Graph theory has been widely used to quantitatively analyze complex networks of molecules, materials, and cells. Analyzing the dynamic complex structure of extracellular matrix can predict cell-material interactions but has not yet been demonstrated. In this study, graph theory-based mathematical modeling of RGD ligand graph inter-relation is demonstrated by differentially cutting off RGD-to-RGD interlinkages with flexibly conjugated magnetic nanobars (MNBs) with tunable aspect ratio. The RGD-to-RGD interlinkages are less effectively cut off by MNBs with a lower aspect ratio, which decreases the shortest path while increasing the number of instances thereof, thereby augmenting RGD nano inter-relation. This facilitates integrin recruitment of macrophages and thus actin fiber assembly and vinculin expression, which mediates pro-regenerative polarization, involving myosin II, actin polymerization, and rho-associated protein kinase. Unidirectional pre-aligning or reversibly lifting highly elongated MNBs both increase RGD nano inter-relation, which promotes host macrophage adhesion and switches their polarization from pro-inflammatory to pro-regenerative phenotype. The latter approach produces nano-spaces through which macrophages can penetrate and establish RGD links thereunder. Using graph theory, this study presents the example of mathematically modeling the functionality of extracellular-matrix-mimetic materials, which can help elucidate complex dynamics of the interactions occurring between host cells and materials via versatile geometrical nano-engineering.
Keywords: Graph theory; RGD graph; RGD nano inter‐relation; macrophage regulation; remote manipulation.
© 2024 Wiley‐VCH GmbH.