Interface dynamics of competing tissues

Tissues can be characterized by their homeostatic stress, i.e. the value of stress for which cell division and cell death balance. When two different tissues grow in competition, a difference of their homeostatic stresses determines which tissue grows at the expense of the second. This then leads to the propagation of the interface separating the tissues. Here, we study structural and dynamical properties of this interface by combining continuum theory with mesoscopic simulations of a cell-based model. Using a simulation box that moves with the interface, we find that a stationary state exists in which the interface has a finite width and propagates with a constant velocity. The propagation velocity in the simulations depends linearly on the homeostatic stress difference, in excellent agreement with the analytical predictions. This agreement is also seen for the stress and velocity profiles. Finally, we analyzed the interface growth and roughness as a function of time and system size. We estimated growth and roughness exponents, which differ from those previously obtained for simple tissue growth.

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