Coupling a cellular-based vertex model to a flow network to study lumen morphology within spheroids that overexpress hyaluronic acid

Lumen formation, the emergence of fluid-filled structures in tissues, helps drive organ morphology in development. Lumen shapes are determined by the interplay between multi-cellular forces and fluid pressure between cells. Interestingly, lumen malformation plays a critical role in disease. For instance, lumen formation leads to mammary cysts within breast tissue, a condition that can be painful and possibly contribute to tumorigenesis. Mammary cysts contain fluid that is enriched in glycosaminoglycans including hyaluronic acid (HA). HA overexpression has been shown to play a pivotal role in promoting cancer cell metastatic potential at the single cell level, however how HA overexpression impacts multi-cellular behavior remains unclear. To gain clarity, we study how increased production of HA by mammary epithelial cells potentially influences lumen size, shape, and positioning within an in vitro cellular collective called a spheroid. To do so, we devise a computational modeling approach coupling a cellular-based model for tissues, a vertex model, to a flow network representing HA and extracellular fluid between cells. We predict the shape, size, and location of lumen within spheroids given the emergence of leaky cellular junctions due to HA overexpression and differential cellular swelling. Comparing experimental data with simulations, we find that specific patterns of differential cellular swelling tend to result in lumen formation near the periphery of the spheroid, rather than its core.