Optimal mechanical interactions direct multicellular network formation on elastic substrates

Cells probe their local environment by exerting mechanical forces on the surrounding medium. During tissue morphogenesis, cells may be driven by matrix-mediated mechanical interactions, which align them 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 sufficiently strong. We validate model predictions of an intermediate substrate stiffness which optimizes mechanical interactions and network formation by conducting experiments with endothelial cells cultured on hydrogel substrates of varying stiffness. Additionally, we quantitatively analyze experimental images and compare percolation and cell cluster shapes to simulations. Ultimately, we generate a phase diagram of a composite order parameter which captures large scale transport properties and small-scale morphological features which demonstrates strong agreement between simulations and experiments.