Ligand Inter-Relation Analysis Via Graph Theory Predicts Macrophage Response

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.