Cell and tissue mechanics in cell migration

Abstract

Migrating cells generate traction forces to counteract the movement-resisting forces arising from cell-internal stresses and matrix adhesions. In the case of collective migration in a cell colony, or in the case of 3-dimensional migration through connective tissue, movement-resisting forces arise also from external stresses. Although the deformation of a stiffer cell or matrix causes larger movement-resisting forces, at the same time a larger stiffness can also promote cell migration due to a feedback between forces, deformations, and deformation speed that is mediated by the acto-myosin contractile machinery of cells. This mechanical feedback is also important for stiffness sensing, durotaxis, plithotaxis, and collective migration in cell colonies.

Keywords: Acto-myosin interaction; Cell mechanics; Cell migration; Hill-curve; Mechanotransduction; Tissue mechanics.

Fig. 1

Creep and stress relaxation behavior of the extracellular matrix leads to a continuous decline of the apparent stiffness. Here, a power-law exponent of 0.08 was assumed. Within 1 hour, the stress required to maintain a given matrix deformation has declined by approximately 50%.

Fig. 2

Different spreading and migration behavior of cells attached to soft versus stiff substrates is a consequence of the inverse relationship between the maximum shortening velocity and force generation due to the internal resistance and reaction kinetics of force-bearing cytoskeletal structures. It follows that cells on a stiff substrate generate larger forces and migrate more slowly compared to cells on a soft substrate. Note that the velocity vs. force curve (Hill-curve, blue) and the matrix deformation vs. matrix force relationship for stiff and soft matrices (red) can be superimposed in the same diagram only if cell-matrix contacts remain stable during a contraction cycle.

Fig. 3

Collective migration in a cell sheet and the outward directed movement of “leader” cells during a wound healing or cell spreading assay arises from the viscoelastic interaction of cells with their neighbors and the matrix, similar to the mechanical (repulsive) interactions of densely packed particles after the mechanical constraint has been released. Friction between the particles with the matrix, due to matrix adhesion, leads to larger tractions and hence larger outward movements at the boundaries compared to the center. The same principle also applies to attractive interactions between actively migrating cells that exert tension on their neighbors [37].