  Cells self-organize into functional, ordered structures during tissue
morphogenesis, a process that is evocative of colloidal self-assembly into
engineered soft materials. Understanding how inter-cellular mechanical
interactions may drive the formation of ordered and functional multicellular
structures is important in developmental biology and tissue engineering. Here,
by combining an agent-based model for contractile cells on elastic substrates
with endothelial cell culture experiments, we show that substrate
deformation-mediated mechanical interactions between cells can cluster and
align them into branched networks. Motivated by the structure and function of
vasculogenic networks, we predict how measures of network connectivity like
percolation and fractal dimension, as well as local morphological features
including junctions, branches, and rings depend on cell contractility and
density, and on substrate elastic properties including stiffness and
compressibility. We predict and confirm with experiments that cell network
formation is substrate stiffness-dependent, being optimal at intermediate
stiffness. Overall, we show that long-range, mechanical interactions provide an
optimal and general strategy for multi-cellular self-organization, leading to
more robust and efficient realization of space-spanning networks than through
just local inter-cellular interactions.
