Migration, Force Generation and Mechanosensing of Cells in Collagen Gels

Abstract

Collagen gels are frequently used to study cell migration in a three-dimensional environment. Mechanical properties of collagen gels are governed by non-affine deformation of the collagen fibrils, such as buckling and tautening, resulting at the macroscopic scale in strain stiffening under shear and a strong lateral contraction under stretch. It is currently unknown how these macroscopic properties play out at the scale of a migrating cell, and how this depends on the cell geometry. To explore this question, we develop a non-linear elastic material model for collagen gels based on observations from confocal microscopy that fibrils can evade mechanical stress using their internal degrees of freedom. This non-affine behavior results in a non-linear force length relationship of fibril segments and leads to a macroscopic strain stiffening and lateral contraction. In particular, we show that tautening of fibrils results in a strong material stiffening against expanding forces, e.g. from a migrating cell with a diameter larger than the network pore diameter. By this mechanism, even a soft collagen gel can sterically constrain a migrating cell. Using our material model, we compute cell traction forces, induced stresses as well as material stiffening, from collagen fiber displacements during the migration of MDA-MB 231 breast carcinoma cells through dilute (0.6 mg/ml, Young's modulus 85 Pa) and dense (2.4 mg/ml, Young's modulus 1100 Pa) collagen gels. We find that cells exert highly localized forces onto the matrix, leading to a localized ∼2-fold material stiffening. However, the average traction force magnitude increases with collagen concentration by ∼3-fold, from 40nN in dilute gels to 120nN in dense gels. This observation may help explain why cells can migrate more efficiently in stiffer gels, despite their narrower pore diameter.