Cell-based, mathematical modeling of collective cell behavior has become a prominent tool in developmental biology. Cell-based models represent individual cells as single particles or as sets of interconnected particles and predict the collective cell behavior that follows from a set of interaction rules. In particular, vertex-based models are a popular tool for studying the mechanics of confluent, epithelial cell layers. They represent the junctions between three (or sometimes more) cells in confluent tissues as point particles, connected using structural elements that represent the cell boundaries. A disadvantage of these models is that cell–cell interfaces are represented as straight lines. This is a suitable simplification for epithelial tissues, where the interfaces are typically under tension, but this simplification may not be appropriate for mesenchymal tissues or tissues that are under compression, such that the cell–cell boundaries can buckle. In this paper, we introduce a variant of VMs in which this and two other limitations of VMs have been resolved. The new model can also be seen as on off-the-lattice generalization of the Cellular Potts Model. It is an extension of the open-source package VirtualLeaf, which was initially developed to simulate plant tissue morphogenesis where cells do not move relative to one another. The present extension of VirtualLeaf introduces a new rule for cell–cell shear or sliding, from which cell rearrangement (T1) and cell extrusion (T2) transitions emerge naturally, allowing the application of VirtualLeaf to problems of animal development. We show that the updated VirtualLeaf yields different results than the traditional vertex-based models for differential adhesion-driven cell sorting and for the neighborhood topology of soft cellular networks.

Additional Metadata
Keywords Bubbly vertex model, Cell rearrangement, Cell sorting, Cell-based modeling, Cellular Potts Model, Developmental biology, Epithelial morphogenesis, Epithelial tissues, Junction remodeling, Vertex-based model
Persistent URL dx.doi.org/10.1007/s11538-019-00599-9
Journal Bulletin of Mathematical Biology
Wolff, H.B, Davidson, L.A, & Merks, R.M.H. (2019). Adapting a plant tissue model to animal development: Introducing cell sliding into VirtualLeaf. Bulletin of Mathematical Biology, 1–20. doi:10.1007/s11538-019-00599-9