Mechanical cell competition in a model of epithelial layer with size dependent proliferation

We investigate the competition of two cell types in an epithelial layer driven by differences in their mechanical properties. A simple one-dimensional model of a cell layer is represented as a chain of overdamped elastic springs with turnover of cells described as stochastic birth and death events. First we investigate the effects of size-dependent cell division probability in establishing equilibrium density of a single cell type. Then we focus on the competition of mechanically different cells as a simple model of invasive cancer. We show that a sharp size threshold for cell division leads to equilibrium density dependent on the cell stiffness and is different from the biological equilibrium density resulting from the balance of birth and death rates. In a system composed of two distinct cell types mechanical differences lead to invasion waves. We derive an analytical approximation for the travelling wave speed and show that the competitive advantage of cells with different stiffness is determined by the relationship between the mechanical and biological equilibrium density in the cell layer.