has predominantly suggested the opposite view, i.e. that growth and cell 8 cycle progression are not coordinated (8)(9)(10). Similarly, in 2013 our group developed a mathematical analysis (ergodic rate analysis, ERA) that predicted the existence of a size-determine that animal cells monitor their size and correct deviations in cell size. Our results show that, like S. cerevisiae, animal cells that are smaller than their target size spend longer periods of 2 growth in G1. Surprisingly, however, we found that in addition to a G1 length extension in small cells, animal cells also employ a conceptually different strategy of size correction. During two 4 distinct points in cell cycle, anabolic growth rates are transiently adjusted so that small cells grow faster and large cells grow slower. These periods of growth rate adjustments function to 6 lower cell size variability, promoting size uniformity. To our knowledge, such a reciprocal coordination of growth rate with cell size has not been previously observed in any organism. Previous literature has defined cell size as cell volume (12,13) or cell mass (14). In this 12 study, we define cell size by a cell's total macromolecular protein mass, as this metric most closely reflects the sum of anabolic processes typically associated with cell growth (15) and with 14 activity in growth promoting pathways such as mTOR (16). In contrast, cell volume is a more labile phenotype, sensitive to ion channel regulation and fluctuations in extracellular osmolarity.
If cell size checkpoints do not exist, and the size of a cell is not a determinant of S phase entry, the reason that S phase cells are larger than G1 cells must be that S-phase cells have had 18 more time to grow since their last division. Thus, to test whether a cell size checkpoint regulates S phase entry we compared cells in S-phase to cells of the same age (i.e. time elapsed since last 20 division) that are still in G1.
To measure cell size together with the amount of time elapsed since a cell's last division, we took the following approach. We used time-lapse microscopy to image live HeLa and Rpe1 2 cells for 1-3 days, and then immediately fixed them and applied AlexaFluor 647-Succinimidyl Ester (SE-A647), a quantitative protein stain that we previously established as a an accurate 4 measure of cell mass (11). (For more supporting evidence on the use of this method, see supplementary file 1-1.) We computationally tracked thousands of individual cells over the 6 course of the time-lapse movies and recorded the amount of time that elapsed between each cell's "birth" via mitosis and its fixation, which we will refer to as the cell's "age". To 8 distinguish S-phase cells from cells in G1, we used cell lines stably expressing mAG-hGem (17), a fluorescent reporter of APC activation and G1 exit. This experimental design allowed us to measure the age, size, and cell cycle stage of each cell at the time of fixation. Figure 1A shows the average cell size as a function cell age (i.e. time since division). As Furthermore, the mean size of G1 cells plateaus as cells begins to enter S-phase, consistent with difference between identically aged G1 and S phase cells is statistically significant (student's ttest p< 3.92e-04) and was observed in three additional independent replicate experiments 2 (p<0.009, p<5.80e-08, p<9.07e-15).
If cells enter S-phase only after attaining a threshold size, cells that are born small are 4 expected to have longer G1 periods. To test this, we assayed the correlation of cell size at birth with a direct measurement of G1-length in single cells. Since we cannot use the protein staining 6 technique in live cells, we measured the size of the nucleus as a proxy for cell size, using timelapse microscopy. In yeast, the nucleus is known to grow continuously throughout all stages of 8 cell cycle and is correlated with cell size (19), and we found that the same is true in our experimental model (supplementary file 1-2). To further verify that nuclear growth accompanies cellular growth, independent of cell cycle progression, we arrested the cell cycle with aphidicolin and still observed a dramatic increase in nuclear size as cells grew (supplementary file 1-fig.

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S2C). When we monitored nuclear growth in single cells expressing nuclear-localized cell cycle markers(17), we observed a negative correlation between size of the nucleus at birth and G1 14 duration ( fig. 1C). This result confirms that cells that are smaller at birth compensate with increased periods of growth in G1 and is consistent with the model of a cell size threshold at G1 16 exit.
To further test whether information about cell size is communicated to the cell cycle 18 machinery, we examined the effect of slowing down cellular growth rates on the length of G1. If cells leave G1 only when a particular size has been reached, slowing down their growth rate is 20 expected to prolong G1, as cells would require more time to reach the threshold size. Growth rate can be slowed down with drugs such as the mTORC1 inhibitor rapamycin. Culturing cells in 70 nM rapamycin caused a 60% decrease in the average growth rate and a compensatory 80% increase in G1 duration, resulting in only a 20% reduction in cell size ( fig. 2A-E). Figure 2 shows that the influence of rapamycin on growth rate and on G1 length is far more dramatic than its influence on cell size. Previous studies have already shown that in 4 addition to its effect on cell size, rapamycin also alters G1 length (20)(21)(22). In those studies, the dual influence of rapamycin on both size and G1 length were interpreted to suggest two 6 independent (pleiotropic) functions of the drug (23)(24)(25). However, our current results suggest an alternative, more parsimonious interpretation. Namely, that the influence of rapamycin on G1 8 length is an indirect consequence of its influence on growth rate. According to this interpretation, the inhibition of cell growth by rapamycin results in a gradual reduction of cell size which, in turn, triggers compensatory increases in G1. This new interpretation is consistent with the negative correlation that we observe between cell size and G1 length, even in the absence of  The rate of cell growth is adjusted in a size-dependent manner The results described above suggest that size uniformity of animal cells is maintained by 22 keeping small cells in G1 for longer periods of growth. However, terminally differentiated animal cells do not divide and yet, often undergo precise adjustments of cell size (26). This suggests the presence of size specification mechanisms that are not dependent on regular cell 2 divisions. Furthermore, the size threshold model is fundamentally limited in its ability to correct the size of very large cells. If some cells grow fast enough to double even in a very short cell 4 cycle, regulation of cell cycle length alone cannot constrain size variability in the population.
The size of a cell is the product of both growth duration (cell cycle length) and growth 6 rate. If cells have a mechanism to sense their own size, it may be that not only G1 length but also cellular growth rate is adjusted accordingly, to achieve the appropriate cell size. To investigate 8 this possibility, we examined the relationship between cell size and growth rate.
If a cell can sense its own size and adjust its growth rate accordingly -just as a thermostat coordinates heat production with room temperature via short bursts of heat-we might expect these corrections to be transient and subtle. Experimental detection of transient changes in  In the absence of any size-dependent growth rate regulation, the variance in cell size is expected to increase with age, as cells grow, since individual cells in a population will vary in their growth rates. In any given time interval, fast-growing cells will accumulate more mass than  3B). This can be demonstrated by considering a time interval during which cells grow from S1 to S2. Cell size variance at any given time t2 is related to the cell size variance at any previous time t1 by: Therefore, the change in size variance follows: where ∆S is the change in cell size accruing over the time period ∆t, i.e. the growth rate. Since The -value analysis is a new method to interrogate size control in growing cells. As long as the mean cell size is increasing over time, can be interpreted as follows. If a cell's growth rate is independent of its size, directly equals the coefficient of variation (CV) of cellular growth rates. This can be shown by substituting the relationship in eq. 1 into the formula 6 for , noting that, if growth rates are size-independent, variance will increase over time and Cov(S1,∆S) = 0. In this case, = Negative values of G (arising from dips in variance) imply that growth rate is actually not independent of size, and that cell size and subsequent growth rate are negatively correlated.
We can also note that if is much higher than is plausible for the CV of growth rates (which will equal 1 if growth is a Poisson process), it is likely that growth is positively correlated with 12 size, as in the case of exponential growth.
Plotting versus cell age consistently reveals two distinct periods during which cell size and growth rate are negatively correlated (i.e. is negative), in both HeLa and Rpe1 cells There was also a very low rate of apoptosis (<1% of cells imaged from birth that died before dividing).

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The results of the -value analysis are surprising. G1 checkpoints that link cell cycle progression to cell size have been previously observed in yeast (4). A few reports have suggested 10 that G1 duration depends on growth rate rather than cell size (27,28). However, a process that stabilizes cell size by transient corrections of growth rate has not been previously observed in 12 any organism. In fact, such a possibility was never previously hypothesized except in our own previous publication of ERA (11), but since ERA is fundamentally incapable of distinguishing 14 changes in growth rate from changes in cell cycle progression rate, that suggestion remained a speculation. As such, this result represents the first clear evidence that cellular growth rates are 16 adjusted in a cell-size-dependent manner to increase uniformity in a population.
To test the conclusions of the -value analysis, we asked whether the correlation of growth rate and cell size could be observed directly in live cells. Using time-lapse microscopy, we monitored nuclear growth in hundreds of live cells over several days. Comparing growth and number of cells present. From these measurements, we calculated the average growth rate and cell cycle length of cells in each condition. Cell cycle length was also independently measured, by monitoring the proliferation of live cells in each condition with differential phasecontrast microscopy over the course of three days.
2 Figure 5A,B shows that chemical perturbations of growth rate and perturbations of cell cycle length had surprisingly small effects on cell size. Consistent with the dual-mechanism model, treatment with all but one of the tested compounds resulted in coordinated changes of both cell cycle length and growth rate, such that normal cell size was maintained ( fig. 5C, fig.   6 6C,D,F,G). Furthermore, while the inhibitors of cell cycle regulators produced an immediate effect on cell cycle length, their effect on growth rate was observed only after prolonged 8 treatment (Fig. 5E). This suggests that the effect of these inhibitors on growth rate is indirect and is mediated by a property that accumulates over time, presumably cell size. Similarly, cycloheximide, rapamycin and Torin-2 induced an immediate decrease in growth rate, while the effect of these drugs on cell cycle length was observed after a delay (Fig. 5F). Naively, changing

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To further test these conclusions, we overexpressed cyclin E to shorten the duration of cell cycle. Since CDK inhibitors that lengthened cell cycle were counteracted by a reduction in 18 growth rate, we asked whether shortening the cell cycle would result in an increased growth rate. Figure 5D shows that, as anticipated, the shorter cell cycles caused by cyclin E overexpression 20 are compensated for by faster rates of cell growth, rendering cell size relatively unchanged.
Of the tested perturbations to cell cycle regulators, only the cdk4/6 inhibitor palbociclib increased cell cycle length without a compensatory decrease in growth rate, causing an unusual increase in cell size ( fig. 6A,B). Future studies investigating how palbociclib perturbs the crosstalk between cell cycle progression and cell growth may provide clues to the mechanisms of 2 cell size sensing.
A quantitative prediction of the dual-mechanism model is that growth rate, , and cell cycle length, , are coordinated to maintain cell size at its fixed target size: 8 This means that growth rate and cell size are related by, = , where is a constant target size. Figure 5 shows that our measurements are in agreement with this prediction. The curves in  decreases growth rate by 50% would result in a 50% decrease in cell size. Results from our experiment show that, for many drugs, this expectation is false. While drug treatments produced 16 up to fourfold changes in both growth rate and cell cycle length, the resulting changes in cell size were mostly under 30%. As mentioned above, while the influence of CDK inhibitors on cell cycle progression was immediate, their influence on growth rate was observed only after many hours of drug treatment (Fig. 5E), supporting the conclusion that the decrease in growth rate is a 20 response to the gradual increase in cell size that occurs during a lengthened cell cycle.
Conversely, while the influence of mTOR inhibitors on growth rate was immediate, their cells have evolved regulation that buffers cell size from changes in cell cycle length or growth rate. In this light, it may be interesting to examine why cells have evolved to tolerate changes in 2 cell cycle length and growth rate but not changes in cell size.
Finally, in an attempt to disrupt the processes that maintain cell size uniformity, we 4 treated cells with the HSP90 inhibitor radicicol. HSP90 is known to suppress phenotypic variability (29) and has also been found to regulate both cell cycle progression(30,31) and 6 mTORC1 mediated growth in response to cellular stress (32). Remarkably, culturing cells in radicicol not only decoupled growth rate and cell cycle length, but also resulted in a marked 8 increase in cell size heterogeneity ( fig. 6A,E). This finding illustrates that cell size uniformity is a regulated phenotype that can be perturbed by disrupting the coordination of growth and cell cycle progression.

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Discussion: 14 The subject of cell size uniformity has been largely unexplored. It was not even clear whether size uniformity is important or why size is so uniform despite variation in growth rates ways, and with assays that can separately quantify each mode of regulation, we are in a position to uncover its molecular identity.

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In tissues, growth and shrinkage are often due to control of cell proliferation and apoptosis but some cell types such as neurons and muscle cells are controlled by cell growth rather than proliferation. Hence, in non-dividing cells that maintain size we may find part of the circuitry used in proliferating cells. Although pathways, such as mTOR, that promote cell growth

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have been delineated (16,33), it remains unclear how a common set of pathways may specify a different size in each cell type, while ensuring precise uniformity within cells of a common type.

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The approaches developed here can be combined with perturbations of these pathways to answer this fundamental question. With that knowledge, we can begin to explore the consequences of              Jennifer Waters and Lara Petrak. Celina Qi assisted in computational analysis of time-lapse movies. We would like to thank Yuval Dor and Nish Patel for helpful discussions and advice.