Solid-liquid transitions in active multi-phase field models of biological tissue*

The rheological properties of biological tissue play an important role in developmental biology and cancer metastasis. Most previous theoretical work has employed particle-based or vertex/Voronoi models to demonstrate that tissue can transition between liquid-like and solid-like states. More recently, multi-phase field models of cells as motile and deformable particles have been proposed as versatile tools that can describe both confluent and non-confluent tissue, while independently varying cell density, cell motility and the nature of cell-cell interactions. We have used a multi-phase field model to study the phase behavior and rheology of a tissue monolayer. A new ingredient implemented in our work is the intercellular friction among cell edges that can build-up anisotropic local stresses and have profound effects on tissue rheology. We find that the interplay between motility and cellular adhesion at a fixed density (below confluence) can drive transition between a solid state, when the adhesion is strong compared to motility, to a liquid as motility overcomes adhesion. Using this model, we have performed both shear relaxation and microrheology simulations to examine the behavior of the tissue yield stress as a function of intercellular friction.