Heterogeneous force network in 3D cellularized collagen networks.

Collagen networks play an important role in coordinating and regulating collective cellular dynamics via a number of signaling pathways. Here, we investigate the transmission of forces generated by contractile cells in 3D collagen-I networks. Specifically, the graph (bond-node) representations of collagen networks with collagen concentrations of 1, 2 and 4 mg ml are derived from confocal microscopy data and used to model the network microstructure. Cell contraction is modeled by applying correlated displacements at specific nodes of the network, representing the focal adhesion sites. A nonlinear elastic model is employed to characterize the mechanical behavior of individual fiber bundles including strain hardening during stretching and buckling under compression. A force-based relaxation method is employed to obtain equilibrium network configurations under cell contraction. We find that for all collagen concentrations, the majority of the forces are carried by a small number of heterogeneous force chains emitted from the contracting cells, which is qualitatively consistent with our experimental observations. The force chains consist of fiber segments that either possess a high degree of alignment before cell contraction or are aligned due to fiber reorientation induced by cell contraction. The decay of the forces along the force chains is significantly slower than the decay of radially averaged forces in the system, suggesting that the fibreous nature of biopolymer network structure can support long-range force transmission. The force chains emerge even at very small cell contractions, and the number of force chains increases with increasing cell contraction. At large cell contractions, the fibers close to the cell surface are in the nonlinear regime, and the nonlinear region is localized in a small neighborhood of the cell. In addition, the number of force chains increases with increasing collagen concentration, due to the larger number of focal adhesion sites in collagen networks with high concentrations.