The role of local and long-range stresses in cephalic furrow formation in the Drosophila melanogaster embryo
Cephalic furrow (CF) is a transient epithelial invagination that forms during early gastrulation in the Drosophila melanogaster embryo. The initial stage of cephalic furrow formation (CFF) involves a shortening of initiator cells, generation of a localized asymmetric protrusion inwards, and then subsequent descent of cells into the yolk sac area. We present an analysis of how local forces associated with cell-membrane tensions and cell pressures interact with the long-range tensile stress developing along the furrow to generate the invagination. We propose two numerical models which capture different aspects of CFF. First, we formulate a force-center model of CF to show how the spatiotemporal heterogeneity of initiator-cell activation observed in vivo is a result of tensile-stress-feedback-based intercellular coordination. We also argue that this kind of mechanical stress-based activation mechanism likely contributes to robustness of the overall process. Second, we use our multi-node lateral vertex model to analyze the mechanical dynamics of the anterior-posterior cross-section of CF. This approach allows us to quantify the balance between cortical membrane tension forces, cellular pressures, and the inward force produced by the tension along the curved apical surface of the embryo. Comparing our simulations to experimental images, we discuss the crucial and indispensable role of the tension-induced inward force, especially during the initial stages of CFF where the localized asymmetric protrusion is formed. We argue that without this inward force the initial descent of the initiator cells into the furrow would not be possible, and that at later stages the inward force provides redundancy to this process and thus aids CFF robustness.