A rigid body framework for multi-cellular modelling

Multi-cellular modelling, where tissues and organs are represented by a collection of individual interacting agents, is a well established field, encapsulating several different approaches. In particular, off-lattice models, which represent cells using points that are free to move in space, have been applied to numerous biological problems in both two and three dimensions. The fact that a cell can be represented by point objects is useful in a wide range of settings, particularly when large populations are involved. However, a purely point-based representation is not naturally equipped to deal with objects that inherently have length like cell boundaries or external membranes. In this paper we introduce a novel off-lattice modelling framework that exploits rigid body mechanics to represent cells using a collection of one-dimensional edges (rather than zero-dimensional points) in a viscosity-dominated system. The rigid body framework can be used, among other things, to represent cells as free moving polygons, to allow epithelial layers to smoothly interact with themselves, and to model rod shaped cells like bacteria. We demonstrate the value of our new framework by using it in these three applications, showing that this approach can replicate established results, as well as offer solutions to problems that limit the scope of current off-lattice multi-cellular models.