Active microrheology of multi-phase field models of biological tissue

The rheology of biological tissue plays an important role in many developmental processes, from organ formation to cancer invasion. We use a multi-phase field model of motile cells to simulate microrheology experiments of a tissue monolayer. When unperturbed, the tissue exhibits a transition between a rigid glassy state and a fluid state tuned by cell motility and deformability as measured by the  ratio of the costs of steric cell-cell repulsion and cell-edge deformation. We find that solid-like tissues exhibit a finite threshold force for the onset of motion of a probe, corresponding to a finite yield stress for the  tissue. We study the dependence of the yield stress on cell motility and deformability and show that it vanishes in the liquid state. The onset of motion is qualitatively different in  low and high deformability regimes. At high deformability, the tissue is compliant and adapts to deformations, resulting in a smooth onset of motion. At low deformability, the probe induces both deformations and translations of cells in its immediate neighborhood, and the onset of motion appears discontinuous. Near the onset of motion, cell shapes are radially compressed in front of the probe with a wake of elongated shapes behind it, suggesting that cell shapes play a role similar to that density in systems of rigid particles.