Elongated Cells Drive Morphogenesis in a Surface-Wrapped Finite-Element Model of Germband Retraction.

During Drosophila embryogenesis, the germband first extends to curl around the posterior end of the embryo and then retracts back; however, retraction is not simply the reversal of extension. At a tissue level, extension is coincident with ventral furrow formation, and at a cellular level, extension occurs via convergent cell neighbor exchanges in the germband, whereas retraction involves only changes in cell shape. To understand how cell shapes, tissue organization, and cellular forces drive germband retraction, we investigate this process using a whole-embryo, surface-wrapped cellular finite-element model. This model represents two key epithelial tissues-amnioserosa and germband-as adjacent sheets of two-dimensional cellular finite elements that are wrapped around an ellipsoidal three-dimensional approximation of an embryo. The model reproduces the detailed kinematics of in vivo retraction by fitting just one free model parameter, the tension along germband cell interfaces; all other cellular forces are constrained to follow ratios inferred from experimental observations. With no additional parameter adjustments, the model also reproduces quantitative assessments of mechanical stress using laser dissection and failures of retraction when amnioserosa cells are removed via mutations or microsurgery. Surprisingly, retraction in the model is robust to changes in cellular force values but is critically dependent on starting from a configuration with highly elongated amnioserosa cells. Their extreme cellular elongation is established during the prior process of germband extension and is then used to drive retraction. The amnioserosa is the one tissue whose cellular morphogenesis is reversed from germband extension to retraction, and this reversal coordinates the forces needed to retract the germband back to its pre-extension position and shape. In this case, cellular force strengths are less important than the carefully established cell shapes that direct them. VIDEO ABSTRACT.

Cellular mechanics of germ band retraction in Drosophila.

Germ band retraction involves a dramatic rearrangement of the tissues on the surface of the Drosophila embryo. As germ band retraction commences, one tissue, the germ band, wraps around another, the amnioserosa. Through retraction the two tissues move cohesively as the highly elongated cells of the amnioserosa contract and the germ band moves so it is only on one side of the embryo. To understand the mechanical drivers of this process, we designed a series of laser ablations that suggest a mechanical role for the amnioserosa. First, we find that during mid retraction, segments in the curve of the germ band are under anisotropic tension. The largest tensions are in the direction in which the amnioserosa contracts. Second, ablating one lateral flank of the amnioserosa reduces the observed force anisotropy and leads to retraction failures. The other intact flank of amnioserosa is insufficient to drive retraction, but can support some germ band cell elongation and is thus not a full phenocopy of ush mutants. Another ablation-induced failure in retraction can phenocopy mys mutants, and does so by targeting amnioserosa cells in the same region where the mutant fails to adhere to the germ band. We conclude that the amnioserosa must play a key, but assistive, mechanical role that aids uncurling of the germ band.

Modeling cell elongation during germ band retraction: cell autonomy versus applied anisotropic stress.

The morphogenetic process of germ band retraction in Drosophila embryos involves coordinated movements of two epithelial tissues - germ band and amnioserosa. The germ band shortens along its rostral-caudal or head-to-tail axis, widens along its perpendicular dorsal-ventral axis, and uncurls from an initial 'U' shape. The amnioserosa mechanically assists this process by pulling on the crook of the U-shaped germ band. The amnioserosa may also provide biochemical signals that drive germ band cells to change shape in a mechanically autonomous fashion. Here, we use a finite-element model to investigate how these two contributions reshape the germ band. We do so by modeling the response to laser-induced wounds in each of the germ band's spatially distinct segments (T1-T3, A1-A9) during the middle of retraction when segments T1-A3 form the ventral arm of the 'U', A4-A7 form its crook, and A8-A9 complete the dorsal arm. We explore these responses under a range of externally applied stresses and internal anisotropy of cell edge tensions - akin to a planar cell polarity that can drive elongation of cells in a direction parallel to the minimum edge tension - and identify regions of parameter space (edge-tension anisotropy versus stress anisotropy) that best match previous experiments for each germ band segment. All but three germ band segments are best fit when the applied stress anisotropy and the edge-tension anisotropy work against one another - i.e., when the isolated effects would elongate cells in perpendicular directions. Segments in the crook of the germ band (A4-A7) have cells that elongate in the direction of maximum external stress, i.e., external stress anisotropy is dominant. In most other segments, the dominant factor is internal edge-tension anisotropy. These results are consistent with models in which the amnioserosa pulls on the crook of the germ band to mechanically assist retraction. In addition, they suggest a mechanical cue for edge-tension anisotropy whereby cells do not globally orient their internal elongation axis towards the amnioserosa, but instead orient this axis perpendicular to the local principal stress direction.

Enabling user-guided segmentation and tracking of surface-labeled cells in time-lapse image sets of living tissues.

To study the process of morphogenesis, one often needs to collect and segment time-lapse images of living tissues to accurately track changing cellular morphology. This task typically involves segmenting and tracking tens to hundreds of individual cells over hundreds of image frames, a scale that would certainly benefit from automated routines; however, any automated routine would need to reliably handle a large number of sporadic, and yet typical problems (e.g., illumination inconsistency, photobleaching, rapid cell motions, and drift of focus or of cells moving through the imaging plane). Here, we present a segmentation and cell tracking approach based on the premise that users know their data best-interpreting and using image features that are not accounted for in any a priori algorithm design. We have developed a program, SeedWater Segmenter, that combines a parameter-less and fast automated watershed algorithm with a suite of manual intervention tools that enables users with little to no specialized knowledge of image processing to efficiently segment images with near-perfect accuracy based on simple user interactions.

Combining laser microsurgery and finite element modeling to assess cell-level epithelial mechanics.

Laser microsurgery and finite element modeling are used to determine the cell-level mechanics of the amnioserosa-a morphogenetically crucial epithelium on the dorsal surface of fruit fly embryos (Drosophila melanogaster). In the experiments, a tightly focused laser ablates a subcellular hole (1 microm in diameter) that passes clean through the epithelium. The surrounding cells recoil from the wound site with a large range of initial recoil velocities. These depend on the embryo's developmental stage and the subcellular wound site. The initial recoil (up to 0.1 s) is well reproduced by a base finite element model, which assumes a uniform effective viscosity inside the cells, a constant tension along each cell-cell boundary, and a large, potentially anisotropic, far-field stress--one that far exceeds the stress equivalent of the cell-edge tensions. After 0.1 s, the experimental recoils slow dramatically. This observation can be reproduced by adding viscoelastic rods along cell edges or as a fine prestressed mesh parallel to the apical and basal membranes of the cell. The mesh also reproduces a number of double-wounding experiments in which successive holes are drilled in a single cell.

Probing embryonic tissue mechanics with laser hole drilling.

We use laser hole drilling to assess the mechanics of an embryonic epithelium during development-in vivo and with subcellular resolution. We ablate a subcellular cylindrical hole clean through the epithelium and track the subsequent recoil of adjacent cells (on ms time scales). We investigate dorsal closure in the fruit fly with emphasis on apical constriction of amnioserosa cells. The mechanical behavior of this epithelium falls between that of a continuous sheet and a 2D cellular foam (a network of tensile interfaces). Tensile stress is carried both by cell-cell interfaces and by the cells' apical actin networks. Our results show that stress is slightly concentrated along interfaces (1.6-fold), but only in early closure. Furthermore, closure is marked by a decrease in the recoil power-law exponent, implying a transition to a more solid-like tissue. We use the site and stage dependence of the recoil kinetics to constrain how the cellular mechanics change during closure. We apply these results to test extant computational models.

Using a continuum model to decipher the mechanics of embryonic tissue spreading from time-lapse image sequences: An approximate Bayesian computation approach.

Advanced imaging techniques generate large datasets capable of describing the structure and kinematics of tissue spreading in embryonic development, wound healing, and the progression of many diseases. These datasets can be integrated with mathematical models to infer biomechanical properties of the system, typically identifying an optimal set of parameters for an individual experiment. However, these methods offer little information on the robustness of the fit and are generally ill-suited for statistical tests of multiple experiments. To overcome this limitation and enable efficient use of large datasets in a rigorous experimental design, we use the approximate Bayesian computation rejection algorithm to construct probability density distributions that estimate model parameters for a defined theoretical model and set of experimental data. Here, we demonstrate this method with a 2D Eulerian continuum mechanical model of spreading embryonic tissue. The model is tightly integrated with quantitative image analysis of different sized embryonic tissue explants spreading on extracellular matrix (ECM) and is regulated by a small set of parameters including forces on the free edge, tissue stiffness, strength of cell-ECM adhesions, and active cell shape changes. We find statistically significant trends in key parameters that vary with initial size of the explant, e.g., for larger explants cell-ECM adhesion forces are weaker and free edge forces are stronger. Furthermore, we demonstrate that estimated parameters for one explant can be used to predict the behavior of other similarly sized explants. These predictive methods can be used to guide further experiments to better understand how collective cell migration is regulated during development.