Abstract
Cells can sense and respond to mechanical signals over relatively long distances across fibrous extracellular matrices. Recently proposed models suggest that long-range force transmission can be attributed to the nonlinear elasticity or fibrous nature of collagen matrices, yet the mechanism whereby fibers align remains unknown. Moreover, cell shape and anisotropy of cellular contraction are not considered in existing models, although recent experiments have shown that they play crucial roles. Here, we explore all of the key factors that influence long-range force transmission in cell-populated collagen matrices: alignment of collagen fibers, responses to applied force, strain stiffening properties of the aligned fibers, aspect ratios of the cells, and the polarization of cellular contraction. A constitutive law accounting for mechanically driven collagen fiber reorientation is proposed. We systematically investigate the range of collagen-fiber alignment using both finite-element simulations and analytical calculations. Our results show that tension-driven collagen-fiber alignment plays a crucial role in force transmission. Small critical stretch for fiber alignment, large fiber stiffness and fiber strain-hardening behavior enable long-range interaction. Furthermore, the range of collagen-fiber alignment for elliptical cells with polarized contraction is much larger than that for spherical cells with diagonal contraction. A phase diagram showing the range of force transmission as a function of cell shape and polarization and matrix properties is presented. Our results are in good agreement with recent experiments, and highlight the factors that influence long-range force transmission, in particular tension-driven alignment of fibers. Our work has important relevance to biological processes including development, cancer metastasis, and wound healing, suggesting conditions whereby cells communicate over long distances.