Modularity-based mathematical modeling of ligand inter-nanocluster connectivity for unraveling reversible stem cell regulation.

The native extracellular matrix is continuously remodeled to form complex interconnected network structures that reversibly regulate stem cell behaviors. Both regulation and understanding of its intricate dynamicity can help to modulate numerous cell behaviors. However, neither of these has yet been achieved due to the lack of designing and modeling such complex structures with dynamic controllability. Here we report modularity-based mathematical modeling of extracellular matrix-emulating ligand inter-cluster connectivity using the graph theory. Increasing anisotropy of magnetic nano-blockers proportionately disconnects arginine-glycine-aspartic acid ligand-to-ligand interconnections and decreases the number of ligand inter-cluster edges. This phenomenon deactivates stem cells, which can be partly activated by linearizing the nano-blockers. Remote cyclic elevation of high-anisotropy nano-blockers flexibly generates nano-gaps under the nano-blockers and augments the number of ligand inter-cluster edges. Subsequently, integrin-presenting stem cell infiltration is stimulated, which reversibly intensifies focal adhesion and mechanotransduction-driven differentiation both in vitro and in vivo. Designing and systemically modeling extracellular matrix-mimetic geometries opens avenues for unraveling dynamic cell-material interactions for tissue regeneration.