Interplay of cell shapes and oriented cell divisions promotes robust morphogenesis of developing epithelia

A general framework for describing epithelial morphogenesis and zebrafish pre-EVL system

The morphological variety of epithelial layers falls within a defined range of cell shapes (e.g., squamous, cuboidal and columnar) that arise during development. This allows us to simplify measurements and comparisons by representing cell shapes with a single parameter: the ratio of length scales of the cell's lateral (along the surface) and radial (perpendicular to the surface) dimensions (L/R, Figure 1A). The dynamics of the population can thus be described as a temporal evolution of a distribution of L/R ratios of a number of cells (Figure 1B). These simplifications allow an intuitive, quantitative representation of epithelial morphogenesis, capturing not all but an essential component of the shape changes of the cells.

The presumptive EVL (pre-EVL) is a monolayer of surface cells of the zebrafish early embryo that have epithelial polarity (Figures S1A–B, Data S1, Text 1) and barrier function (Figure S1C). The pre-EVL arises during early cleavage mainly composed of round/cuboidal cells. Unlike "mature" epithelia that are lineage-separated from other tissues with a basal lamina, the pre-EVL has cells leaving the layer through divisions as it goes on to become a highly squamous epithelium (EVL, Figure 1C) over several meta-synchronous cell cycles (Kimmel et al., 1995). It thus represents a key early stage of epithelial development that more "mature" epithelia may pass through (Data S1, Text 1). To understand the pre-EVL morphogenetic process, we imaged the pre-EVL using nuclear and membrane fluorescent proteins (Figures S1D–E, Movie S1). We measured cell shapes (L/R) at the time point centered between 2 consecutive cell divisions (Figures 1D,S1F; other time points to be discussed later) between 128-cell and ~2k-cell stages (in this time window the cells have similar widths within the surface plane, Figures S1G–H, Data S1, Text 2). The measured shape distributions of the surface cells show a flattening shift (to the right on the L/R plot) with time and a wide range of cell shapes (Figure 1E), whereas the deep cells under the surface keep uniform and roughly spherical shapes (Figure 1F). The flattening is earlier than known lineage restriction or EVL specific marker expressions (Figures S1I–J, Ho 1992; Sagerström et al., 2005). These results are consistent with previous observations of this system (Kimmel and Law, 1985; Kane et al., 1992; Zhang et al., 2011) and allow a quantitative analysis of cell shape changes on both population and single-cell levels.

Tissue surface area, cell volume and cell number constrain the average surface cell shape

To understand how the surface layer may become more flattened or columnar over time, we assessed the dynamics of key geometrical parameters that are associated with cell shapes, namely the total surface area (A) of the layer, the number (N_S) of surface cells and the volume of individual surface cells (V_C). Intuitively, these parameters relate to the average aspect ratio (<L/R>) of the cells in the following ways: first, the average surface area of cells satisfies: A/N_S ≈L²; second, the volume of a cell is approximately V_C≈L²R (See Data S1, Text 3 for a discussion of these simplifications). These equations can be combined to express <L/R> in terms of A, V_C and N_S. While the actual value may differ slightly depending on the distribution of cell shapes (Data S1, Text 4), <L/R>≈(A/N_S)^1.5/V_C (eq.1) serves as a close estimate of the actual <L/R>.

Following eq.1, we first measured A both macroscopically (Figure S2A) and using calculated average L² from single cell measurements (Figures S2B–C). The results are congruent and indicate that A is stable with under 10% fluctuations between the 5 time points of L/R measurements (Figure 2A). Thus, unlike the later epiboly stage (Kane et al., 2005), the expansion of the tissue surface area contributes little to cell flattening in pre-EVL. Next, we measured V_C using global average (Figure S2A), average L²R (Figures S2B,D), and full membrane segmentations (Figure S2E, Movie S2). The results agree on the conclusion that the average V_C closely follows an ideal exponential decrease curve (Figure 2B) by halving at every cell cycle, indicating no significant cell growth during this time. Individual cells halve their volumes roughly equally at divisions (7.3%±5.2% difference from average V_C of two daughters, n=43 pairs; Figure S2F, Olivier et al., 2010). According to eq.1, a halving V_C would double <L/R> after each cell cycle if A and N_S do not change. However, the measured increase in <L/R> is less rapid than this (Figure 1E), potentially because of the increase of N_S. As a fraction of cells are known to leave the surface layer during divisions (Kimmel et al., 1995), N_S is expected to increase at a slower rate than doubling per cell cycle. We measured N_S dynamics (Figure S2G) and found that it follows a highly consistent increasing trend (Figure S2H). Interestingly, this trend is slower than predicted by a model (Data S1, Text 5) where surface cells are rigid and do not change shape (Figure 2C), suggesting that flattening is required for cells to cover the entire surface area. Reassuringly, by combining our A, V_C and N_S measurements using eq.1 we obtain an increasing trend of <L/R> that is consistent with whole embryo estimation and the actual <L/R> values (Figure 2D).

Together, these results show how an epithelial layer of a given morphology obeys the geometrical constraints of surface area, cell volume and cell number. In pre-EVL, the N_S parameter changes in a specific manner which quantitatively explains the increase of <L/R> (i.e. flattening). How, then, is N_S regulated?

Surface cell number changes through differentially oriented divisions predicted by cell shapes

To investigate how N_S is regulated, we tracked individual cells through time to follow how their divisions affected N_S. Consistent with previous studies (Kimmel and Law, 1985), we found that two types of divisions occur in the surface cells: the surface-deep (S-D) division, producing one surface daughter and one deep daughter (Figure 3A), and the surface-surface (S-S) division, producing two surface daughters (Figure 3B). After an S-D division the surface daughter's L/R ratio continues to change but is close to double that of the mother, and the deep daughter becomes spherical (Figure 3C), whereas after an S-S division the L/R ratios of the daughters change in ranges close to half that of the mother (Figure 3D). Thus S-S divisions contribute to crowding while S-D divisions contribute to flattening. The balance between these division types at each cell cycle affects both N_S and <L/R>.

How are division orientations decided? Is cell division the only factor that affects N_S? To address these questions we reconstructed full lineage trees of surface cells by tracking future EVL cells from cell cycle 1 to 13 (Figure 3E; data not shown). We found essentially no instances of cell extrusion in unperturbed embryos and no internalization into deep layers without division. We also found that deep cells do not move to the surface (this is not surprising since the surface cells have already adopted distinct polarity and tight junctions (Figures S1A–B)). Thus, the increase of N_S only occurs through S-S divisions. Consistent with previous studies (Ho 1992), we found that S-D divisions start to appear at the 6^th cell cycle and stop at the 13^th when the EVL becomes a separate lineage compartment from the deep cells. S-D and S-S divisions may appear at different branch levels and their appearance does not follow a fixed lineage pattern. Thus, although S-S and S-D divisions have predictable effects on N_S and the shape of daughter cells, the history of divisions in a lineage is variable and not strongly predictive of the next division type. It seems unlikely that division orientation is determined by lineage.

An intriguing possibility is that the shape of the cells determines whether the mother cell undergoes S-S or S-D division. It has long been recognized that cell shape correlates with division orientation (Hertwig 1884) and several molecular mechanisms have been proposed to account for this relationship (Grill and Hyman, 2005; Kunda and Baum, 2009; Wuhr et al., 2010; Minc et al., 2011). To test this in our system, we tracked surface cells at different times to their divisions after measuring their L/R ratio. Indeed, highly flattened cells always undergo S-S divisions and highly columnar cells always undergo S-D divisions, while at intermediate L/Rs an overlapping zone of both choices exists (Figure 3F). We calculated the fraction of S-D divisions as a function of L/R and fitted it with a Hill function (Figure 3G). The transition to favoring S-S division occurs when the L/R increases over a Threshold (Th) of 1.3, and has a remarkably high Hill coefficient of 10 (Sharpness, Sh). Consistent with cell tracking, the centrioles align along the future division axes (Figure S3A) and the division orientation is predominantly either parallel or perpendicular to the surface (Figure S3B). Furthermore, when cell shape is forced to change by embryo squishing (Figure S3C), or injection of an oil droplet (Figure S3D), the division orientation aligns with the new long axis. These data show that while the cells have established polarity and perhaps cortical cues that might bias division orientation, the cell shape (L/R) is the dominant determinant of the probability of S-S/S-D division of surface cells (the "division rule").

Our results imply that many features of pre-EVL development follow directly from the cell shape distribution: since the shape of a single cell strongly correlates with its division orientation, the cell shape distribution (Figure 1E) becomes predictive of the fraction of S-S/S-D divisions of the population, which in turn will determine the change in N_S. This offers a mechanism for the characteristic N_S increase (Figure 2C) that explains the dynamics of <L/R> (Figure 2D, eq.1). Thus to understand the behavior of the epithelial layer, we need to understand the factors that influence the distribution of cell shape. Simple models that do not account for cell-cell interactions, such as pure geometrical partitioning from an initial distribution (Figure S3E), spatial heterogeneity across the embryo (Figure S3F), or shape variation from unevenness of cell volumes (Figure S3G) do not explain the observed distributions, indicating that other factors such as mechanical interactions between cells need to be considered.

Cell shapes form log-normal distributions mediated by mechanical interactions

Each cell division significantly changes the L/R of the cells remaining on the surface. An S-S division produces two surface daughters, with L/Rs near 0.5× that of the mother. An S-D division, in contrast, produces one surface daughter with an L/R near 2× that of the mother (Figures 3C–D). This pattern of multiplicative change can produce log-normal distributions (Limpert et al., 2001, Data S1, Text 6), and a log-normal distribution indeed fits the observed L/R data (Figures 4A,S4A, Data S1, Text 6). This allows us to simplify the description of the cell shape distributions with just two parameters: the average (μ) of ln(L/R) and the standard deviation (σ) of ln(L/R). We find that μ increases over time as the average cell flattens, while σ remains stable (Figure 4B).

A direct application of the division rule (Figure 3G) to the log-normal distributions, while correctly predicting the change of N_S (Figure S4B), does not produce a new log-normal distribution (Figure S4C). This prompted us to examine cell shape changes following cell divisions (Figure 4C). Immediately after cytokinesis most cells are close to spherical but quickly assume a multiple-peak distribution as expected from binary 0.5× or 2× L/R changes from divisions. However, the multiple peaks then merge, producing a single major peak. These data show that the varied initial cell shapes resulting from divisions are homogenized over time.

We hypothesize that the mechanical forces that locally regulate cell shape (Heisenberg and Bellaiche, 2013) are responsible for the changes during and after divisions. Cell-cell interactions such as adhesion tend to increase cell-cell contact surface by modulating the contact surface tension (Figure S4D, Maitre et al., 2012). In the absence of adhesion, cells tend to be spherical due to cortical tension (Figure S4E, Manning et al., 2010). The cell surface angle (θ) at the contact/no-contact transition point (Figures 4D,S4D) increases as adhesion reduces surface tension at cell-cell contact surface. We define the ratio of reduction as γ, and γ=1−cosθ (Data S1, Text 7). In surface cells, γ fluctuates during the cell cycle (Figures S4F–G) as θ decreases during mitosis and increases afterwards.

To investigate the effect of the cell mechanics (measured by γ) on the cell shape distribution, we simulated the dynamics of force-mediated cell shape changes using Surface Evolver (Brakke 1992) taking into account geometrical constraints, surface tension and cell-cell interaction (Figure 4E, Data S1, Text 8). This minimal model starts with a two-peak cell shape distribution (Figure 4F) analogous to Figure S4C to mimic the condition immediately after divisions. The distribution quickly evolves to have only one major peak and closely fits log-normal for several iterations (Figures 4F–G, Movie S3). Further iterations slowly reduce the fit (Data S1, Text 8). Interestingly, larger γ drives faster distribution change (Figure 4H), suggesting the increase of γ following divisions promotes cell shape homogenization. These data support the idea that cell mechanics reduce energy-unfavorable cell shapes and re-establish the cell shape distribution following divisions. The Surface Evolver model also predicts that change of γ affects <L/R> mildly, which agrees with the observed dynamics of <L/R> after divisions (Figure 4C, inset) and results of γ perturbations using Nocodazole and cdh1 knockdown (Figures S4H–K).

Our results are consistent with an origin of the shape of L/R distributions coupling divisions and mechanics. Cell divisions cause large fold-changes of L/R of surface cells, which are then modified during interphase by mechanical force balance between cells and their neighborhoods. A log-normal model characterized by a changing μ and stable σ (See Data S1, Text 9 for a discussion on the nature and value of σ) reasonably describes the cell shape distributions. This understanding of the cell shape distribution (γ, σ) along with the geometrical constraints (A, V_C, N_S) and the division rule (Th, Sh) provides us an opportunity to fully model the morphogenesis of pre-EVL and epithelial layers in general.

Quantitative recapitulation of surface morphogenesis using an integrated model

To integrate the rules of geometry, cell division and cell-cell interaction to understand the dynamics of cell shape distributions (Ω, Figure 5A), we first required Ω to meet both the geometrical constraints (A, V_C, N_S) and a mechanically determined log-normal shape (γ, σ). To simplify coding, we implemented the mild influence of γ on <L/R> using geometrical correlations (Figures S5A–B, Data S1, Text 10). An Ω that satisfies all the properties (A, V_C, N_S, γ and σ) is mathematically unique (Figure S5C, Data S1, Text 11). This allows us to determine <L/R> and recapture the observed Ω evolution using measured N_S at each cell cycle as input (Figure 5B). We then took one step further to implement the division rule (Th, Sh) into the model (Figure S5C) to compute the fraction of S-D divisions given a modeled Ω at one stage and use the predicted N_S to compute Ω at the next cell cycle stage, leading to a full interplay model. This model satisfactorily reproduces the morphogenesis process, although it diverges from reality at the final time point of 2k cell stage (Figure 5C) with an overestimate of N_S. One possible explanation for this is that in the simulation we used fixed Th, Sh, and γ values while in reality they may change over time.

Our interplay model allows us to predict the course of pre-EVL morphogenesis with a small set of rules and initial conditions. Moreover, the feedback cycle between Ω and N_S provides a potential self-regulation mechanism for the population. Although it is unlikely to be the only way to achieve surface flattening, this interplay design may confer additional advantages such as developmental robustness and evolvability.

Robustness of morphogenesis from the interplay between shape and division

Developmental processes exhibit robustness in reaching teleonomic morphological/patterning goals, a phenomenon called “canalization” (Waddington 1942). Such robustness can be achieved through feedback interactions at a molecular level (Alon 2007) that allow regulatory networks to "steer" the dynamic process to the correct trajectory in the face of noise, errors, and varied environments. Our results reveal a system of cellular and mechanical interactions that also contain analogous feedbacks. We therefore hypothesized that the cellular/tissue level interplay between N_S and the cell shape distribution provides morphogenetic robustness. For example, when the surface area A reduces under constant N_S, the more crowded population will have more columnar cells, biasing their division orientations at the next cell cycle to more S-D. Consequently, N_S will be relatively reduced to decrease crowding. To test this idea, we performed yolk extraction on 256-cell stage embryos and followed cell shape changes (Figures 6A,S6C). The loss of a portion of yolk causes immediate shrinkage of the surface resulting in a crowding shift of cell shapes (Figure S6A, data not shown). Intriguingly, the embryos recover later to be smaller but developmentally normal (Figure 6C) with correct surface flattening (Figures 6E,S6D). Similarly, when we remove surface cells via micropipettes to reduce N_S (Figures 6B,S6C), the neighbors of the lost cells stretch over to cover the ablation site, effectively biasing their next division choice towards S-S (Figure S6B), thus compensating for the loss (Figures 6D,S6D). These data show that the morphogenesis of the surface layer is robust to changes and variations in A and N_S. Our model argues that, without the interplay between cell shape and division orientation, this robustness would not exist (Figure 6E, Data S1, Text 12). The model further predicts that embryos will scale N_S to A after A is changed. Indeed, N_S of individual embryos perturbed at 128- or 256-cell stages is proportionally reduced by ~2k-cell stage and follows the predicted N_S/A relationship (Figure 6F). Increased cell extrusion at the apical surface was also observed in yolk-extracted embryos (data not shown), suggesting additional mechanisms of N_S reduction are in place (Eisenhoffer et al., 2012) to ensure the scaling of A and N_S.

To test the system's robustness against changes in V_C, we created tetraploids (Figures 6G,S6E–F,H, Fankhauser 1945, Herbst 2002). In tetraploid embryos, cells undergo the maternal-zygotic transition at an earlier cell cycle stage due to the increased nuclear-cytoplasmic ratio (Newport and Kirschner, 1982). The resulting advanced cell-cycle slow-down of tetraploid cells (Figure S6G) leads to more cell growth before division compared to diploid controls at later stages of surface morphogenesis (Figure 6H). This effectively provides a perturbation on V_C. We found tetraploid embryos start to have fewer surface cells at the comparable stages (Figures 6I–J), while <L/R> is not significantly different from diploid controls and far higher than predicted by assuming no feedback to N_S from cell shapes (Figure 6K, Data S1, Text 13). Indeed, the interplay model predicts an increase in the S-D division rate of tetraploid surface cells caused by the change in V_C, which agrees with experimental measurements (Figure 6L, Data S1, Text 13).

Together, these data indicate that the interplay between cell shapes and division orientation of the surface population ensures the robust arrival at the "target" <L/R> of a specific epithelial type. Many perturbed embryos (14/20 for yolk extraction, 7/16 for cell ablation, and 5/8 for tetraploids) successfully finished epiboly (indicating proper EVL differentiation). These results imply that, despite being important constraints, the global geometrical properties (A, V_C, N_S) of the epithelial layer do not define the direction of morphogenesis. Instead, local rules such as division orientation control regulates the dynamics of the population. What, then, is the key factor that determines final epithelial type?

The interplay model reveals a general link between tissue morphology and the division rule

To understand how the model parameters (Th, Sh, γ and σ) affect the morphogenetic process, we performed in silico experiments to alter their values (Data S1, Text 14). The change of Th produces a full spectrum of resulting epithelial morphologies from squamous to columnar (Figure 7A) and corresponding N_S changes (data not shown). Sh on the other hand influences the system only mildly unless it moves near 0 (i.e., cell-shape-independent division orientations) (Figures 7B). γ changes can moderately alter <L/R> as we have discussed earlier. However, over time the effect of an early γ change is compensated through the interplay (Figures 7C), indicating that as long as other constraints are met, mechanical interactions between cells could vary with little effect on the over-time morphogenetic outcome. σ has been between 0.25 and 0.40 in all conditions we measured. Interestingly, a σ that is smaller than 0.25 (tighter distribution) is predicted to cause oscillations of <L/R> through divisions (Figures 7D). This result suggests that heterogeneity in cell shapes is important for the monotonic, gradual shape change of the population.

The modeling results thus suggest that the regulation of parameter Th plays the most important role in morphogenesis by setting its direction. To directly test this prediction not knowing the molecular mechanisms of Th regulation, we performed a range of perturbations focusing on the spindle positioning machinery and cell polarity components (Data S1, Text 15). Among these, the overexpression of Crumbs (Crb, Chalmers et al., 2005) produces a phenotype of a much less flattened EVL (Figures 7E–F). Strikingly, this changed EVL morphology reproducibly persists into later stages (Figure S7A, data not shown) in ~20% of embryos (18/94, others fail to finish epiboly). After EVL formation (around sphere stage), cells in Crb injected embryos pull back from the margin rather than spread out (Figures S7B,H), reducing A which might contribute to the reduced <L/R>. In the earlier pre-EVL stages, however, A and V_C are similar to controls but cells are more columnar and N_S shows a faster increase (Figures 7F,I, S7B–D). According to our model, this N_S increase at pre-EVL stages and the formation of a stably less squamous EVL at later stages (Figure S7A) strongly suggests a change in Th (γ is also reduced in Crb injected embryos (Figure S7E) but is insufficient to explain the phenotype). To test this, we tracked cells from Crb+ embryos. Surprisingly, we observed instances of "oblique" divisions (16/122, Figure S7G, Chalmers et al., 2003) which are rare in controls in later stages. The oblique divisions have an almost S-D orientation yet the deeper daughter retains a small apical surface and remains a surface cell. Consequently, the population has more S-S divisions and Th is effectively reduced to ~1.2 (Figures 7H, S7E). This changed Th in our interplay model produces a reasonable prediction of pre-EVL morphogenesis of the Crb+ embryos (Figure 7I). While how Crb promotes oblique divisions and changes Th remains unknown, this result strongly supports our model that Th is a key parameter in defining cell shapes in pre-EVL/EVL.

Can a different Th explain the diverse surface layer shapes in other embryos such as sea urchin and frog (Wray 1997; Chalmers et al., 2003)? To answer this question, We input corresponding initial conditions (non-essential) and an altered Th value to simulate these systems (Data S1, Text 14). We are indeed able to predict exclusive S-S divisions and a columnar epithelium for sea urchin with a low Th (0.2), and a cuboidal surface layer for frog embryos with an intermediate Th (0.8) (Figure 7E). These results arise as different Th values produce different N_S trajectories (Figure 7F). The model predicts that for most Th values the S-D division ratio will converge to a steady state of ~0.41 (Figure S7I). This value can be derived as 2-2^2/3 under the no-growth and all-divide assumption (Data S1, Text 16). In frog embryos, a steady S-D division ratio is indeed observed after 128-cell stage by Chalmers et al., 2003 at a lower reported value (Figure S7J). These results supports the idea that a Th change may underlie apparent differences of cell shapes in different embryonic surface epithelia.

Potential application of the interplay model to other systems

In this study we performed systematic imaging of the pre-EVL which was key for obtaining quantitative dynamics of the variables that influence epithelial cell shape. Using these data we were able to efficiently exclude alternative hypotheses and arrive at the simple interplay model. It is important to note that, given the ubiquity of epithelia that arise in development, cell shapes can change in other ways independent of oriented divisions. For example, in the class of more mature epithelia where S-D divisions are not present, morphogenesis is likely mainly regulated by other processes such as alternative N_S regulation (e.g., in-plane proliferation, cell extrusion), apical constriction (e.g., drosophila ventral furrow, vertebrate neural fold), and tissue non-autonomous expansion by external driving forces (e.g., late EVL, growing alveoli). Nonetheless, when polarity is perturbed or growth/proliferation rate becomes abnormal (Th, V_C or N_S changes, e.g., carcinoma initiation, polycystic kidney disease, neural tube defects, Matsuyama et al., 2009), it is possible that S-D divisions appear in these normally low-Th systems. On the other hand, a number of epithelia exhibit S-D divisions during development and homeostasis and disruption of these division orientations are shown to affect morphogenesis (e.g., mammary epithelium, basal epidermis, embryonic lung epithelium, Taddei et al., 2008; El-Hashash et al., 2011, see Data S1, Text 17 for a review). These systems resemble pre-EVL in the sense of division modes. However, whether the mother cell shape is correlated with the division choice and whether similar interplay generates/maintains epithelial cell shapes in these systems remain to be elucidated. More generally, we suggest that the interplay logic does not necessarily need to be implemented on division orientation. In other systems, similar regulatory effects could be achieved by cell shape feedback on N_S via proliferation rate or extrusion/internalization rate. To test these possibilities, it is essential to acquire quantitative dynamic data as presented here, which remains technically challenging for many systems.

Molecular mechanisms linking cell shape and division orientation

Consistent with other studies (Hertwig 1884; Chalmers et al., 2003; Baena-Lopez et al., 2005; Gibson et al., 2011), our results show that the division orientation of surface cells is strongly biased by cell shape (in our case L/R along the orthogonal-to-surface axis). Our model predicts that tuning the threshold relating cell shape to division orientation can produce distinct morphogenetic behaviors leading to different epithelial types. Consistent with this idea, in Crumbs injected embryos where threshold is lowered, the embryos obtain an EVL of stably different cell shapes into later stages. However, it remains unclear how the threshold is set in the EVL or other tissues. Apparently it is a tunable parameter in nature considering the wide range of division modes in different epithelia that emerge in the same embryo and across different species. To measure its own shape, a cell may utilize a microtubule network to probe the cortex which in turn generates forces on the nucleus and spindle to determine the division plane (Wuhr et al., 2010; Minc et al., 2011). This mechanism allows spatially restricted molecular cues to influence the force balance, which can cause polarized anchoring of centrosomes and rotation of the spindle (Galli and van den Heuvel, 2008; Rebollo et al., 2009; Peyre et al., 2011). Therefore the observed threshold values are likely reflective of how such molecular polarity cues interact with or sometimes override the "default" cell shape/long axis determinant (Gillies and Cabernard, 2011). In addition to spindle orientation, the partitioning of junctions and/or polarized membranes might also play a role. The oblique divisions in the Crumbs phenotype may reflect an excessive amount of apical membrane that prevents the presumptive deep daughter cell to leave the surface layer, as Crumbs is known to promote apical polarity and adherens junctions (Wodarz et al., 1995; Pocha and Knust, 2013). Understanding how the polarity of surface cells mechanically influences the cytoskeleton, spindle and cell content partitioning may reveal the molecular basis of variation in threshold values and explain the observed differences between various epithelial tissues and between systems such as fish, frog and sea urchin.

Improved compensation, scaling and evolvability from the interplay design

Developmental systems generate consistent forms in the face of variations and perturbations, yet are capable of evolving to produce new forms, two apparently opposed goals. Our interplay model offers insights into how both robustness and evolvability are achieved in epithelial development. First, cell-cell interactions equilibrate cell shapes into a defined distribution. Drastic changes of individual cell shapes are quickly compensated and have little impact on the population. Second, through feedback the epithelium will aim for a defined morphology and appropriate size regardless of changes in global conditions. For example, we show that N_S scales with A to ensure that <L/R> is robust to egg size and blastoderm/yolk ratio, hence individuals could recover from damage and species could evolve new life history strategies (e.g., small clutch of large eggs vs. large clutch of small eggs) without having to acquire complex compensatory mutations to maintain proper EVL shape and cell number. Third, the change of Th alone allows generation of the full range of cell shapes without the need to coordinately evolve other parameters, an example of facilitated variation to promote evolvability (Gerhart and Kirschner, 2007). For example, with a reduction of Th, the surviving Crumbs-injected embryos become essentially "thick-skinned". Finally, collective cell shape changes mediated by the interplay may build up mechanical stresses that can be used to do morphogenetic work (e.g., buckling, invagination, spreading, Eiraku et al., 2011; Sato and Clevers, 2013), providing a means of developing new tissue structures just by modifying a few cellular parameters.

In summary, our work reveals an interplay design principle that allows tissue properties to emerge robustly from simple interactions of similar individual cells. The importance of local, cellular rather than global properties in driving morphogenesis renders tissue-level, populational goals under the control of single cell behaviors that can be exploited by molecular changes during development and evolution.

Zebrafish strains and maintenance

See Extended Experimental Procedures for protocols and references for transgenic strains used in this study. All fish related procedures were carried out with the approval of Institutional Animal Care and Use Committee (IACUC) at Harvard University.

Timelapse confocal imaging

1–64 cell stage embryos (transgenic or injected) were dechorionated and mounted animal pole up (or sideways) into a dorsal mount (Megason 2009). Live imaging was performed using a Zeiss 710 confocal microscope (objectives: Plan-Apochromat 20× 1.0 NA, C-Apochromat 40× 1.2 NA) with a home-made heating chamber maintaining 28°C. Laser lines 488nm, 514nm, 561nm and 594nm were used. See Figure S1, Extended Experimental Procedures for details.

Image Data analysis

Segmentation and tracking were performed using GoFigure2 (www.gofigure2.org) and ACME (Mosaliganti et al., 2012, Xiong et al., 2013). For a detailed protocol see Extended Experimental Procedures. Measurement of L/R ratios was carried out using ZEN (Carl Zeiss) software 3D distance functionality. Measurements were analyzed and plotted with Matlab (Mathworks) and Microsoft Excel. See also Figure S2, Movie S2, Extended Experimental Procedures.

Modeling

Simple geometry models were drawn on paper. The mechanical model was coded using Surface Evolver (Brakke 1992). The full interplay model and its simulations were coded using Matlab (Mathworks). See Data S1, Extended Experimental Procedures for details. See also documentation of the scripts in the supplemental files.