The Tight Backbone Spread Model for Simulating 3D Epithelial Cell Layer Dynamics

Abstract Modeling the morphogenesis of epithelial tissues requires faithful simulation of cell-level dynamics, including changes in shape and neighborhood relations. Traditional two-dimensional models, such as cell-centered Voronoi tessellations, are limited in their ability to represent the curved three-dimensional geometry of epithelial layers found in biological systems. In this work, we introduce a formal three-dimensional modeling approach for epithelial structures based on the concept of backbone spreads, and we analyze its geometric properties. Building upon this framework, we propose an adapted Metropolis–Hastings algorithm to compute epithelial tissue configurations that minimize a given energy functional. We provide theoretical guarantees on the algorithm’s efficiency and demonstrate its practical effectiveness on the examples of tubular and spheroidal epithelia. Furthermore, we examine the diversity of cell shapes and connectivity patterns that arise in the simulations, and we analyze their frequency in relation to key model parameters. Notably, our simulations reveal novel cell configurations that, to our knowledge, have not been previously described in the literature. Our results highlight the ability of the backbone spread model to capture complex epithelial cell structures while also allowing for efficient simulation of dynamic reconfigurations.