Modeling Cephalic Furrow Architecture in the Drosophila Melanogaster Embryo Using an Automated Multi-node Lateral Vertex Model Approach

Cephalic furrow (one of the early morphogenetic movements in Drosophila melanogaster embryos) gives rise to a deep epithelial invagination. The furrow formation involves a sequence of cell-shape changes in the invagination region that generate the initial protrusion and drive the subsequent descent of cells into the yolk sac. The cell-shape changes that are produced by active modifications of the apical, lateral, and basal membrane lengths require a complex balance between the cortical membrane tension forces and cellular pressure forces in a system of mechanically coupled cells. To investigate this force balance and its role in the invagination process, we have developed an advanced two-dimensional multi-node lateral vertex model that includes a multi-node representation of cellular membranes. The multi-node approach allows us to capture the membrane curvatures associated with cell-to-cell pressure variation. We have also developed a numerical algorithm that automatically generates shapes of mechanically coupled cells based on the length and curvature of the cell membranes measured in vivo. The observation of the response of the calculated cell shapes to mechanical perturbations enables us to assess the robustness of the invagination process and determine the role of various mechanical components, such as cortical tensions, cellular pressures, and tissue-tension variations resulting from other, concurrently occurring, morphogenetic movements.