A Morphodynamic Network Model to Describe Cell Organization and Nematic Ordering in Monolayers

Abstract

To robustly model nematic ordering in cell monolayers, it is crucial to accurately capture cell geometries, which in turn direct the formation of patterns in cell alignment. In this regard, existing agent-based models (ABMs), such as vertex and Voronoi models, lack generality. Current models often fail to accommodate complex cell geometries (such as elongated or non-convex cells) or implement thermodynamically well-posed rules for cell rearrangements. These features are essential for describing the biophysics of morphogenetic processes where irregular cell shapes and dynamic cell 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 center-based ABM in which the cell centers (nodes) are connected to form a dynamic triangulation (network). The node positions and network structure, recording connections between neighboring cells, evolve according to a split-step approach. First, node positions are updated with the network structure (or topology) fixed, then the network topology is updated with node positions fixed. We apply the MNM to study the morphodynamic behavior of cell monolayers, including fluidization, elasto-visco-plastic responses, nematic ordering, and substrate-induced cell alignment. The MNM is designed to capture complex behaviors and morphologies, offering a flexible and robust tool for studying multicellular phenomena.