Drosophila embryo cellularization is tuned by the viscoelastic properties of membrane-cortex linkers

The generation of an epithelial sheet transforms fruit fly embryos from a single syncytial cell directly into a tissue. During this process, the apical microvillus membrane is pulled between peripherally anchored nuclei in a process known as furrow invagination. Experimental measurements have shown that the furrow invagination velocity undergoes slow-to-fast and fast-to-stalled transitions during the formation of individual cells. The causes of such changes are due to multiple intersecting molecular mechanisms, including dynamics of motor proteins, microtubules, and F-actin. To describe the dynamics of furrow invagination, we developed a continuum model where the membrane-cortex is treated as a viscoelastic Burger body. Our model is constrained by previously published experimental data and considers the roles of cytoskeletal forces, cytoplasmic drag, motor protein forces, membrane tension, and kinetics of linker proteins. Our model reveals that the experimentally observed transitions in furrow velocity are likely associated with time-dependent changes to the viscoelastic properties of the membrane-cortex. These dynamic changes can result from the kinetics of force-dependent molecular linkers. We further predict that a combination of series and parallel assembly of these viscoelastic linkers coupled with the depletion of the membrane reservoir can capture the experimentally observed dynamics. Finally, we use our model to explain how loss of intracellular and surface membrane reservoirs can alter 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.