Graph polyhedral divisions in growing cell aggregates

Abstract

In the recently proposed Graph Vertex Model (GVM), cellular rearrangements are implemented as local graph transformations of the cell aggregate, represented by a knowledge graph [1]. This study extends GVM to incorporate cell division, a critical biological process involved in morphogenesis, homeostasis, and disease progression. Like cellular rearrangements, cell division in GVM begins by identifying a subgraph of nodes and links, involved in the division, by matching suitable graph patterns or templates within the full knowledge graph. The matched subgraph is then transformed to incorporate topological changes within the knowledge graph, caused by the division event. Importantly, when this transformation is applied to a polygon in a 2D tiling, it performs the transformation, required to divide a polygon, indicating that the 3D graph transformation is general and applicable also to 2D vertex models. Our extension of GVM enables the study of the dynamics of growing cell aggregates in 3D to offer new insights into developmental processes and cancer growth.