Graph Vertex Model of 3D Cell Aggregates and the Early Fly Embryo*

Cell rearrangements are fundamental mechanisms driving large-scale deformations of living tissues. In 3D cell aggregates, cells rearrange by local topological transitions of the network of cell interfaces, most conveniently described by the vertex model. Since these transitions are not yet mathematically properly formulated, the 3D vertex model is difficult to implement and the few existing implementations rely on highly customized and virtually non-reproducible software solutions. To solve this, we propose Graph Vertex Model (GVM), a reformulation of the vertex model, which stores the topology of the cell network into a knowledge graph. By naturally capturing the inherent relations between vertices, edges, cell interfaces, and cells, GVM's data structure allows defining cell-rearrangement events by simple graph transformations that are easy to implement and are unified between 2D and 3D space-filling packings. We apply a similar approach to live-imaging data of the early fly embryo. We develop GRAPE, an online queryable graph database that allows interactive analyses of an entire embryo with all 6000 surface cells accurately segmented, tracked, and cell divisions identified. Results of queries are projected color-coded onto an embryo's 3D render, additionally represented in a graph format, and readily downloadable for further analysis. By capturing topological properties of cell networks in their very essence, GVM may represent a paradigm-shifting concept in the field of tissue mechancis.