Free and interfacial boundaries in individual-based models of multicellular biological systems

The problem of boundary effects is well-posed within many areas of mathematics. However, in individual-based modelling, it is unclear how cell boundary conditions affects the overall population dynamics. There are multiple modelling choices that could be employed, depending upon the particular type of model being used. Here, we present three distinct and widely used off-lattice models of cell dynamics: overlapping spheres, Voronoi tessellation and vertex models. We define three cell boundary descriptions, of varying complexities, for each of the models. We then consider biological case studies to observe how, across each of the different modelling paradigms, results can differ significantly. We find that the Voronoi tessellation model is the most sensitive to changes in the cell boundary description, while the timescale of tissue evolution when using an overlapping spheres model is coupled to the boundary description. Lastly, the vertex model is demonstrated to be the most stable to changes in boundary description, though still exhibits timescale sensitivity. Future individual-based modellers should consider how cell boundaries are defined in their models, even if they are not explicitly interested in tissue shape. We provide an initial investigation of common models and cell boundary descriptions in frequently investigated biological scenarios and discuss their benefits and drawbacks for future models to consider. 2. Author summary Individual-based models are emerging as a useful tool for exploring biological phenomena. However, the qualitative and quantitative impacts of varying the description of cell boundaries and interfaces on simulation results in these models have not been investigated. In this work we study different boundary descriptions in three off-lattice individual-based models: overlapping spheres, Voronoi tessellation and vertex models. For each model, we investigate three biological scenarios that highlight the importance of cell boundaries in computational simulations; void closure, tissue growth and tissue collision. We observe that in all biological scenarios considered the choice of cell boundary description can significantly influence simulation results. Specifically, the overlapping spheres model evolves on a different timescale depending on the cell boundary description used, the Voronoi tessellation model can introduce computational artefacts that need to be carefully resolved, and the vertex model is the least sensitive to changes in cell boundary description. Choosing an inappropriate model or cell boundary description can have implications for parameter fitting and may lead to a misinterpretation of the mechanisms driving biological behaviours. We conclude that the appropriate choice of cell boundary depends on the biological phenomenon being studied and the metrics of interest.