Detalle de: Efficient Modeling of 3D Epithelial Cell Structure Dynamics via Backbone Spreads

: An important means to study the morphogenesis of epithelial cell structures is faithful modeling and simulation of the underlying cell dynamics. In particular, changes in cell shapes and cell neighborhoods have to be captured to gain understanding of organ development and other complex processes. A typical 2D tissue model is cell-center based Voronoi tessellation. However, since epithelial cells form curved layers in three-dimensional space, a 2D model cannot encompass all relevant aspects. In this paper, we provide a formal 3D model for epithelial cell structures based on the notion of backbone spreads and study its geometric properties. Based thereupon, we devise a modified version of the well-known Metropolis-Hastings algorithm to find cell tissue configurations that minimize a given energy function. We prove that our new algorithm is very efficient from a theoretical perspective and also demonstrate its good performance in practice on the example of tubular epithelia. Furthermore, we show that a rich set of cell shapes and connectivity structures emerge in our model, and we analyze their frequency of occurrence with respect to the model parameters.