Graph topological transformations in space-filling cell aggregates

Cell rearrangements are fundamental mechanisms driving large-scale deformations of living tissues. In three-dimensional (3D) space-filling cell aggregates, cells rearrange through local topological transitions of the network of cell-cell interfaces, which is most conveniently described by the vertex model. Since these transitions are not yet mathematically properly formulated, the 3D vertex model is generally difficult to implement. The few existing implementations rely on highly customized and complex software-engineering solutions, which cannot be transparently delineated and are thus mostly non-reproducible. To solve this outstanding problem, we propose a reformulation of the vertex model. Our approach, called Graph Vertex Model (GVM), is based on storing the topology of the cell network into a knowledge graph with a particular data structure that allows performing cell-rearrangement events by simple graph transformations. Importantly, when these same transformations are applied to a two-dimensional (2D) polygonal cell aggregate, they reduce to a well-known T1 transition, thereby generalizing cell-rearrangements in 2D and 3D space-filling packings. This result suggests that the GVM’s graph data structure may be the most natural representation of cell aggregates and tissues. We also develop a Python package that implements GVM, relying on a graph-database-management framework Neo4j. We use this package to characterize an order-disorder transition in 3D cell aggregates, driven by active noise and we find aggregates undergoing efficient ordering close to the transition point. In all, our work showcases knowledge graphs as particularly suitable data models for structured storage, analysis, and manipulation of tissue data.Author summary: Space-filling polygonal and polyhedral packings have been studied as physical models for foams and living tissues for decades. One of the main challenges in the field is to mathematically describe complex topological transformations of the network of cell-cell interfaces that are present during cell rearrangements, accompanying plastic deformations and large-scale cellular flows. Our work addresses this challenge by storing the topology of the network of cell-cell interfaces into a knowledge graph with a specific data structure, uniquely defined by a metagraph. It turns out that this graph technology, also used by tech giants such as Google and Amazon, allows representing topological transformations as graph transformations, that are intuitive, easy to visualize, and straight-forward to implement computationally.