A morphodynamic network model to describe cell organization and nematic ordering in monolayers

To robustly model nematic ordering in cell monolayers, it is crucial to accurately capture cell geometries, which, in turn, direct patterns in cell alignment. In this regard, existing agent-based models (ABMs), such as Voronoi tesselation models, lack generality. Current approaches often fail to accommodate complex cell geometries (for example, elongated or non-convex cells) or implement thermodynamically well-posed rules for cell rearrangements. These features are essential for describing morphological processes where irregular cell shapes and dynamic rearrangements play central roles. To address the limitations of existing models, we present a novel computational framework, termed the morphodynamic network model (MNM), for simulating confluent cell monolayers. The MNM is a cell-centre-based ABM in which cell centres (nodes) are connected in a dynamic triangulation (network). Node positions and network structure, recording connections between neighbouring cells, evolve according to a split-step scheme. First, node positions are updated with the network topology fixed, then the network topology is updated with node positions fixed. We apply the MNM to study the morphodynamic behaviour of cell monolayers, including fluidization, elasto-visco-plastic responses, nematic ordering and substrate-induced cell alignment. The MNM is designed to capture complex behaviours and morphologies, offering a flexible tool for studying multicellular phenomena.