Melting of two-dimensional biological tissues containing active Ornstein–Uhlenbeck cells

The solid–liquid transition of biological tissues is numerically investigated in the presence of Ornstein–Uhlenbeck noise. We demonstrate that the melting scenario of the system is controlled by three parameters: temperature, the persistence time that controls the nonequilibrium properties of the system, and the target shape index that characterizes the competition between cell–cell adhesion and cortical tension. An increase in the persistence time always causes the system to transition from disordered (liquid state) to ordered (solid state). For stiff cells (small target shape index), on increasing temperature, the system undergoes the first order melting for short persistence time, while it undergoes a continuous solid–hexatic transition followed by a discontinuous hexatic–liquid transition for long persistence time. For soft cells (large target shape index), the melting always occurs via a continuous solid–hexatic transition followed by a discontinuous hexatic–liquid transition and the parameter range where the hexatic phase occurs increases with the persistence time. These behaviors are confirmed by the evolution of the density of topological defects. The phase diagrams of the system are also presented based on three parameters (temperature, the shape index, and the persistence time). Our study may contribute to the understanding of melting in two dimensional systems with many-body interactions and deformable particles. (paper)