Drosophila embryo cellularization is modulated by the viscoelastic dynamics of cortical-membrane interactions

The generation of an epithelial sheet transforms fruit fly embryos from a single syncytial cell directly into a tissue. For this to happen, the apical microvillus membrane is pulled between peripherally anchored nuclei in a process known as furrow invagination. Experimental measurements of furrow invagination velocities have shown that the rate of invagination undergoes slow-to-fast and fast-to-stalled velocity transitions during the formation of individual cells. The causes of such changes are due to multiple intersecting mechanisms and molecular components, including motor proteins, microtubules, and F-actin. In this work, we develop a continuum model to describe the dynamics of furrow invagination. Our model is constrained by previously published experimental data and considers the roles of cytoskeletal forces, cytoplasmic drag, motor protein forces, and membrane tension. We find that the viscous forces produced by the cytoskeleton sliding beneath the plasma membrane dictates furrow velocity. We propose that the slow phase is slow because there is a high density of microvilli, which increases the number of viscous contact points between the plasma membrane and the underlying cytoskeleton. This in turn, results in a higher resistance to furrow invagination. We predict that the fast phase may benefit from fewer cytoskeleton-to-plasma membrane contact points, thus reducing viscous forces and promoting the slow-to-fast switch. Then, we use perturbation and loss-of-function simulations to show that microvillus and sub-apical membrane reservoirs are vital to setting furrow invagination dynamics. This work demonstrates how coupling between the cytoskeleton, the plasma membrane, and distinct membrane reservoirs affects the plasticity and dynamics of cellularization.