Emergent order in athree-dimensional vertex model for organoids

Organoids, or in vitro cellular collectives from which brain-like, or intestine-like structures, for example, emerge give us a high throughput glimpse into the window of organogenesis. To make quantitative predictions regarding the morphology and rheology of a developing organoid, we construct and study a three-dimensional vertex model. In such a model, the cells are represented as deformable polyhedrons with cells sharing faces such that there are no gaps between them. In a bulk model, we find a rigidity transition as a function of the target cell shape index. For a cellular collective with a finite boundary, we uncover emergent, cellular ordering near the boundary. We explore how this ordering affects the interior of the cellular collective in the presence of external stresses and internal, active stresses. Such emergent ordering might underline the pattern in organogenesis.