A Vertex Model of <i>Drosophila</i> Ventral Furrow Formation

<div><p>Ventral furrow formation in <i>Drosophila</i> 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 <i>in vivo</i>, 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 <i>in vivo</i> analysis of ventral furrow formation in wildtype and <i>twi</i> 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.</p><p>Summary</p><p>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.</p>