Fig. 1: Schematic overview of the modeling of interconnected ligand nanocluster for stem cell behavior regulation.

a The liganded GNPs on the material surface, which act as ligand nodes constituting interconnected ligands, are homogeneously arranged with equal inter-distances. Due to equal inter-distances, ligand nodes are connected in a way to form equilateral triangles, resulting in a ligand network model with the edges. b In the graph theory, the network is partitioned into clusters by the Louvain algorithm based on modularity. Intra-cluster edges were marked by thin green lines, and inter-cluster edges were marked by highlighted white lines. The average number of edges between neighboring clusters is referred to as “# inter-cluster edges”. c The presence of anisotropic (“aniso.”) nano-blockers between the ligand nodes obstruct ligand-to-ligand interconnections, thereby reducing the overall # ligand inter-cluster edges. The lowest anisotropy group (“Low aniso.”) exhibits the highest # inter-cluster edges, which promotes the focal adhesion and mechanotransduction of stem cells, and thereby their differentiation, both in vitro and in vivo. In contrast, the highest anisotropy group (“High aniso.”) exhibits the lowest # inter-cluster edge, which inhibits the adhesion and differentiation of stem cells.