Universal distribution of cell shapes in active systems

We use agent-based modeling of cells as deformable particles, to explore the distribution of cell shapes in active-driven systems. The deformable cells move using an active brownian force model in a quasi-two-dimensional geometry. We characterize the cell shape using S=P²/4πA, the non-dimensional ratio of perimeter P to area A. S=1 for a circle and is larger for any other shape. We compare systems containing cells with fixed (elastic) shape parameter to those with dynamic (plastic) shape parameter. The shape parameter must be greater than 1.15 for the cells to completely cover space. In these dense states, the cells must deform to move. In the fixed S₀ systems, the area of the cell is fixed and the perimeter is an elastic spring with rest-length P₀=√4πAS₀. In the dynamic system, the rest-length of the perimeter can relax based on the local stress. For fixed S₀ systems, a critical shape parameter S^* =1.34 emerges. For S₀*, the cells tend to stretch their perimeter, increasing S. For S₀>S^*, the cells tend to compress their perimeter. In the dynamic systems, a broad universal distribution of shape parameters emerges regardless of the initial distribution of shapes. This broad distribution is peaked near S=1.15, but has very long high S tails extending above S=3. The broad distribution matches that found in high mobility MDCK cell monolayers.