A 3D finite element model of ventral furrow invagination in the Drosophila melanogaster embryo.
ABSTRACT The paper describes a mechanical model of epithelial tissue development in Drosophila embryos to investigate a buckling phenomenon called invagination. The finite element method is used to model this ventral furrow formation in 3D by decomposing the total deformation into two parts: an imposed active deformation, and an elastic passive deformation superimposed onto the latter. The model imposes as boundary conditions (i) a constant yolk volume and (ii) a sliding contact condition of the cells against the vitelline membrane, which is interpolated as a B-Spline surface. The active deformation simulates the effects of apical constriction and apico-basal elongation of cells. This set of local cellular mechanisms leads to global shape changes of the embryo which are associated with known gene expressions. Using the model we have tested different plausible hypotheses postulated to account for the mechanical behaviour of epithelial tissues. In particular, we conclude that only certain combinations of local cell shape change can successfully reproduce the invagination process. We have quantitatively compared the model with a 2D model and shown that it exhibits a more robust invagination phenomenon. The 3D model has also revealed that invagination causes a yolk flow from the central region to the anterior and posterior ends of the embryo, causing an accordion-like global compression and expansion wave to move through the embryo. Such a phenomenon cannot be described by 2D models.
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ABSTRACT: Cell monolayers line most of the surfaces and cavities in the human body. During development and normal physiology, monolayers sustain, detect and generate mechanical stresses, yet little is known about their mechanical properties. We describe a cell culture and mechanical testing protocol for generating freely suspended cell monolayers and examining their mechanical and biological response to uniaxial stretch. Cells are cultured on temporary collagen scaffolds polymerized between two parallel glass capillaries. Once cells form a monolayer covering the collagen and the capillaries, the scaffold is removed with collagenase, leaving the monolayer suspended between the test rods. The suspended monolayers are subjected to stretching by prying the capillaries apart with a micromanipulator. The applied force can be measured for the characterization of monolayer mechanics. Monolayers can be imaged with standard optical microscopy to examine changes in cell morphology and subcellular organization concomitant with stretch. The entire preparation and testing protocol requires 3-4 d.Nature Protocol 12/2013; 8(12):2516-2530. · 8.36 Impact Factor
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ABSTRACT: Ventral furrow formation in Drosophila is an outstanding model system to study the mechanisms involved in large-scale tissue rearrangements. Ventral cells accumulate myosin at their apical sides and, while being tightly coupled to each other via apical adherens junctions, execute actomyosin contractions that lead to reduction of their apical cell surface. Thereby, a band of constricted cells along the ventral epithelium emerges which will form a tissue indentation along the ventral midline (the ventral furrow). Here we adopt a 2D vertex model to simulate ventral furrow formation in a surface view allowing easy comparison with confocal live-recordings. We show that in order to reproduce furrow morphology seen in vivo, a gradient of contractility must be assumed in the ventral epithelium which renders cells more contractile the closer they lie to the ventral midline. The model predicts previous experimental findings, such as the gain of eccentric morphology of constricting cells and an incremental fashion of apical cell area reduction. Analysis of the model suggests that this incremental area reduction is caused by the dynamical interplay of cell elasticity and stochastic contractility as well as by the opposing forces from contracting neighbour cells. We underpin results from the model through in vivo analysis of ventral furrow formation in wildtype and twi mutant embryos. Our results show that ventral furrow formation can be accomplished as a "tug-of-war" between stochastically contracting, mechanically coupled cells and may require less rigorous regulation than previously thought. For the developmental biologist it is a fascinating question how cells can coordinate major tissue movements during embryonic development. The so-called ventral furrow of the Drosophila embryo is a well-studied example of such a process when cells from a ventral band, spanning nearly the entire length of the embryo, undergo dramatic shape change by contracting their tips and then fold inwards into the interior of the embryo. Although numerous genes have been identified that are critical for ventral furrow formation, it is an open question how cells work together to elicit this tissue rearrangement. We use a computational model to mimic the physical properties of cells in the ventral epithelium and simulate the formation of the furrow. We find that the ventral furrow can form through stochastic self-organisation and that previous experimental observations can be readily explained in our model by considering forces that arise when cells execute contractions while being coupled to each other in a mechanically coherent epithelium. The model highlights the importance of a physical perspective when studying tissue morphogenesis and shows that only a minimal genetic regulation may be required to drive complex processes in embryonic development.PLoS ONE 09/2013; 8(9):e75051. · 3.53 Impact Factor
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ABSTRACT: The present work describes a 3D Finite Elements model of the Drosophila embryo designed to investigate large strains of epithelial tissues during embryogenesis. Three movements standing out for specific mechanical constraints are simulated: ventral furrow invagination, cephalic furrow formation and germ band extension. A deformation gradient decomposition is used to couple an imposed active deformation, according to the morphogenetic movement considered, and a passive elastic deformation consequence of the latter. The model also imposes boundary conditions such as the rigid contact with the vitelline membrane and the yolk pressure. The concurrent simulation of the three events is allowed; here we present the mechanical and the numerical formulation of the highly non-linear problem with special emphasis on the incorporation of cell deformations into a sound mechanical framework.