Tissue confinement regulates cell growth and size in epithelia

Cell proliferation is central process in tissue development, homeostasis and disease. Yet how proliferation is regulated in the tissue context remains poorly understood. Here, we introduce a quantitative framework to elucidate how tissue growth dynamics regulate cell proliferation. We show that tissue growth causes confinement that suppresses cell growth; however, this confinement does not directly affect the cell cycle. This leads to uncoupling between rates of cell growth and division in epithelia and, thereby, reduces cell size. Division becomes arrested at a minimal cell size, which is consistent across diverse epithelia in vivo. Here, the nucleus approaches a volume limit set by the compacted genome. The loss of Cyclin D1-dependent cell size regulation results in an abnormally high nuclear-to-cytoplasmic volume ratio and DNA damage. Overall, we demonstrate how epithelial proliferation is regulated by the interplay between tissue confinement and cell size regulation. Highlights - In epithelia, regulation of cell growth and cycle are uncoupled - Cell growth is regulated by tissue-scale dynamics, which determine confinement - Cell volume in epithelial tissue is described by G1 sizer model with a tunable growth rate - Volume of cells in epithelial tissues is near a minimum set by genome size


Summary
Cell proliferation is central process in tissue development, homeostasis and disease. Yet how proliferation is regulated in the tissue context remains poorly understood. Here, we introduce a quantitative framework to elucidate how tissue growth dynamics regulate cell proliferation. We show that tissue growth causes confinement that suppresses cell growth; however, this confinement does not directly affect the cell cycle. This leads to uncoupling between rates of cell growth and division in epithelia and, thereby, reduces cell size. Division becomes arrested at a minimal cell size, which is consistent across diverse epithelia in vivo. Here, the nucleus approaches a volume limit set by the compacted genome. The loss of Cyclin D1-dependent cell size regulation results in an abnormally high nuclear-to-cytoplasmic volume ratio and DNA damage. Overall, we demonstrate how epithelial proliferation is regulated by the interplay between tissue confinement and cell size regulation.

INTRODUCTION
Regulation of cell proliferation is a central question for understanding tissue development, growth and homeostasis (Murray and Hunt, 1993;Nurse, 2000). In contrast to the exponential proliferation of isolated cells (Broach, 2012;Scott and Hwa, 2011), multicellular tissue requires tight coupling between cell proliferation and tissue growth (Irvine and Shraiman, 2017). One proposed mechanism for regulating proliferation in epithelia is the so-called process of "contact inhibition of proliferation" (henceforth referred to as contact inhibition) where cell proliferation becomes highly restricted due to spatial constraints imposed by the tissue (Irvine and Shraiman, 2017;McClatchey and Yap, 2012). The disruption of contact inhibition results in cell overgrowth and altered tissue architecture (Fomicheva and Macara, 2020;Kim et al., 2011;Leontieva et al., 2014). Therefore, contact inhibition is thought to play a key role in maintaining tissue homeostasis and preventing tumor formation (Irvine and Shraiman, 2017;Mendonsa et al., 2018). However, because contact inhibition is regulated through multiple signaling pathways and largely unknown parameters, we currently lack a framework for understanding the process across diverse tissues. This is evident from the literature where contact inhibition is described as dependent on cell density (Ibar et al., 2018), adhesion signaling (Kim et al., 2011;McClatchey and Yap, 2012) and mechanical stress (Irvine and Shraiman, 2017;Pan et al., 2016). As these variables are difficult to manipulate independently, it remains unclear how tissue geometry and growth dynamics impacts size and growth of constituent cells.
The regulation of size and growth of isolated mammalian cells is, by contrast, well understood (Cadart et al., 2018;Tan et al., 2021;. Single cells go through cycles of coupled growth and division and have stable cell size due to feedback between cell growth and division. However, there appear to be different feedback mechanisms acting in different contexts. For example, single cells mainly sense the total amount of cell growth throughout the cell cycle to regulate the length of cell cycle phases (Cadart et al., 2018;Tan et al., 2021). In contrast, mouse epidermal tissue shows feedback via a cell size checkpoint preventing small cells from entering S phase (Xie and Skotheim, 2020). Due to limited data in vivo it remains unclear if this is a consequence of tissue specific behavior in the skin or could reflect a difference in regulation between single cells and epithelial tissue. Several lines of evidence suggest the latter is true. For instance, the cell cycle duration can be on the scale of weeks or months in vivo (Sender and Milo, 2021), challenging established dilution-based mechanisms of cell cycle regulation . Further, prior work has shown a possible switch to size-dependent regulation of the cell cycle in cell culture models of epithelial tissue (Puliafito et al., 2017(Puliafito et al., , 2012. However, we lack a systematic study that explores how tissue-scale growth dynamics impact regulation of cell size and growth in epithelia.
To understand how cell proliferation is regulated in epithelium, we first performed a meta-analysis of cell size data and found that epithelial cell sizes are remarkably consistent and highly context dependent. The cell size in epithelial tissue in vivo is always smaller than single cells in culture. However, we could recapitulate the in vivo cell size using a cell culture model of epithelial tissue formation, indicating that tissue-scale phenomena impact cell size regulation. To quantitatively explore this, we employed model epithelial tissues with varied growth rates. We then introduce a general framework to quantify how tissue-scale growth dynamics constrain cell growth, providing a measure of "tissue confinement". We show that increasing tissue confinement reduces cell growth and YAP/TAZ signaling but does not impact the cell cycle duration directly. Instead, cell cycle duration is regulated by cell size. There is a sharp cell cycle arrest at a cell volume of ~1000 µm 3 , consistent with cell size found in vivo. In both epithelial and single cell contexts, cell size regulation is well described by a "G1 sizer model" with a tunable growth rate. In epithelia cyclin D1 protein levels are strongly cell size-dependent and overexpression of cyclin D1 reduces the minimal cell size. This suggests that the levels of cyclin D1 controls size-dependent cell cycle arrest. We see that abnormally small cells display DNA damage as these cells approach a size limit set by the volume occupied by the fully compacted genome. This suggests that, in addition to mediating cell cycle arrest during contact inhibition, cell size regulation pathways are critical for maintaining epithelial homeostasis. Overall, we demonstrate the general mechanisms of cell growth and division regulation in epithelia which provides new insight into proliferative processes in tissue development, homeostasis, and disease.
To test this hypothesis, we utilized several different epithelial cell lines (Madin-Darby canine kidney (MDCK), Caco-2 and HaCaT) to measure the cell volume in either subconfluent colonies (SC) or mature epithelium (ME). Controlling cell plating density allowed for the formation of subconfluent colonies each comprised of 50-1000 cells or a nearly confluent monolayer on collagen gels (see Methods). After the initial plating of monolayers, cell dynamics drive changes in their density, shape and speed over the next 1-2 days (Devany et al., 2021); we define a mature epithelium as the time at which these properties stop changing in time (see Methods). Cell sizes were visualized with a fluorescently tagged membrane protein (stargazin-gfp (CACNG2-gfp) or stargazin-halotag) (Fig. 1C). To facilitate measurement of cell volume, cells were trypsinized, resuspended and then imaged (Fig. 1C, Fig. S1, see Methods). When in sub-confluent colonies, the cell volume of all three epithelial cell types is ~2800 μm 3 (Fig. 1D, SC), consistent with the mean value of single cells in Fig. 1B (Fig. 1D, dashed line (ii)). Further, we found that ME culture conditions reduced the cell volume by 60% to plateau at ~1000 μm 3 (Fig. S3), a size consistent with in vivo data reported in Fig. 1B (Fig. 1D, dashed line (i),). We performed the same experiment on two cell lines which do not form coherent colonies, retinal pigment epithelial cells (RPE-1) and Mouse embryonic fibroblasts (MEF) and did not see size reduction ( Fig. S4). This suggests this context-dependency of cell size may be specific to epithelium. Together, these data suggest that contact inhibition qualitatively changes cell size regulation across diverse epithelia.

Cell size reduction involves an uncoupling of growth and the cell cycle
To query how cell growth and division rates change during the transition from subconfluent colonies to mature epithelium, live cell imaging was used to monitor changes in cell size and number. The data was aligned such that t=0 h denotes the onset of confluence (OC). For all earlier times, cells are in subconfluent colonies. By t > 12 h the cell movement has ceased, and density is constant; we denote this as a mature epithelium ( Fig. 2A). We first consider cell division and growth rates for t << 0 h (SC), t ~ 0 h (OC) and t >> 0 h (ME). Cell division rate, obtained by cell counting measurements, was completely arrested in the ME but only suppressed by ~40% at OC, as compared to SC (Fig. 2B, black bars). By contrast, the cell growth, obtained by quantifying the rate of protein dilution using pulse chase labeling (see Methods), was suppressed almost entirely at OC (Fig. 2B, purple bars). These data indicate suppression of cell growth and cycle are not tightly coupled during the transition from subconfluent to confluent tissue. Instead, cell growth is suppressed acutely at OC whereas cell cycle progression is only impacted in later stages (Fig. 2C). In single cells, cell growth and division are coupled to maintain a constant size . A division rate exceeding the growth rate would, instead, be expected to result in cell size reduction.
To test this hypothesis, we measured the cell size between t=0 and 18 h during the transition from OC to ME. Over this time, the cell height remained constant, such that changes in cell area were accurate indicators of cell volume (Fig. S2C). The average cell area from a population of ~1000 cells decreases by ~50% from OC (t = 0 h) to ME (Fig. 2D). To determine the mechanism driving changes in cell volume we performed single cell tracking. Cells that divided near the beginning of the experiment (t=0 h) were identified and tracked through the experiment. Individual cell trajectories revealed that the cell size reduction occurred by successive cell division events in the absence of cell growth (Fig. 2E, F). Indeed, across a large population of mother-daughter cell pairs, the cell size of a daughter cell 8 hr (~1/2 cell cycle time, τ) post cell division remained approximately half that of the mother cell size (Fig. 2G). This indicates minimal cell growth during the cell cycle. This is in stark contrast with subconfluent cells, where a cell grows at a constant rate and doubles in size prior to division into two daughter cells (Cadart et al., 2018). For single cells, we would expect the cell to grow by ~50% at 8 hours post division, resulting in a slope of ~3/4 (Fig. 2G, dashed line).
To demonstrate that cell division is necessary for cell size to decrease, experiments similar to those in Fig. 2A were performed with a Tet-On p27 MDCK cell line to artificially arrest the cell cycle in the presence of doxycycline (Sherr and Roberts, 1999). In the absence of dox (-dox), the volume decreases in ME compared to SC, similar to our previous experiments (Fig. 2H, I). Addition of doxycycline at OC prevented cell volume decrease in ME (ME +dox p27), and the volume of these cells remained similar to that of SC (Fig. 2H, I). Induction of a mutant p27 which does not arrest the cell cycle (+dox p27ck) (Vlach, 1997) had no effect on cell size in ME (Fig. 2I). Together, these data demonstrate that temporal uncoupling of cell growth and cell cycle result the cell size reduction during formation of mature epithelial tissue. At the onset of confluence, cell growth is highly suppressed and cell volume reduces by division in absence of cell growth (Fig 2J). Then at later times the cell cycle also becomes arrested, and cells reach a final cell size which is comparable to epithelium in vivo. We next sought to understand regulation of cell growth and cycle in the epithelium.

Tissue confinement regulates cell growth
These data motivate the need to introduce a quantitative framework to relate the tissue and cell growth rates. We first consider the growth of a multi-cellular tissue with initial area 0 and timedependent area, ( ). Then, consider this tissue broken up into individual cells to represent the proliferation dynamics of this tissue in the absence of spatial constraints (Fig. 3A). The collection of single cells grows in total size exponentially, such that the total time-dependent area is described by ( ) ~ 2 / , where τ is the average cell cycle time. The deviation of the tissue growth from this hypothetical maximum exponential rate quantifies the constraints tissue growth places on cell growth. For a certain tissue area, A', if the ratio of the tissue growth rate to the unconfined growth rate: is less than 1, then the tissue growth dynamics constrain cell proliferation. We then define the tissue confinement ( ′ ) = 1 − | ′ | ′ such that there is no confinement effect (C=0) when single cells and tissues have identical growth dynamics and C=1 when tissue growth rate is zero.
We explored this framework using model tissues comprised of large, circular colonies of MDCK cells, chosen for their well-characterized growth dynamics and the facility of controlling their size (Heinrich et al., 2020;Puliafito et al., 2012). Circular colonies of variable size A0 from ~1-7 mm 2 were formed by seeding the cells in a Polydimethylsiloxane (PDMS) stencil atop a glass coverslip (Fig. 3B&C). The stencil was then released to allow for colony expansion for Δt=48 hours (Fig.  3D). Importantly, the colony expansion is determined by radial migration speed of cells at the periphery to increase the colony radius by ∆ (Fig. 3B, arrow). Consistent with previous studies, the radial expansion rate was independent of colony size (Fig. 3D, Fig. S5). This results in a growth rate that scales quadratically with colony area (see Methods). For a given colony area, variation in provides additional control over colony growth rate (Fig. 3E). Under control conditions, varied between experiments from 15-30 μm/hr (Fig. S5). This tissue growth rate was not impacted when inhibiting cell division but was reduced by inhibiting cell migration by a focal adhesion kinase inhibitor (FAKi) (Fig. S5). Thus, variations in both the initial colony size and expansion velocity provide a wide range of tissue growth rates.
We generated model curves of the expected colony growth rates for the ranges of areas and edge velocities observed experimentally (Fig. 3F, solid lines). These rates were then compared to that expected for exponential growth of single cells, using the experimentally measured doubling time of 15 h (Fig. 3F, dashed line). For small areas, exponential growth is smaller than the growth rate of the expanding colony (Fig. 3F); here tissue-scale growth dynamics do not constrain cell proliferation. This is the behavior for SC. By contrast, for large areas, expanding colony growth rates become substantially lower than the exponential growth of single cells (e.g. Fig. 3F, gray shaded region). Here, tissue growth dynamics constrain cell proliferation. The colony area when exponential growth and quadratic growth rates are equal demarks the transition between these two regimes and, here, = 0 (Fig. 3F, black X). For each given growth model, the confinement is plotted as a function of colony area (Fig. 3G, lines). Confinement was determined from experimental data with varying 0 and (Fig. 3G, points). These experimental conditions then provide a means to systematically explore cell behavior in varied from <0.25 to ~0.8. Thus, our tissue confinement framework provides a quantitative method to assess how tissue-scale growth dynamics are expected to constrain growth of single cells.
To test the utility of this framework, we explored cell growth and signaling in tissues with varied levels of confinement. To query cell growth, we labeled the cells at t=0 with CellTrace, a fluorescent dye which reports on biomass production by its dilution (i.e. more growth leads to lower cell intensity) (see Methods). The total growth is determined from the CellTrace images by the ratio of intensity − 1 = ∆ . Since the growth rate of confluent monolayers is close to zero (Fig. 2B), the intensity of the confluent monolayer ~( = 0) , can be used as the standard to compare to the intensity of expanding colonies (Fig. 4A, C=1). This allows for determination of the growth rate by / − 1. For ∆ = 48 hours, subconflucent cells show significant 10-fold CellTrace dilution consistent with the cells doubling every 15h (Fig. 4A, C=0). We then used expanding colonies with varied 0 to explore intermediate levels of confinement from 0.2 to 0.8. In smaller colonies with C=0.2, cell growth is already suppressed to <50% that of sub-confluent conditions. By C=0.6, growth is restricted to <10% that of the subconfluent cells and is suppressed to nearly zero by C=0.8 (Fig. 4A). Changes in growth can also be modulated by changing the edge velocity. In our experiments, we observed that differences in migration rate significantly impact the cell growth, as predicted by our modeling (Fig. 4C). In all conditions, the intensity is remarkably uniform across the tissue suggesting that the growth regulation mechanism is a tissue-scale phenomenon.
To query cell growth signaling under confinement, we also performed immunostaining against YAP. YAP is a transcription factor implicated in regulating cell proliferation during contact inhibition (Aragona et al., 2013;McClatchey and Yap, 2012;Zheng and Pan, 2019). When YAP is active, it is localized to the nucleus; when inactive, YAP is localized to the cytoplasm. We see in the conditions with lower confinement, a greater faction of YAP is localized to the nucleus, whereas around C=0.5 it becomes more localized to the cytoplasm (Fig. 4B). This suggests that YAP activity is regulated in response to changes in tissue confinement (Fig. 4B). Taking together, all our experimental data from colonies with varying size and edge velocity (Fig. 3G) reveal a systematic decrease in cell growth and YAP signaling as a function of confinement (Fig. 4D,  points). Moreover, the predicted growth from the definition of tissue confinement is consistent with the experimental data (Fig. 4D, line). All of these data demonstrate the rapid suppression of cell growth at low levels of confinement.
At the onset of confluence, the cell division rate remains similar to subconfluent cells despite the increased confinement (Fig. 2B); this suggests that tissue confinement may not immediately affect the cell cycle. To query the cell cycle, we performed the expanding colony experiments with MDCK cells expressing the pip-degron fluorescent ubiquitination cell cycle indicator (FUCCI MDCK) (Grant et al., 2018) to measure the fraction of cells in S/G2/M in model tissues with varying levels of confinement. We restrict our analysis to short expansion times (∆ = 12 h) before cells have reached the ME state and arrested the cell cycle. In contrast to cell growth (Fig. 4F, peach data), there cell cycle is insensitive to tissue confinement (Fig. 4F, red). Instead, the fraction of cells in S/G2/M is constant (Fig. 4F, dashed line). This data reveals the qualitatively different impact of confinement on cell cycle and growth. Thus, the transient uncoupling between cell cycle and growth observed in Fig. 2B is consistent with a rapid increase in confinement at the onset of confluence.

A G1 sizer arrests the cell cycle in confined epithelium
We next explored how the cell cycle arrests in monolayers at the later stages of contact inhibition. After confinement reduces the growth rate, cell size decreases through successive cell division until the cell cycle becomes arrested (Fig. 2J). Previous work has shown that cell cycle regulation in isolated mammalian cells is cell size independent (Cadart et al., 2018) whereas it can be sizedependent for in in vivo epithelium (Xie and Skotheim, 2020). To examine if cell division is regulated by cell size in our data, we measured how the cell division rate varied as a function of cell size by tracking individual division events. We estimate volumes from the cell area multiplied by the typical cell height of 6.5±1.5 m (Fig. S2, mean±S.D.). Above a volume of 1200 μm 3 , the cell division rate is independent of size (Fig. 5A). However, the division rate sharply decreases for smaller volumes. This trend is observed across a range of experimental conditions and two epithelial cell types, indicating it is a robust feature of cell size regulation in confluent epithelial tissue (Fig. S6). We then used FUCCI MDCK cells to look more closely at the cell cycle regulation for large and small cells. From the FUCCI data, we obtained the S/G2/M duration by tracking single cell trajectories and saw that the duration of the S/G2/M phases is ≈10 hours and independent of cell size (Fig. 5B). In the same data, the duration of the entire cell cycle was estimated by measuring the fraction of cells in each cell cycle phase (see Methods). We see that the cell cycle duration rapidly increases for smaller cells (Fig. 5B, purple data). The division rate in Fig. 5A can also be used to estimate cell cycle duration and shows a similar trend (Fig. 5B, dashed line). Together, these data indicate an increased duration of the G1 phase for smaller cells. This is consistent with previous results that size regulation occurs at the G1-S transition (Cadart et al., 2018;Murray and Hunt, 1993;Xie and Skotheim, 2020).
Motivated by this data, we developed a simple "G1 sizer" model of size-dependent exit from G1 ( Fig. 5C) (Heldt et al., 2018;Xie and Skotheim, 2020). In the model, we simulate an ensemble of cells that grow at a constant rate, have two cell cycle phases G1 and S/G2/M, and divide into two daughter cells with half the mother volume. We added additional features based on experimental observations: (1) There is a sharp volume threshold of the G1-S transition rate and below this minimal size , the transition rate is zero, (2) cells have an S/G2/M duration of = 10 hours independent of cell volume, and (3) a variable cell growth rate G that is normalized to vary from 0 for no growth to 1 for growth in the unconfined condition. Due to rule (2) the minimum cell cycle time is hours and cells will grow by a minimum of before each division. When ≫ , cells are large compared to and the G1-S transition proceeds quickly. In this regime, the cell cycle regulation is size independent (timer-like) with a time between cell divisions (Fig. 5D, G  =1, Fig. S7). However, when the growth rate is suppressed such that << , additional time is required to relieve the size constraint of the G1-S transition (1) (Fig. 5D, G =0.05 , Fig. S7). In this regime, the cell cycle regulation is highly size-dependent (sizer-like).
Plotting the cell size at division as a function of cell size at birth for a range of growth rates shows that the model transitions smoothly from size-dependent to size-independent behavior as a function of growth rate (Fig. 5E, Fig. S8). Size-dependent cells divide at the same size and show no correlation between birth size and division size (Fig. 5E, dashed lines for G=0.05, 0.2). This contrasts with size independent cells which show a correlation between birth size and division size (Fig. 5E, dashed lines for G=0.7 & 1) (Amir, 2014;Cadart et al., 2018;Xie and Skotheim, 2020;. These different regulation mechanisms also occur in distinct cell size ranges consistent with previous work showing that large, rapidly growing, single cells are size independent (Cadart et al., 2018) and small, slowly growing cells, in vivo are size-dependent (Xie and Skotheim, 2020).
Having developed an understanding of the model at constant or near-constant growth rates, we tested if the model could also predict the cell size distributions found in the experiments of monolayer formation and maturation in Fig. 2B. We simulate monolayer formation in our model by a rapid quench of cell growth rate from 1 to 0 at t=0 and measure the cell size distribution over time (Fig. 5F). The simulation results (Fig. 5F, black) are consistent with those of the experiment (Fig. 5F, peach). This suggests that the G1 sizer model together with an understanding of how confinement impacts cell growth (Fig. 4F) is sufficient to explain transitions in size of isolated cells to those in epithelial tissue.

Size-dependent Cyclin D degradation leads to cell cycle arrest
To investigate molecular mechanisms of size control, we took advantage of our Tet-inducible cell lines to manipulate cell size in confluent monolayers. We prepared monolayers at the onset of confluence with Tet-On p27 and Tet-On p27ck cells. At t=0 we added doxycycline (+dox) to induce expression. After 5 days, both monolayers are in a cell cycle and growth arrested ME state, but the +dox p27ck cells are 40% the size of +dox p27 cells ( Fig. 2I; Fig. 6A). RNA sequencing revealed almost no differences in the steady-state transcriptome of these samples (Fig. 6B). However, close examination revealed several weak signatures (Fig. S9) including a slight downregulation of cyclin D1, 2, 3 in the smaller contact inhibited cells (Fig. 6B, inset). The G1/S transition has a steep dependence on cyclin D concentration (Fan and Meyer, 2021) so it is possible that small changes in cyclin D concentration are sufficient to arrest the cell cycle. Furthermore, cyclin D is strongly post transcriptionally regulated by degradation (Alao, 2007). To check if this difference in RNA abundance leads to changes in protein levels, we looked at cyclin D1 (cyD1) protein levels via immunofluorescence in ME formed with Tet-On p27 cells (+dox p27) and cocultures including Tet-On p27ck cells (+dox p27/p27ck). Since p27 is known to interact with cyclin D, we tested that its overexpression did not change the cyclin D1 levels by inducing p27 after ME formation (Delay +dox p27). Interestingly, we found significant difference in cyclin D1 abundance, with nearly undetectable levels in cells with a nuclear area <100 m 2 (Fig. 6 C; Fig.  S10). We observed that the intensity of CyD1 drops rapidly with decreasing cell size, measured by the nuclear area (Fig. 6D). The same trend was seen for all monolayer preparations, suggesting that the cyclin D1 level is regulated by a size-dependent pathway. This suggests that in addition to transcriptional changes in cyclin D, additional size-dependent post transcriptional regulation occurs, possibly as reported in other contexts (Alao, 2007;Masamha and Benbrook, 2009).
To test if decreased cyclin D levels are required to arrest the cell cycle, we overexpressed cyclin D1 in contact inhibited cells. We used Tet-On Cyclin D1-GFP (CyD) or Tet-On Cyclin D1 T286A T288A-GFP (CyDAA, a degradation resistant mutant) cells and induced the expression of additional cyclin D1 at OC. We then looked at the cell size 3 days later, after it had reached a plateau. We observe that overexpression of either CyD or CyDAA leads to decrease in minimal cell size in ME, compared to control (-dox) (Fig. 6E,F). Therefore, restoring Cyclin D1 in small cells is sufficient to initiate the cell cycle. This suggests that the depletion of cyclin D is necessary for size-dependent arrest of the cell cycle. We also overexpressed the viral oncoprotein E1a which is known to bind and inactivate Rb pocket proteins and activate the G1/S transition (Whyte et al., 1989). Cells that overexpressed E1a also showed decreased size, suggesting that cyclin D depletion arrests the cell cycle by inhibiting the G1/S transition (Fig. 6F).

Cell cycle arrest occurs near cell size minimum set by the genome size
We next wanted to understand why the cell cycle normally arrests at a volume of ~1000 m 3 . A possible constraint on cell size comes from the volume occupied by the genome. As the cell size decreases, the nucleus gets smaller and chromatin gets more compact (Viana et al., 2021). A simple estimate suggests low chromatin concentrations ~5% by volume in an average subconfluent mammalian cell (Volnuc~1/3Volcell ~800um 3 vs Volgenome ~ 40um 3 ) (Milo and Phillips, 2015). However, the concentration would increase several fold as cell size reduces and the total chromatin per cell remains constant. Previous measurements of chromosome size by TEM and AFM have shown that the volume of a full set of chromosomes are approximately 50-100 m 3 (Fritzsche and Henderson, 1996;Heslop-Harrison et al., 1989) and 50% chromatin by volume (Ou et al., 2017), thus, setting a lower limit on cell size. When we stained both the DNA and cell membrane, we observed that the abnormally small Tet-On CyDAA cells appear to have an unusually large nucleus relative to the cell size (Fig. 7A). This was surprising given that there is typically a tight scaling relationship between cell size and nuclear size (Viana et al., 2021). Comparing the cell volume against the nuclear volume for epithelium prepared under our previously described conditions, we observe this scaling relationship except in the Tet-On CyDAA cells in the presence of doxycycline (Fig. 7B, peach). Instead, we observe that the ratio of nuclear to cell size is rapidly increasing as cell size decreases below 1000 m 3 (Fig. 7C) and approaches the regions where DNA compaction exceeds the chromosomal values or where nuclear size would exceed cell size (Fig. 7B, gray, Fig.  7C gray). We hypothesized that increasing chromatin concentration could disrupt normal chromatin function, leading to DNA damage. In abnormally small cells we observed phospho-H2A.X foci indicating locations of DNA damage (Fig. 7D, E). This suggests that normal cells arrest near a cell size minimum but outside the range where DNA damage occurs frequently. DNA damage is known to arrest the cell cycle through Rb/Cyclin D independent mechanisms (Shaltiel et al., 2015) preventing further size reduction. Therefore, in epithelia, proliferative homeostasis is maintained by an interplay between cell growth in proportion to tissue constraints and cell sizedependent G1/S regulation which arrests cell size near a minimum (Fig. 7F).

DISCUSSION
While growth and division are coupled in single cells, we observe their regulation is uncoupled in epithelial tissue. The tissue growth dynamics regulate cell growth whereas cell division is regulated solely by cell size. Differences in these two rates drive changes in cell size depending on the tissue environment. In single cells, the environment places no constraint on cell growth leading to high growth rates and large cell size. In contrast, in mature epithelia, tissue growth rates are low and reduce cell size to a minimum. In this regime, cell size regulation is critical for maintaining cell homeostasis and preventing DNA damage. The consistency in cell size distributions across diverse epithelial cell types (Fig. 1B) suggest that our models should be broadly applicable to understand contact inhibition and cell size regulation across diverse biological systems.
Canonically, growth factor signaling is thought to be the main pathway to control and coordinate proliferation (Liang et al., 2017;Schlessinger and Ullrich, 1992). We identify an independent role for tissue confinement in controlling cell growth. While we exploited model tissues with a particular type of growth dynamics driven by edge migration, these ideas can be easily extended to arbitrary systems so long as the tissue growth dynamics can be readily characterized (Fig. S11). Tissue growth is driven by diverse processes, including migration, tissue buckling or mechanical stretch and occurs in response to cell turnover (Cowin, 2004;Guillot and Lecuit, 2013), all of which would reduce tissue confinement. Previous work has implied that cell growth and YAP/TAZ signaling in epithelium are regulated by mechanical stress (Irvine and Shraiman, 2017;Pan et al., 2016;Puliafito et al., 2012;Shraiman, 2005;Streichan et al., 2014). Our framework provides a means to isolate the roles of physical constraints on cell growth regulation. Importantly, confinement is a geometric quantity readily determined from timelapse microscopy. Our data show that confinement is a strong predictor of YAP/TAZ activity, demonstrating the utility of our model to study the mechanisms underlying epithelial growth control. However, future work is needed to determine the relationships between tissue confinement, growth and mechano-transduction.
Our observation of a transition between size-dependent and independent behaviors in epithelia may explain prior observations of size regulation in mammalian cells (Cadart et al., 2018;Xie et al., 2022;Xie and Skotheim, 2020). In our computational model we find that a size-dependent G1/S transition gives rise to both sizer-like and timer-like behaviors of cell size regulation at low and high growth rates, respectively (Fig. 5E). In future work, such a cell cycle model may be extended to other cell types or non-mammalian systems which show uncoupling between growth and division like Chlamydomonas or cyanobacteria (Li et al., 2016;Liao and Rust, 2021). Furthermore, the molecular mechanisms of G1 sizer regulation have remained elusive (Xie et al., 2022;Xie and Skotheim, 2020;Zhurinsky et al., 2010). By experimentally manipulating cell size, we showed that cyclin D1 regulation underlies G1 sizer behavior in epithelium. Cyclin D1 is strongly post transcriptionally regulated by degradation (Alao, 2007), suggesting that upstream kinase localization or activity may function in the size sensing pathway. Our observations may lead to future work to connect cyclin D1 regulation directly to cell size sensing.
Finally, below the minimal size set by cyclin D1 regulation, significant DNA damage occurs suggesting an important role of size regulation in maintaining cell homeostasis. Cancers which are driven by mutations in genes implicated in cell size regulation, such as small cell cancer, may show similar DNA damage leading to additional mutations. Alongside recent work which shows that very large cells become nonfunctional (Cheng et al., 2021;Lanz et al., 2021;Neurohr et al., 2019), the lower bound set by the genome size establishes a range of cell sizes for viable diploid mammalian cells from ~200-10000 µm 3 , similar to the range observed across different cell types (Milo and Phillips, 2015). Overall, our understanding of the proliferative behaviors in epithelium provides a new basis for studying development, homeostasis, and disease in complex epithelial tissues across diverse biological contexts.

Declaration of interests
The authors declare no competing interests.

Data Availability
RNA sequencing data will be deposited at the Gene Expression Omnibus prior to publication. Plasmids will be deposited to addgene prior to publication. Analysis and simulation code will be published to Github prior to publication. Image data and histology analysis will be deposited to figshare prior to publication.

Lead Contact Statement
Further information and requests for resources and reagents should be directed to and will be fulfilled by the lead contact, Margaret Gardel (gardel@uchicago.edu).