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Cell-based, mathematical modeling of collective cell behavior has become aprominent tool in developmental biology. Cell-based models represent individualcells as single particles or as sets of interconnected particles, and predictthe collective cell behavior that follows from a set of interaction rules. Inparticular, vertex-based models are a popular tool for studying the mechanicsof confluent, epithelial cell layers. They represent the junctions betweenthree (or sometimes more) cells in confluent tissues as point particles,connected using structural elements that represent the cell boundaries. Adisadvantage of these models is that cell-cell interfaces are represented asstraight lines. This is a suitable simplification for epithelial tissues, wherethe interfaces are typically under tension, but this simplification may not beappropriate for mesenchymal tissues or tissues that are under compression, suchthat the cell-cell boundaries can buckle. In this paper we introduce a variantof VMs in which this and two other limitations of VMs have been resolved. Thenew model can also be seen as on off-the-lattice generalization of the CellularPotts Model. It is an extension of the open-source package VirtualLeaf, whichwas initially developed to simulate plant tissue morphogenesis where cells donot move relative to one another. The present extension of VirtualLeafintroduces a new rule for cell-cell shear or sliding, from which T1 and T2transitions emerge naturally, allowing application of VirtualLeaf to problemsof animal development. We show that the updated VirtualLeaf yields differentresults than the traditional vertex-based models fordifferential-adhesion-driven cell sorting and for the neighborhood topology ofsoft cellular networks.

Adapting a plant tissue model to animal development: introducing cell sliding into VirtualLeaf