Tension-driven topological transitions in a 3D Epithelial Vertex Model

Recent studies indicate that cells within curved or tilted epithelial sheets can undergo complex three-dimensional (3D) intercalations along the apical-basal axis. This process allows cells to have distinct neighbors on their apical and basal surfaces, a deviation from simple prismatic or frusta-like shapes, resulting in scutoid geometries that maintain overall tissue architecture. However, the dynamic physical mechanisms that govern cell-neighbor intercalation in densely packed tissues are not well understood. To address this gap, we developed a minimal 3D vertex model to investigate the physical principles governing scutoid formation, stability, and resolution. Our model represents the tissue as coupled apical and basal vertex layers connected by lateral edges. We find that tension along the apical-basal axis plays a critical role in controlling 3D cell shape and neighbor topology. Apical-basal tension not only regulates the stability of scutoid geometries, but also controls the formation of new scutoids and the frequency of cell rearrangements. These results suggest that the regulation of apical-basal tension profoundly influences large-scale topological transitions within the tissue, rendering it more fluid-like. We also compare our theoretical predictions with cell morphology and protein localization patterns observed during Drosophila germband extension.