Optimizing multicellular network formation on elastic substrates

Cells probe their local environment by exerting forces on the surrounding medium. During tissue morphogenesis, cells are driven by these matrix-mediated, mechanical interactions, and align into functional, ordered structures. By combining a linear elastic model for substrate-mediated cell-cell mechanical interactions and an agent-based model for cell movement, we show that force dipoles modeling contractile cells on elastic substrates form branched networks that percolate when the interactions are strong enough. This suggests a mechanics-driven mechanism for the morphogenesis of multicellular networks such as endothelial cell networks during vasculogenesis. Motivated by the transport functions of biological networks, we characterize our simulated force dipole networks in terms of a percolation order parameter and morphological features such as junctions, branches, and rings and show how they depend on substrate mechanics, cell density and noise. Consistent with experiments, we find that percolating networks form at an optimal range of substrate stiffness. Lastly, we find networks are robust to low levels of activity and confinement can help induce network formation.