Circular bead-like shapes of cell adhesion structures in 2D case

Due to the strong deformation ability of cells, the cell adhesive stacking systems are more intricate than atom stacking systems. A general method to reveal their configurations still remains challenging. In this work a theoretic model is proposed to study the circular bead-like adhesion structures composed by equal cells in the two-dimensional (2D) case. Based on the free energy minimization theory, the equilibrium shape equations are obtained and analytical solutions are investigated for high symmetrical structures without volume constraints. All results are confirmed by the finite element method. These shapes are close to some bio-structures, such as the cross section of raspberry and orange. The symmetrical breaking is studied for high symmetrical structures with volume constraints and it reveals that there are abundant degenerated states in a cell adhesion system. These results are helpful for understanding the formation mechanism of the self-organizing cell adhesion structures.