Author response: Size-dependent patterns of cell proliferation and migration in freely-expanding epithelia (2020)

Article Figures and data Abstract eLife digest Introduction Results Discussion Materials and methods Data availability References Decision letter Author response Article and author information Metrics Abstract The coordination of cell proliferation and migration in growing tissues is crucial in development and regeneration but remains poorly understood. Here, we find that, while expanding with an edge speed independent of initial conditions, millimeter-scale epithelial monolayers exhibit internal patterns of proliferation and migration that depend not on the current but on the initial tissue size, indicating memory effects. Specifically, the core of large tissues becomes very dense, almost quiescent, and ceases cell-cycle progression. In contrast, initially-smaller tissues develop a local minimum of cell density and a tissue-spanning vortex. To explain vortex formation, we propose an active polar fluid model with a feedback between cell polarization and tissue flow. Taken together, our findings suggest that expanding epithelia decouple their internal and edge regions, which enables robust expansion dynamics despite the presence of size- and history-dependent patterns in the tissue interior. eLife digest Cells do not exist in isolation. Instead, they form tissues, where individual cells make contact with their neighbors and form microscopic ‘architectures’. Epithelia are a type of tissue where cells are arranged in flat sheets, and are found in organs such as the lining of the kidney or the skin. Tissues need to grow, especially early in life. If tissues are damaged – for example, if the skin is cut or grazed – cells also need to divide (to create new healthy cells) and move as a group (to close the wound). Such coordinated motions result in cells exhibiting distinct group behaviors, similar to those observed within crowds of people or schools of fish. If coordination breaks down, problems can happen such as uncoordinated tissue growth seen in cancer. However, how cell movements are coordinated is still not fully understand. For example, researchers know that cells’ positions within a group can determine how they behave, meaning that even the same type of cell could behave differently at the edge or center of a tissue. This suggests that the initial size and shape of a tissue should influence its subsequent growth and behavior; however, the nature of this influence is still largely unknown. Heinrich et al. therefore wanted to determine the differences in the way larger and smaller tissues grow. Microscope imaging was used to track the growth of circular, artificial tissues made from single-layered sheets of dog kidney cells grown in the laboratory. Comparing how quickly the tissues expanded revealed that the area of tissue circles that started out smaller increased at a much faster rate than that of tissue circles that were larger to begin with. This turned out to be because the edges of the tissues grew at a constant speed, independent of their initial size or shape, but circles with a smaller area have a larger proportion of cells on their edges. The motions of the cells at the center of the tissues had no effect on how the edges of the tissue grew. A final observation was that the way tissues of a given size behaved depended on whether they had grown to be that size, or they started off that big. These results shed light on how groups of cells interact in growing tissues. In the future, this information could be used to predict how different tissues grow over time, potentially helping scientists engineer better artificial tissues or organs for transplantation. Introduction Writing in 1859, physiologist Rudolf Virchow presented the concept of the ‘Zellenstaat’ or ‘Cell State,’ describing tissues as ‘a society of cells, a tiny well-ordered state’ (Virchow, 1855). This social framework motivated Abercrombie and Heaysman, 1954 work on cellular behavior that elucidated how encounters between cells can regulate locomotion and proliferation via contact inhibition. Since then, concerted interdisciplinary effort has been brought to bear on understanding how cell-cell interactions give rise to the complex collective behaviors driving so many crucial biological processes. One of the most foundational collective behaviors is collective cell migration—the directed, coordinated motion of cellular ensembles that enables phenomena such as gastrulation, wound healing, and tumor invasion (Friedl and Gilmour, 2009). Given this importance, considerable effort spanning biology, engineering, and physics has been directed towards understanding how local cellular interactions can give rise to globally coordinated motions (Alert and Trepat, 2020; Hakim and Silberzan, 2017). Studies of collective cell migration are most often performed using epithelial tissues due to their fundamental role in multicellular organisms and strong cell-cell adhesion, which in turn gives rise to elegant, cohesive motion. Moreover, given that epithelia naturally form surfaces in vivo, studying epithelial layers in vitro has a physiological basis that can inform our understanding of processes such as healing (Poujade et al., 2007), envelopment (Steinberg, 2007), and boundary formation (Dahmann et al., 2011). These features have made epithelia both the gold standard in collective cell migration studies, and one of the most well-studied models for biological collective behaviors. Due to the complexity of collective behaviors, much effort has gone towards reductionist assays that restrict degrees of freedom and ensemble size to simplify analysis and interpretation. One such approach is to confine a tissue within predefined boundaries using micropatterning to create adhesive and non-adhesive regions (Doxzen et al., 2013; Deforet et al., 2014; Notbohm et al., 2016; Pérez-González et al., 2019; Peyret et al., 2019; Petrolli et al., 2019). Such confinement mimics certain in vivo contexts such as constrained tumors as well as aspects of compartmentalization during morphogenesis (Lecuit and Lenne, 2007). Alternately, many studies have explored the expansion of tissues that initially grow into confluence within confinement but are later allowed to migrate into free space upon removal of a barrier. A popular assay of this type relies on rectangular strips of tissue that are allowed to expand in one or both directions (Poujade et al., 2007; Trepat et al., 2009; Petitjean et al., 2010; Reffay et al., 2011; Nnetu et al., 2012; Serra-Picamal et al., 2012; Zhang et al., 2017; Uroz et al., 2018; Tlili et al., 2018), where averaging along the length of the strip can reveal coordinated population-level behaviors such as complex migration patterns, non-uniform traction force fields, and traveling mechanical waves. Other studies have focused on the isotropic expansion of micro-scale (< 500 μm diameter) circular tissues using the barrier stencil technique (Jang et al., 2017) as well as photoswitchable substrates (Rolli et al., 2012). Still more work has explored approaches to induce directional migration, from geometric cues to applied electric fields (Vedula et al., 2012; Cohen et al., 2014). In contrast to micro-scale confinement assays, other work has focused on large, freely-expanding tissues of uncontrolled initial size and shape, which grow from either single cells (Puliafito et al., 2012; Huergo et al., 2011) or cell-containing droplets (Lee et al., 2013; Beaune et al., 2014). Related experiments track long-term growth of cell colonies via images taken once per day over several days, but this low temporal resolution cannot access timescales over which migration is important (Huergo et al., 2011; Simpson et al., 2013). Thus, there is still a lack of assays to study long-term expansion and growth of large-scale tissues with precisely-controlled initial conditions, especially initial tissue size, shape, and density. To address this gap, we leveraged bench-top tissue patterning (Poujade et al., 2007; Cohen et al., 2016) to precisely pattern macro-scale circular epithelia of two sizes (>1 mm in diameter) and performed long-term, high frequency, time-lapse imaging after release of a barrier. To elucidate the consequences of size effects on the tissue, we tracked every cell, relating the overall expansion kinetics to cell migration speed, cell density, and cell-cycle dynamics. We find that, whereas the tissue edge dynamics is independent of the initial conditions, the tissue bulk exhibits size-dependent patterns of cell proliferation and migration, including large-scale vortices accompanied by dynamic density profiles. Together, these data comprise the first comprehensive study of macro-scale, long-term epithelial expansion, and our findings demonstrate the importance of exploring collective cell migration across a wider range of contexts, scales, and constraints. Results Expansion of millimeter-scale epithelia of different sizes and shapes We began by characterizing the overall expansion and growth of tissues with the same cell density but different initial diameters of 1.7 mm and 3.4 mm (a 4X difference in area, with tissues hereafter referred to as either ‘small’ or ‘large’), using an MDCK cell line stably expressing the 2-color FUCCI cell-cycle marker (Sakaue-Sawano et al., 2008; Streichan et al., 2014; Uroz et al., 2018; Beaune et al., 2014; Benham-Pyle et al., 2016). We patterned the tissues by culturing cells in small and large circular silicone stencils for ∼18 hr (Cohen et al., 2016; Poujade et al., 2007), whereupon stencils were removed and tissues were allowed to freely expand for 46 hr (Figure 1A, Figure 1—video 1), while images were collected at 20 min intervals using automated microscopy (see Materials and Methods). Our cell seeding conditions and incubation period were deliberately tuned to ensure that the stencils did not induce contact inhibition of proliferation prior to stencil removal (checking FUCCI to ensure the tissue was not arrested in G1). Upon stencil removal, tissues expanded while maintaining their overall circular shape throughout the 2 day experiment. Unless otherwise noted, cell density at stencil removal was ∼2700 cells/mm2, a value consistent with active and growing confluent MDCK epithelia (Streichan et al., 2014; Uroz et al., 2018). Figure 1 with 5 supplements see all Download asset Open asset Expansion dynamics of millimeter-size cell monolayers. (A) Footprint throughout 46 hr growth period of representative small (left) and large (right) circular tissues, with the tissue outlines drawn at 4 h increments. Initial diameters were 1.7 mm and 3.4 mm. (B) Small circles exhibit faster relative area, A⁢(t)/A0, increase than large circles, where A0 and A⁢(t) are the areas of tissues at the beginning of the experiment and at time t, respectively. Purple points show the relative area increase, A⁢(t+t0)/A⁢(t0), of small tissues from the time t0=30 h when they reached the size of the large circles. (C) Average tissue density ρ⁢(t)=N⁢(t)/A⁢(t) has non-monotonic evolution in small tissues but monotonically increases in large tissues, where N⁢(t) is the number of cells in a tissue at time t. (D) Edge radial velocity vr is largely independent of initial tissue size and cell density. We grouped initial cell densities as ρ1=[2350,3050] cells/mm2, ρ2=[1650,2350] cells/mm2, and ρ3=[1300,1650] cells/mm2. (E) Experimental data on tissue shape and model fits. Assuming a constant migration speed vn in direction normal to the edge, we can predict the area expansion dynamics of elliptical tissues with different aspect ratios. The model fits our data for all tissues with vn≈29.5 µm/hr, yielding normalized χ2 values of 0.79, 0.13, and 0.06 for aspect ratios of 8, 4, and 1 respectively (χ2< 1 indicates a good fit; see Materials and methods). In B, data are from n = 16 tissues across five independent experiments (small and large circles). In C, n = 11 across four experiments for small circles, and n = 9 across three experiments for large circles. In D, n = 16 across five independent experiments for small and large circles, ρ=ρ1; n = 13 across three experiments for small circles, ρ=ρ2; and n = 11 across three experiments for small circles, ρ=ρ3. In E, n = 4 across two experiments for a/b = 1 and a/b = 4, and n = 5 across two experiments for a/b = 8. Shaded regions correspond to standard deviations. First, we measured relative areal increase (Figure 1B) and relative cell number increase (Figure 1—figure supplement 1) of small and large tissues. By 46 hr, small and large tissues had increased in area by 6.4X and 3.3X, respectively, while cell number increased by 9.2X and 5.5X, respectively. Since proliferation outpaces area expansion in long-term growth, average tissue density increased by the end of the experiment. The evolution of average tissue density was more complex, however, as small tissues experienced a density decrease from 4 to 12 hr while large tissues exhibited a monotonic increase in cell density (Figure 1C). Accordingly, at any given time after stencil removal, large tissues had a higher density than small tissues. Non-monotonic density evolution has been observed in thin epithelial strips (Poujade et al., 2007) and likely arises from competition between migration and proliferation dynamics, which we discuss later. We then related area expansion to the kinematics of the tissue edge. To quantify edge motion, we calculated the average radial velocity of the tissue boundary, vr⁢(t), at 1 hr intervals over 46 hr (Materials and methods). We found that vr is independent of both tissue size and a wide range of initial cell densities, in all cases reaching ∼30 μm/h after ∼16 hr (Figure 1D). Before reaching this constant edge velocity, vr ramps up during the first 8 hr after stencil removal, and, notably, overshoots its long-time value by almost 30%. We hypothesize that the overshoot is due to the formation of fast multicellular finger-like protrusions that emerge at the tissue edge in the early stages of expansion and then diminish (Figure 1—video 2). This hypothesis is supported by a recent model showing that edge acceleration (as observed during the first 8 hr in Figure 1D) leads to finger formation (Alert et al., 2019). It is remarkable that the edge radial velocity vr⁢(t) is independent of the initial tissue size and density, especially considering that cell density evolution shows opposite trends at early stages of expansion for small and large tissues (Figure 1C). This observation suggests that the early stages of epithelial expansion are primarily driven by cell migration rather than proliferation or density-dependent decompression and cell spreading. The observation that vr is independent of tissue size ought to explain why small tissues have faster relative area expansions than large tissues. We hypothesized that the relation between tissue size and areal increase could be attributed primarily to the perimeter-to-area ratio. Assuming a constant edge velocity vn normal to the tissue boundary, the tissue area increases as d⁢A=P⁢vn⁢d⁢t, where P is the perimeter of tissue and d⁢t is a small time interval. Thus, the relative area increase d⁢A/A=(P/A)⁢vn⁢d⁢t scales as the perimeter-to-area ratio, which is inversely proportional to the radius for circular tissues, so the relative area increases faster for smaller tissues (Figure 1B). To verify that the perimeter-to-area ratio is proportional to the relative area increase, we analyzed elliptical tissues with the same area and cell density but different perimeters (Figure 1—video 3). Increasing the perimeter-to-area ratio of a tissue by increasing its aspect ratio indeed leads to faster relative area expansion (Figure 1E). A simple, edge-driven expansion model with linear increase of the tissue major and minor axes predicts A⁢(t)/A⁢(0)=(a+vn⁢t)⁢(b+vn⁢t)/(a⁢b), where a and b are the initial major and minor axes of the tissue. This model fits our data well assuming the same edge speed vn≃29.5 μm/h for all tissues (Figure 1E). This observation suggests that edge speed is mostly independent of edge curvature. However, we measure a smaller edge speed at the major axes of ellipses, which are high-curvature points with radius of curvature rc≲0.75 mm (Figure 1—figure supplement 2). Such high curvatures are concentrated around the major axes of our elliptical tissues. However, most of the tissue edge has a smaller curvature, and therefore advances at a curvature-independent speed. Further, even high curvature regions blunt due to expansion over time (see Figure 1—video 3). As a result, our model with a single edge speed vn≃29.5 μm/h is sufficient to capture the area expansion of both circular and elliptical tissues (Figure 1E). Together, our findings demonstrate that epithelial shape and size determine area expansion dynamics via the perimeter-to-area ratio. This relationship results from the fact that tissues exhibit a constant, size-independent, migration-driven edge speed normal to tissue boundary. Since initial tissue size does not affect boundary dynamics, but does impact the relative growth and expansion of the tissue, we hypothesize that cells in the tissue bulk exhibit tissue size-dependent behaviors. Spatiotemporal dynamics of migration speed and radial velocity Having demonstrated the role of the boundary in the expansion of large-scale epithelia, we sought to relate tissue areal expansion rate to internal collective cell migration dynamics. We used Particle-Image-Velocimetry (PIV, Materials and methods) to obtain flow fields describing cell migration within freely expanding epithelia (Poujade et al., 2007; Petitjean et al., 2010; Angelini et al., 2010; Cohen et al., 2014; Aoki et al., 2017). We constructed kymographs (Materials and Methods) to display the full spatiotemporal flow patterns of the tissue (Figure 2A,B; Serra-Picamal et al., 2012; Zhang et al., 2017), averaging over the angular direction and over 16 tissues (for representative kymographs, see Figure 2—figure supplement 1). We also separately show time evolution (Figure 2C) and spatial profiles (Figure 2D) of speed and radial velocity to compare small and large tissues. Figure 2 with 1 supplement see all Download asset Open asset Speed and radial velocity in inner and outer tissue zones. (A,B) Average kymographs of (A) speed and (B) radial velocity vr throughout expansion for small (left) and large (right) tissues. (C) Evolution of the average speed of boundary (top) and center (bottom) zones, defined as regions extending ∼200 μm from the tissue center and tissue edge, respectively. This width of the zones corresponds approximately to the velocity-velocity correlation length for MDCK cells (Petitjean et al., 2010). While the speed in the edge zone remains high in both small and large tissues, the speed in the center zone begins to decrease ∼24 hr sooner in large tissues than in small tissues, as the central zone of the small tissues has particularly high speed from to (D) of speed (top) and radial velocity (bottom) at hr, from the edge of the tissue that the tissues are from the edge of the tissue data are from n = 16 tissues across five independent experiments (small and large circles). Speed and radial velocity profiles of large and small tissues for the first 500 μm from the tissue edge. The average difference between the profiles in this zone is μm/h and μm/h respectively, while the standard for any in either is of speed and radial velocity reveal the of an edge of radial cell motion (Figure with similar to the radial edge velocity in Figure to μm from the tissue edge, the speed and radial velocity profiles are for small and large tissues (Figure showing that cell motion the tissue edge is independent of tissue The tissue in contrast, exhibit size-dependent behaviors. For both small and large tissues, a of cell speed and radial velocity the tissue at μm/h (Figure and B, This is approximately faster than the tissue edge speed, consistent with of rate in cell monolayers et al., 2012). after the of radial velocity the a of low radial velocity that increases in in the center of both small and large tissues (Figure This decrease of radial velocity is accompanied by a in cell speed in the center of large tissues but not in small tissues, in which cell speed remains high hr (Figure and We the behavior of this but central of small tissues in the of large-scale vortices The of low radial velocity out from the center of small tissues with the formation and expansion of a vortex (see Figure Figure 1 for representative These large vortices are observed in both small and large tissues (Figure but they tissue-spanning sizes in small tissues. Figure with 5 supplements see all Download asset Open asset formation in expanding tissues. (A) seen from hr of cell in small (left) and large (right) tissues. We to its local (B) rate of of around the of the tissue with than grow to large-scale in the tissue We show for the values of the For the we as in Pérez-González et al., (C) Average kymographs of show that the vortex in small tissues in the center and to mm = while in large tissues is during the early stages of tissue expansion = The a vortex (D) vortex size time and of vortex Small tissue vortices are more with (E) For small tissues, the time of vortex with the initial cell density. To the form and of these we tracked individual cell motion and cell to their et al., 2016) for a representative small and large tissue vortex (see Figure and Materials and Methods). We for the time that the vortex was most which was hr in the small tissue (Figure and hr in the large tissue (Figure the vortex period in small tissues, cell are primarily radial in the boundary but in the central zone (Figure see Figure supplement 1 for vortex To the of the we on a model of tissue that the cell as a active polar fluid et al., 2017; Pérez-González et al., 2019; et al., 2019). with our velocity (Figure we that cells at the edge zone are and whereas cells in the bulk of the tissue are and We cell polarization at a via a that the dynamics (Alert and Trepat, Here, is the that is the that the first the to and the spatial of the As a result of these the radial at the tissue edge over a length into the tissue to models of tissue we the in which the to the tissue velocity This is a of active polar with a et al., 2013; et al., 2014; et al., 2017; et al., in models that similar interactions (Alert and Trepat, can to et al., et al., et al., 2011; et al., 2013; et al., 2017; et al., 2018), and et al., et al., 2014; and 2014; et al., et al., 2017; et al., in and tissues. Here, using a we propose that cell not with but is also by tissue and we whether this can to large-scale in the bulk of tissues. To determine the flow we a between internal in the tissue, with and including with active traction with and the with the This force predicts that even if cell and active traction are to a boundary of width μm et al., 2017; Pérez-González et al., cell flow can a length into the tissue. on our (Figure we which is larger than the velocity correlation length of ∼200 μm in the tissue bulk (Petitjean et al., 2010). A linear analysis of 1 and 2 shows that of number around the and grow with a rate This result shows that, if the of an active polar fluid by 1 and 2 is to of than a value given by (Figure This analysis suggests that, for tissues larger than this value the tissue bulk becomes and to flow at large scales, consistent with the of large-scale The of this is the feedback between cell polarization and the due to migration of The fact that a size of the of is for this explain why large-scale vortices have not been observed in studies, which smaller tissues. kinematics To quantify the kinematics of the large-scale we the Before averaging over tissues, we the direction of of tissue to correspond to This direction was in of tissues and in of tissues, with a size of this the vortex core has Accordingly, the outer of the vortex exhibits (Figure see Figure supplement 2 for kymographs and of representative which corresponds to the that when the central flow to the outer radial flow (Figure We a vortex radius as the radial of the center of the which is mm at hr in small tissues (Figure To vortex dynamics across different tissues with vortex and to capture the and of we calculated the where are the spatial of the (Alert et al., The is the density of the as a of the and therefore a measure of the vortex at a length The kymographs of the show that most of the is found at a length of mm (Figure supplement 3). For tissue we the vortex by the value of as well as its and time of We these three on a which shows that vortices in small tissues have higher than those in large tissues (Figure in small tissues are also larger relative to tissue size, the size of vortices in small and large tissues is similar (Figure vortex several later in small tissues than in large tissues (Figure We hypothesized that this difference is due to large tissues a faster density increase than small tissues (Figure 1C). To this we the initial cell density of small tissues and observed that the time of vortex