Apical Oscillations in Amnioserosa Cells: Basolateral Coupling and Mechanical Autonomy

Abstract

Holographic laser microsurgery is used to isolate single amnioserosa cells in vivo during early dorsal closure. During this stage of Drosophila embryogenesis, amnioserosa cells undergo oscillations in apical surface area. The postisolation behavior of individual cells depends on their preisolation phase in these contraction/expansion cycles: cells that were contracting tend to collapse quickly after isolation; cells that were expanding do not immediately collapse, but instead pause or even continue to expand for ∼40 s. In either case, the postisolation apical collapse can be prevented by prior anesthetization of the embryos with CO₂. These results suggest that although the amnioserosa is under tension, its cells are subjected to only small elastic strains. Furthermore, their postisolation apical collapse is not a passive elastic relaxation, and both the contraction and expansion phases of their oscillations are driven by intracellular forces. All of the above require significant changes to existing computational models.

Introduction

Morphogenetic events in embryogenesis are often accompanied by changes in cell shape (1–5). Although cell shape changes can and do drive tissue remodeling in isolated tissues, the situation is much more complicated for adjacent tissues that undergo complementary changes. If cells of tissue A contract along one axis and cells of tissue B extend in the same direction, it is not immediately clear which process is a case of active reshaping and which, if either, is a passive response. Such complementary changes in adjacent tissues occur in Drosophila embryogenesis during germband retraction and dorsal closure (6–8). One can even find complementary cell shape changes within a single morphogenetically active tissue in the form of cell shape oscillations—e.g., in Drosophila dorsal closure, germband elongation, and ventral furrow invagination (9–16). Both between and within tissues, the question of import is this: when an individual epithelial cell changes shape, is this process best characterized as viscoelastic or viscoplastic deformation due to forces internal to the deforming cell or forces exerted on that cell by its neighbors? Here, we address this question in the context of cell shape oscillations in the Drosophila amnioserosa. We use holographic laser microsurgery to mechanically isolate individual cells in vivo. The subsequent isolated-cell responses clearly show that these cells’ shape oscillations are mechanically autonomous—much more so than suggested by previous models (12). We should note that “mechanically autonomous” is used here to imply that the forces driving changes in cell shape are internal to the cell being reshaped. This cell is still subject to paracrine and juxtacrine signals from neighboring cells and its continued oscillation may be dependent on such signals.

Cell shape oscillations occur in amnioserosa cells during the process of dorsal closure, which has long been of interest due to its experimental accessibility (6,7,17) and its similarity to wound healing (18–20). During closure, lateral epidermis cells on the lateral flanks of the embryo elongate and move dorsally as amnioserosa cells on the dorsal surface contract and eventually invaginate (6,7,21). The two flanks of lateral epidermis fuse at the dorsal midline and the invaginated amnioserosa cells undergo apoptosis (21–25). During early dorsal closure, the large squamous cells of the amnioserosa go through repeated cycles of apical expansion and contraction (12). These cycles have oscillation periods of ∼230 s, with neighboring cells typically out of phase. Previous work in the amnioserosa and other morphogenetically active tissues has shown that the contraction phases of periodic cell shape changes are driven by medial contractile networks on the cells’ apical surfaces (9,13,14,16,26). To date, the only examination of the expansion phases has been computational modeling that generated expansion of one cell via contraction of its neighbors (12).

Laser-microsurgery has often been used for evaluating biomechanics in vivo (17,27–34). This technique has typically been used in a negative fashion— i.e., ablate one or more cells of interest and investigate how the loss impacts the short and long-term behavior of adjacent cells. The short-term responses provide information on the mechanical force that was carried by the biological structure(s) that are now missing (31–33,35). The long-term responses provide information on the system’s ability to compensate for that loss (6,17,30). Here, we complement these approaches; instead of ablating a cell of interest, we use a multipoint ablation technique to simultaneously ablate a ring of neighboring cells (36). This mechanically isolates a single cell, i.e., it removes the in-plane forces exerted on that cell by its epithelial neighbors. Although these neighboring cells can still influence the isolated cell via paracrine and juxtacrine signals, the postablation dynamics of the isolated cell are now driven by that cell’s internal forces. Comparison of the pre- and postablation dynamics provides information on whether preablation dynamics were driven by intra- versus intercellular forces.

Materials and Methods

Fly strains and sample preparation

All microsurgical experiments were performed using a transgenic Drosophila strain expressing E-Cad:GFP; Sqh:mCherry (gift from A. Jacinto, Instituto de Medicina Molecular, Lisbon, Portugal). Additional experiments to investigate three-dimensional cell shapes used Resille(117–2)-GFP (37) (gift from J. Zallen, Sloan-Kettering Institute, New York, NY). Embryos were collected and incubated until early-dorsal-closure stage (∼24 h at 15.5°C), dechorionated in a dilute solution of bleach and mounted dorsal-side down on a glass coverslip (28,33). The mounted samples were then placed in a suitable sample holder for confocal imaging under a layer of halocarbon oil (#27; Sigma-Aldrich, St Louis, MO) and a gas-permeable membrane (YSI, Yellow Spring, OH). In some experiments, fly embryos were anesthetized by temporarily replacing the air over the sample with water-vapor-saturated CO₂.

Laser ablation and microscopy

All laser ablation experiments used a laser scanning confocal microscope (LSM 410/Axiovert 135TV; Carl Zeiss, Thornwood, NY) with an attached holographic UV laser ablation system (36). This system simultaneously ablates multiple targeted points by diffracting single pulses from a Q-switched Nd:YAG laser (Minilite II, Continuum, Santa Clara, CA; 5-ns pulsewidth, λ = 355 nm) using a spatial light modulator (PPM X8267, Hamamatsu Photonics K.K., Shimadzu, Japan). Tissues were ablated and imaged as close to the apical surface as possible. All microsurgeries were carried out at pulse energies ∼2–3× threshold to ensure consistent and repeatable ablation. Confocal images were obtained at 4 s/scan, at a resolution of 0.326 μm/pixel, using a 40×, 1.3 NA, oil-immersion objective.

Additional time-resolved 3D image stacks were obtained on a spinning disk confocal microscope (Eclipse Ti; Nikon Instruments, Melville, NY, and Quorum WaveFX-X1, Ontario, Canada) using a 40×, 1.3 NA, oil-immersion objective at 0.22 μm/pixel in-plane resolution, 0.5 μm between image planes and a time of 20 s between image stacks.

Image processing and analysis

We used IMAGEJ (National Institutes of Health, Bethesda, MD) software for basic image-processing tasks. To measure the areas and volumes of cells, we used SEEDWATER SEGMENTER (38), a custom watershed-based segmentation software. The cell area data extracted from segmentation was imported into the software MATHEMATICA 8.0 (Wolfram Research, Champaign, IL), and Fourier-transformed to identify frequency components in the apical area oscillations. Because amnioserosa cells have been shown to pulse with a periodicity of ∼240 s (12,15), we estimated the oscillation phase based on the highest-amplitude frequency component in the range from 1/150 to 1/300 s⁻¹. We limited our analysis to data sets with oscillation amplitude >5% of the mean cell area. To estimate numerical derivatives, we used a second-order, five-point Savitzky-Golay smoothing differentiation filter (39,40).

Computational models of amnioserosa pulsations

Our model is based on Solon et al. (12). The model contains 80 tightly packed polygonal cells. Each interior vertex has elastic links to three neighboring vertices and three cell centroids. Each exterior boundary vertex has elastic links to two neighboring vertices, two cell centroids, and a fixed ellipse, the latter representing attachment to the surrounding lateral epidermis. The motion of each vertex is described by an ordinary differential equation containing passive spring-like terms for the elastic links and active force terms for the time-delayed stretch-induced contractions. For more details, see the Supporting Material. The set of ordinary, time-delayed differential equations was solved numerically using MATHEMATICA 8.0 (Wolfram Research).

Results and Discussion

Our goal is to evaluate the mechanical autonomy of cell shape changes in an embryonic epithelium like the amnioserosa. To do so, we use holographic laser-microsurgery to mechanically isolate a single cell (36). An example of such an experiment is shown in Fig. 1, A–E, and see Movie S1 in the Supporting Material. Our protocol targets all neighbors of the cell to be isolated with ablation near the middle of each neighbor-neighbor interface—like targeting spokes emanating from the cell to be isolated. These interfaces often move during the targeting process, so we ablate two closely spaced points for each interface to maximize the chance for a clean and complete cut (36). The ablated locations are visible in Fig. 1, B and E, as the static dark spots resulting from puncture wounds in the embryo’s encasing vitelline membrane. Leakage through these holes is prevented by a glue layer between the membrane and coverslip (33). Within the embryo, each laser wound extends clean through the ∼6-μm-thick epithelium (33). We specifically target cell-cell interfaces because previous work has shown that such wounds quickly and effectively destroy all mechanical integrity in the two targeted cells (41).

Figure 1.

An example cell-isolation experiment. (A–E) Pre- and postablation confocal images (inverted grayscale) showing retraction of the wound and eventual contraction of the isolated amnioserosa cell in a Drosophila embryo expressing eCadherin::GFP. (Upper left) Times relative to ablation. Overlays denote preablation shapes of the isolated cell (blue dashed) and the outer boundary of the wound (red dotted). A common scale bar is shown in panel E. (F) Comparison of cell shape dynamics for the total area inside the outer wound margins (red) and the apical area of the isolated cell (blue dashed). (G) Two-color confocal scan of an isolated cell imaged 80 s after separation from the surrounding tissue. (Green) E-Cad::GFP and (red) Sqh::mCherry. Note the accumulation of myosin along the outer margin of the wound. (H) Dynamics of myosin signal intensity. Each line shows the radial profile of myosin signal intensity about the centroid of the isolated cell (upper) or outer wound (lower). Separate graphs are necessary because the isolated cell and wound are not exactly concentric. The time at which each profile was measured is color-coded (blue to red from 10 s before to 200 s after ablation). The selected profiles are from the imaging planes that showed the most dynamic myosin profiles: close to the apical surface for the isolated cell; more basal (3-μm deeper) for the outer wound margin. See also Movie S1 in the Supporting Material.

This targeting strategy also provides a clear and immediate indicator of successful cell isolation via separation of the near and far fragments of fluorescently labeled interfaces. By imaging both E-Cad:GFP and Sqh:mCherry in some experiments, we could confirm that there were dynamic medial myosin accumulations associated with preablation cell contractions and that the foci themselves were not immediately disrupted by our ablation protocol; however, these foci did immediately pull away from the isolated cell, so the apical actomyosin network was strongly compromised. The basal actomyosin network was not as severely disrupted. Most of its labeled myosin immediately pulled away from or toward the isolated cell, but there were occasional bridges of actomyosin left between the isolated cell and the outer wound margin at the basal surface. These bridges did not have any obvious effect on the symmetry of initial wound expansion or on rapid changes in isolated cell shape, but they did locally enhance the rate of wound closure at later times (see below). In addition to these basal actomyosin bridges, the isolated cell remains attached basally to an extracellular matrix, but this embryonic matrix has very little rigidity.

Because we are using a holographic technique to ablate multiple locations with a single 5-ns laser pulse, cell isolation is nearly instantaneous; even long-lived cavitation phenomena are complete within 100 μs (36). We thus have access to short- and long-term behavior of both the cell sheet and the isolated cell. Note that all times in our analyses are relative to the image taken immediately preceding ablation. The actual ablation event occurs between images.

As shown in Fig. 1, the outer boundary of the wounded area begins to expand immediately after ablation. This is consistent with previous experiments and clearly shows that the cell sheet as a whole is under tension. The wounded area continues to expand for up to 30 s, but during most of this time, the outer wound boundary remains ragged. It starts to smooth out only as the wound reaches its maximum area and begins to decrease, i.e., as wound healing commences. The isolated cell can behave very differently. In this particular example, the apical area of the isolated cell does not immediately collapse. It only does so ∼40 s after ablation—very close to the time at which wound healing begins. The differences and correlations between the postablation dynamics of wound and isolated cell are most clearly seen in the area-versus-time graph of Fig. 1 F. In other examples of this experiment, the outer wound always behaves similarly; it expands, pauses, and contracts, with a maximum wound area attained several tens of seconds after ablation. On a similar timescale, the isolated cell always begins to collapse.

To further investigate the drivers of these postablation dynamics, we simultaneously imaged both E-Cad:GFP and Sqh:mCherry fluorescence in time-resolved confocal z-stacks. An overlay of these two signals is shown in Fig. 1 G at 80 s after ablation and a depth 3 μm below the cells’ apical surface. At this time and basal depth, a ring of myosin has clearly accumulated around the outer wound margin to form a purse-string. One can also just discern some basal bridges of actomyosin. These are most notable between the isolated cell and the upper-left wound margin. Although there is no basal accumulation of myosin in the isolated cell, this cell does have a circumferential ring of myosin near its apical surface.

The postablation dynamics of apical and basal myosin accumulation are shown in Fig. 1 H. The only peak of myosin accumulation near the apical surface is at the circumference of the isolated cell. This myosin ring was already present before ablation (initial radius ∼10 μm), but becomes slightly stronger and moves inward as the isolated cell collapses (Fig. 1 H, upper graph). Near the basal surface, the peak of myosin accumulation is at the outer wound margin. This accumulation begins to build almost immediately after ablation, grows stronger with time, and moves inward as it helps pull the wound closed (Fig. 1 H, lower graph). There is a concomitant accumulation of myosin in the basal bridges (not shown). Although both of these basal accumulations strengthen until ∼150 s after ablation, the peak myosin signal in the radial profile decreases before this time because the basal bridges drive asymmetric contraction of the wound.

Despite the above consistency in the long-term behavior of isolated cells and surrounding wounds, the immediate postablation behavior of an isolated cell can differ markedly—sometimes contracting, sometimes expanding. This effect was not due to remnants of the ablated cells. We observed similar behavior when we ablated the surrounding cells at both cell-cell interfaces and additional medial points. We thus pursued correlations between an isolated cell’s short-term postablation response and its preablation behavior.

At this stage of embryonic development, individual amnioserosa cells are undergoing periodic expansions and contractions in apical area. Because these pulsation cycles have periods of ∼230 s (12,13,15), we imaged each cell sheet for 600–900 s before ablation to capture multiple contraction cycles. These images were segmented and the apical area versus time information was analyzed for each cell to be isolated to estimate its pulsation amplitude, period, and phase. We restricted subsequent analysis to cells with a pulsation amplitude >5% of that cell’s mean area, finding a period of 235 ± 45 s (mean ± SD, n = 41 cells).

We used two analyses to investigate whether an isolated cell’s short-term postablation response was related to its preablation pulsing behavior:

First, we simply grouped the experiments according to whether the apical area of the cell to be isolated was expanding or contracting just before ablation. As shown in the mean area-versus-time graphs for each group (Fig. 2 A), the postablation responses differ. Cells that were contracting before ablation immediately contract a bit faster after ablation; cells that were expanding, momentarily pause (on average), and then contract in an accelerating manner.

Figure 2.

Dynamic changes in apical area after isolation of pulsating amnioserosa cells. (A) Normalized apical area versus time for cells that were expanding just before ablation (red, N = 25) or those that were contracting (blue dashed, N = 16). (Lines) Mean behavior of each group. (Shaded areas) ±1 standard deviation. Cell areas were individually normalized to each cell’s mean area before ablation and then averaged to generate the group curves. (B) Initial rate of normalized area change, $\dot{A}/\overline{A}$ – where $\dot{A}$ is the rate of change of area and $\overline{A}$ is average preablation area of each cell—for cells isolated at different phases of their respective oscillation cycles. Results are grouped into 12 equal-width bins from –π to +π. Cells that were expanding have a negative phase; contracting cells have a positive phase. A phase of zero represents a cell at a temporally local maximum area. (Horizontal lines) Means for each bin. (Error bars) ±1 standard error of the mean. Two bins had no data and one bin (#) had only one data point. (C) Heat-map plot showing variation in the rate of area change, $\dot{A}/\overline{A}$, as a function of time after ablation and preablation oscillation phase. Rates of area change are shaded according to the legend. The strongest contractions correspond to the most negative rates of area change. The entire set of individual area versus time curves is compiled in Fig. S1 in the Supporting Material.

Second, we binned the experiments according to pulsation phase (12 bins of width π/6 where a phase of zero represents a maximally expanded cell) and calculated the postablation contraction rate, dA/dt, with the area of each cell normalized to its mean area before ablation.

As shown in Fig. 2, B and C, this rate is strongly dependent on the isolated cell’s preablation pulsation phase. The initial postablation contraction rate is strongest (−2% per s) for cells that were already contracting strongly before ablation—i.e., phases near +π/2—and weakest (essentially zero) for cells that were rapidly expanding before ablation—i.e., phases near −π/2. All of these movements are taking place at extremely low Reynolds numbers, so the differences cannot be attributed to inertia. They imply amnioserosa cell shape pulsations that are largely mechanically autonomous; the major driving force for expansion of a cell’s apical area is not tension applied by neighboring cells, but is instead internal to the expanding cell.

On longer timescales, all isolated cells eventually collapse. Most importantly, cells with almost no initial postablation contraction increasingly accelerate their contraction rate over the next ∼40 s (Fig. 2 C). Such accelerating contraction is inconsistent with simple elastic strain relaxation—suggesting the involvement of an active contraction. Area-versus-time graphs for all 41 cell-isolation experiments are included as Fig. S1 in the Supporting Material.

Computational modeling of cell isolation experiments

To further explore the implications of our cell-isolation results, we turned to computational modeling of cell shape oscillations. The model by Solon et al. (12) approximates amnioserosa cells as polygons with each vertex embedded in a viscous fluid and connected to adjacent vertices and cell centroids by elastic springs (for more details, see the Supporting Material). In parallel with each spring, the model includes active force elements that generate time-delayed, stretch-induced contractions. This arrangement yields cell shape oscillations that are typically out of phase in neighboring cells. When a cell is stretched beyond some threshold, a contractile response is triggered; after some time delay, this cell contracts and stretches its neighbors beyond threshold, which triggers contraction in the stretched neighbors and so on, resulting in pulsations with a period slightly longer than twice the time delay. For oscillations to occur in the model, the tissue as a whole has to be under tension.

In the original publication of the model, this tension was produced by selecting an equilibrium length for each spring that was only ∼25% of the average spring length, effectively placing each cell under an extremely high elastic strain (∼3). Such high elastic strain is unrealistic in and of itself—no material is linearly elastic out to a strain of three—but it also directly conflicts our observation of points in the oscillation cycle when isolated cells have little to no immediate collapse, i.e., they are only under small elastic strain.

Despite this conflict, the Solon model is quite successful at simulating both the contraction cycle of amnioserosa cells and the opening of cell-edge wounds after single point ablations (12). To determine whether the conflict actually yields any incorrect model predictions, we reproduced the original high elastic strain model, confirmed that our encoding yielded similar pulsations and wound responses, and then ran simulated cell isolation experiments (Fig. 3 and see Movie S2). Not surprisingly, isolation of cells under high elastic strain leads to their rapid collapse (Fig. 3, A–C). This is a consequence of passive viscoelastic relaxation; any triggered contractions in the model only contribute in a time-delayed manner (>100 s later). The high-elastic-strain model makes adequate qualitative predictions on long timescales—isolated cells contract in both the model and experiments—but it makes incorrect predictions with regard to the initial contraction rate. We ran 93 simulations that each isolated a pulsing cell at different points in its contraction cycle. Although the simulations do produce a phase-dependent response, the modeled cells collapse too quickly at all phases. Compare Fig. 2, A–C, to Fig. 3, C–E. The largest discrepancy occurs for oscillation phases near −π/2, i.e., cells that were expanding rapidly just before ablation. In our experiments, these cells had initial postablation contraction rates near zero, but in the model, they contract too rapidly. Rapid contraction occurs for all oscillation phases in the model because the parallel combination of high tensile elastic strain and active stretch-induced contractions is directed inwards for every cell at all times (see Fig. S4).

Figure 3.

Comparison of high elastic strain and low elastic strain models. (A and B) Simulation of a cell-isolation experiment using a high strain model. (Dashed blue outline) Preablation shape and size of the isolated cell. (C) Normalized apical area versus time for cells that were expanding just before ablation (red, N = 48) or those that were contracting (blue dashed, N = 45). (Lines) Mean behavior of each group. (Shaded areas) ±1 standard deviation. Cell areas were individually normalized to each cell’s mean area before ablation and then averaged to generate the group curves. (D) Initial rate of normalized area change, $\dot{A}/\overline{A}$, for cells isolated at different phases of the oscillation cycle. Results are grouped into 12 equal-width bins from –π to +π. (Horizontal lines) Means for each bin. (Error bars) ± standard error of the mean. (E) Heat-map plot showing variation in the rate of area change, $\dot{A}/\overline{A}$, as a function of time after ablation and preablation oscillation phase. Rates of area change are shaded according to the legend. The strongest contractions correspond to the most negative rates of area change. (F–J) Matching results for simulations using a modified low-elastic-strain model with active wound-induced contraction. See also Movie S2, Fig. S3, Fig. S4, Fig. S5, and Table S1.

We then sought minimal modifications of the model that would maintain preablation oscillations and long-term wound retraction, while also replicating the in vivo behavior of isolated cells. The first change was setting the equilibrium length of each spring equal to its length at the start of the simulation, making this a low elastic strain model. The modeled tissue as a whole is still under tension, but individual oscillating cells can now have a net internal force that is transiently directed outward (whenever the elastic component is under a compression that exceeds the currently active stretch-induced contraction; see Extended Modeling Procedures in the Supporting Material). This modification helps match experimental results for the initial postisolation response; however, by itself, this single modification also prevents the longer-term collapse of isolated cells. We thus introduce a second modification by which all unharmed cells actively reduce the length of their interfaces in contact with ablated cells. This active response is encoded in the model by a time-dependent sigmoidal function that drops the equilibrium length of a vertex-vertex spring to zero if both vertices are adjacent to a wounded cell. This response effectively minimizes the contact length between healthy and wounded cells and its time constant sets the timescale both for active contraction of an isolated cell and rounding up of a wound’s outer boundary.

Although the model as constructed is completely phenomenological, plausible mechanisms for triggering this active response include paracrine or juxtacrine signals from the surrounding wounded cells. These cells no longer exert in-plane forces on the isolated cell, but they could still influence its behavior. Similarly, the active response itself, i.e., decay of the springs’ equilibrium length, could be plausibly associated with recruitment of myosin. This would be consistent with the observed postablation dynamics of myosin, but our model does not identify any specific molecular mechanisms. A similar wound-triggered sigmoidal function is used to eliminate the stretch-induced contractions in cells that contact wounded cells. With the same caveat as above, this function could be plausibly associated with recruitment of myosin to cell-wound interfaces and thus depletion of medial myosin. The combination of these effects means that the long-term shape of an isolated cell is determined by a balance between active wound-induced contraction of its vertex-vertex springs and compression of its unaltered vertex-centroid springs. As shown in Fig. 3, F–J, this low-elastic-strain model reproduces preablation pulsations and more closely simulates the behavior of a single isolated cell. In particular, both its short- and long-term responses match the experimentally observed phase-dependence.

Reproducing the experimental results thus required two codependent modifications of the model of Solon et al. (12): 1), reduction of the elastic strain to near zero and 2), addition of an active contact-dependent response. The first modification is very similar to the assumptions of another recently published model of cell shape oscillations in dorsal closure (42). This model placed active myosin-dependent forces on each cell edge in parallel with passive elastic springs. The springs all had resting lengths of 5 μm and based on the reported cell areas, the actual edge lengths of oscillating cells in this model ranged from 4.6 to 4.9 μm, i.e., low and slightly compressive elastic strains of −0.07 to −0.01. We did not reproduce cell-isolation experiments with this model, but because it is a low elastic strain model, we would expect appropriate short-term behavior, but no long-term collapse. In fact, Wang et al. (42) chose parameters for their model such that an isolated cell undergoes only a slight contraction (see Fig. S1 inset in Wang et al. (42)). This model could likely be modified to fit our experimental results by adding a contact-dependent recruitment of myosin to the edges of cells that border a wounded cell. This would induce a long-term active response similar to our modifications above.

We next ran additional experiments to see if our model modifications are justifiable.

Cell isolation experiments under CO₂ anesthesia

To further investigate the role of active responses, we blanketed fly embryos with CO₂ gas—a common method for anesthetizing adult flies that also works on larvae and embryos (43,44)—and then conducted additional cell isolation experiments. When CO₂ is applied during early dorsal closure, amnioserosa pulsations and their associated dynamic myosin accumulations cease within 4 min (Fig. 4 F), but residual tissue motion continues a few minutes longer, presumably until the cells reach a mechanical equilibrium under passive tension. When CO₂ is removed, initial tissue movements begin in just a few minutes, but the pattern of regular pulsations is not reestablished until ∼30–35 min later (see Movie S3). With up to 2 h of CO₂ exposure, embryos go on to develop normally and hatch. Embryos respond similarly to being blanketed by argon, suggesting that this is not a CO₂-specific effect, but rather a response to hypoxia.

Figure 4.

Cell isolation experiment in a CO₂-anesthetized embryo. (A–E) Pre- and postablation confocal images (inverted grayscale) showing slow retraction of the wound and almost no contraction of the isolated cell. (Upper-left) Times relative to ablation. Overlays denote preablation shapes of the isolated cell (blue dashed) and the outer boundary of the wound (red dotted). A common scale bar is shown in panel E. (F) Comparison of cell shape dynamics for the total area inside the outer wound margins (red) and the apical area of the isolated cell (blue dashed). (Uppermost curve) A cell in a different embryo exposed to CO₂ for the same length of time, but not ablated (black). (Shaded region) Duration of CO₂ exposure. See also Movie S3 and Movie S4.

We chose to wait ∼15 min after starting CO₂ flow before mechanically isolating a single cell. As shown in Fig. 4 and Movie S4, the apical area of the cell to be isolated stabilizes during this exposure, and then undergoes an immediate, but slight, postablation recoil (<12% of its area). During the next 500 s, as the flow of CO₂ continues, the isolated cell retains its shape and area. The outer boundary of the wound opens slowly, but similarly retains its ragged shape. There are no changes in the accumulation of myosin, neither apical nor basal. We then stopped the flow of CO₂ at 500 s after ablation and observed the longer-term resumption of an active response. Only ∼900 s later does the wound start to significantly reshape (Fig. 4 D). This reshaping is accompanied by a weak accumulation of myosin at the wound margin. By 2000 s after ablation (1500 s after CO₂ removal), wound healing is underway, but the isolated cell retains ∼76% of its preablation apical area (Fig. 4 F). Approximately 2500 s after ablation, there finally appears to be a strong contraction of the isolated cell’s apical surface. At this point, the isolated cell’s edges are significantly dimmer than the rest of the tissue—possibly due to the degradation of fluorescently labeled cadherin junctions—which makes quantification of cell area difficult. We were also unable to observe any significant myosin accumulation near the apical surface of the contracting isolated cell. Nonetheless, it is clear that passive relaxation of elastic strain only accounts for a few percent of the isolated cell’s contraction; the large remainder requires an active response. This need for an active process matches the reduced response to laser ablation in other fly tissues treated with Rho kinase inhibitors (31,35).

We then used both models to simulate cell-isolation experiments in embryos anesthetized with CO₂. We modeled anesthesia as the suppression of all active force terms, including the sigmoidal wound-response functions. As expected, the isolated cell and wound boundary behavior in the high-elastic-strain model failed to match experimental data (Fig. 5, A–E); the model’s isolated cell collapsed immediately even under anesthesia. In contrast, the low-elastic-strain model is a good match to our experimental results (Fig. 5, F–I). Most importantly, isolated cells do not collapse under anesthesia (Fig. 5 J). Instead, the isolated cell snaps back to its equilibrium-size postablation, and retains this size until active forces resume (Fig. 5, F–H). We observed a similar behavior in experiments.

Figure 5.

Simulations of cell-isolation experiments in CO₂-anesthetized embryos using the high-elastic-strain (A–E) or low-elastic-strain models (F–J). CO₂ exposure was simulated by transiently suppressing all active contractions from −500 to +500 s. Overlays denote preablation shapes of the isolated cell (blue dashed) and the outer boundary of the wound (red dotted). (E and J) Area versus time for the wound (red) and the isolated cell (blue dashed) using each model. (Shaded area) Time during which active contractions were suppressed.

Three-dimensional shape changes associated with apical contraction cycles

Although both the experiments and their matching simulations imply pulsations of amnioserosa cells that are strongly mechanically autonomous, this autonomy requires what seems like a very strange mechanical situation: epithelial cells with a net internal force that is directed outwards, i.e., an in-plane compressive stress. Two possible sources of this outward force are pressurization of the cell’s cytoplasm or coupling between the apical and basal surfaces of the cell. We thus imaged the three-dimensional structure of pulsing amnioserosa cells using the Resille(117–2)-GFP strain (10,37), which fluorescently labels all cell borders. These cells undergo apical oscillations, albeit with smaller amplitudes and more variable periods. Despite these differences, Resille-GFP enables segmentation of the entire cell volume and analysis of volumetric measures such as cytoplasmic flow or the relationship between apical and basal contraction.

Three-dimensional reconstructions show that these cells are not rigidly prismatic in shape. Instead, there are considerable dynamic changes in the basolateral portion of the cell (Fig. 6 and see Movie S5), including wedging of the cell walls, formation of bulges, and rippling of the basal surface. To determine whether these complex basolateral dynamics are related to the apical area oscillations, we calculated cross-correlations between cells’ apical area and average thickness. Apical area was defined as the in-plane area of a cell at the z position of its adherens junctions. This z position was calculated by hand, selecting a starting value for each cell and then correcting for drift by subtracting off the average z motion of all cells. Average thickness was defined as the ratio of a cell’s total volume to its maximum projected area in the xy plane. We analyzed each of seven cells over a time span of 1100 s. Autocorrelations of the apical areas showed that six of these seven cells were oscillating (periods of 320, 300, 380, 400, 460, and 260 s), but the small amplitudes and variable periods lead to an average autocorrelation (of these six) with only a weak and broad secondary peak (Fig. 6 D, dashed). Despite these weak oscillations, the cross-correlations showed a clear anticorrelation between apical area and average cell thickness both in the average correlation function (Fig. 6 D, solid) and in the individual zero-delay correlation coefficients: −0.97, −0.93, −0.81, −0.80, −0.79, −0.70, and 0.53. The one exceptional cell was oscillating weakly, so we have no explanation for its discrepant behavior. On the whole, these results suggest that volume pushed away from the apical surface during a constricted phase of the cycle is collected in the basolateral domain and returned to the apical domain in the next half cycle. Such pressurized flow of cytoplasm is a plausible source for the cell-internal compressive stress. To insure that this observation was not dependent on our exact choice of apical and basal metrics, we performed similar cross-correlation analysis for volume above and below the adherens plane, as well as apical plane volume versus remaining cell volume. All three analyses yielded similar results and are compiled in Fig. S2 along with the individual traces of these cell metrics.

Figure 6.

Three-dimensional dynamic changes in amnioserosa cell shape. (A–C) Three views are shown for each time point: an xy view of the apical area (bottom right); an xz cross-section (top); and a yz cross-section (left). (Darker/red shading) Extent of one cell. The rougher, outermost surface in each cross-section corresponds to the basal surface. A common scale bar is shown in panel C. (D) Changes in apical area and average cell thickness are anticorrelated: mean area versus thickness cross-correlation (green, solid, N = 6); mean autocorrelation of apical area (purple, dotted). The full set of apical area and thickness versus time graphs is compiled in Fig. S2B. One of the cells in Fig. S2B was excluded from the mean correlation functions because its autocorrelation function showed no evidence of oscillation. See also Movie S5.

Our data cannot distinguish whether the return of cytoplasm to the apical surface is a passive response to basolateral pressure built up during the previous apical contraction or is actively driven by a basal actomyosin contraction. Nonetheless, it is instructive to estimate the order of magnitude for the pressure differences needed to drive such flows. One can do so using either considerations of Poiseuille flow (45) or the classic Stefan solution for axisymmetric squeezing flow (46,47). Using the latter, the maximum pressure difference in a cylinder undergoing creeping flow deformation is $\mathrm{\Delta }P=3\mathit{\eta }\dot{H}{R}^2/4H^3$, where η is viscosity, H is cylinder half-height, and R is radius. Using appropriate dimensions for amnioserosa cells (H ∼3 μm, R ∼10 μm) and a viscosity estimate from sea urchin embryos (η ∼10 Pa•s (48)), the very slow rates observed for oscillatory cell thickness change ($\dot{H}$ < 0.02 μm/s) imply a maximum pressure difference of ∼0.1 Pa, equivalent to a pressure gradient ∼0.1 kPa/cm. This is on the low end of pressure gradients observed in other cytoplasmic flows, e.g., hyphal growth in fungi is driven by pressure gradients of 0.05–10 kPa/cm (45). Although we cannot rule out a basal actomyosin contraction as contributing to the return of fluid to the apical surface, the small values of these pressure gradients suggest such contraction is not needed.

Conclusions

During dorsal closure, the cell shape oscillations of amnioserosa cells are mainly mechanically autonomous. Most importantly, the expansion phase of each cell’s cycle is driven by cell-internal forces, with only a small contribution from the contraction of neighboring cells. Our results on amnioserosa cells isolated via laser-microsurgery are in agreement with observations of α-catenin knockdowns in which shape oscillations continue as the cells partially detach from one another (16). Both experiments show that individual cells can generate tensile and compressive forces to reshape their volume autonomously. Three-dimensional reconstructions of amnioserosa cells suggest that basolateral elasticity allows cytoplasm to be pushed away from the apical surface during constriction, and can help restore the cell to an equilibrium shape when an active contraction ends. Thus, the answer to our initial question is that both the contraction and expansion phases of amnioserosa cell shape oscillations are primarily low-strain viscoelastic deformations due to forces internal to the deforming cell. Forces from adjoining cells nonetheless serve to coordinate the phasing of neighboring cells (largely out of phase).

This conclusion certainly conflicts with previously published computational models of this specific process, but it also calls into question two common assumptions of many vertex models for epithelia. The primary error in the specific amnioserosa-oscillation model is the generation of tension in a cell sheet by assuming fixed boundaries with interior elastic links that are all highly stretched. A corollary error is the assumption that postablation cell movements are the result of passive relaxation of these highly stretched links. These two assumptions are common (12,31,32,35) because they yield qualitatively correct results for the response of an epithelium to ablation at a single point. Beyond that point of agreement, our experiments and closely matched models show that these two assumptions misrepresent cellular mechanics in the amnioserosa. Additional experiments are needed to determine their validity in other tissues.

Our results instead suggest that epithelia are more appropriately modeled as sheets with movable boundaries subject to a far-field tensile stress and with interior elastic links that are barely stretched. The slowing expansion of single point wounds would then be due to a combination of far-field stress, local stretching of elastic links tangential to wound boundaries, and an active response by cells that neighbor a wound. The first two have been included in some models (41), but the last is a new realization. Our modeling suggests that this active response is the same one that drives the apical collapse of mechanically isolated cells. Both occur on the same timescale, both can be eliminated by CO₂ anesthesia, and both correlate with the peripheral accumulation of myosin—albeit apically in the isolated cell and basally for the outer wound margin. In simulations, both can be modeled as a single contact-dependent process. We do not know the exact biochemical trigger for this response, but it could be as simple as a lack of adhesions to neighboring cells.

This attention to computational details in the mechanical representation of epithelia is important because models are not ends unto themselves. Computational models of epithelial morphogenesis are tools that make hypotheses explicit and thus test the plausibility of cellular and molecular mechanisms. If the underlying cellular mechanics are misrepresented, then plausibility can easily be misinterpreted. The modifications we made to the original high-strain model of Solon et al. (12) are a first step toward improving the mechanical representation, but the images presented in Fig. 6 make it clear that even extremely squamous epithelia like the amnioserosa need to be properly modeled in three dimensions. Such models are much more computationally demanding, but are clearly required as the field moves forward.