Non-Convex Cell Epithelial Modeling Unveils Cellular Interactions

Epithelial tissues exhibit cell spatial patterns that have long been studied. Recently, such cell tessellation, made of con- vex cells, was modeled to make possible the artificial random displacement of cells. This approach led to a powerful sta- tistical method to test the significance of an apparent cell to cell relationship using only one image. However, this para- metric model fails to properly reconstruct non-convex cell shapes that can be found in epithelial tissues from animal and plant. Here, we propose a non-parametric model that can be used to reconstruct and shuffle a tesselation of non-convex cell shapes. To illustrate the usefulness of this approach, we show, using only one image, that the number of contacts be- tween stem cell clusters and ependymal cells at mouse adult stage is significantly higher than expected at random. We also show in this way that stomata are already evenly spread in the young Arabidopsis thaliana leaf epidermis, suggesting that variable cell shapes are not responsible for this pattern.