Figure 7

CPM simulations of individual cells within the four parameter regions.(A) Parameter settings at which the simulations are performed. In all simulations, ε=3,065. In regions I–IV, τ=−10⁵, −2·10⁴, 10⁵, and 2×10⁵, respectively. (B) Analytically derived bifurcation diagram of the cell dynamics as a function of τ (or equivalently J), with ε fixed at 3,065. Both equilibrium perimeter p ^∗ and area a ^∗ are shown. For J>68,584 (see Eq. 14b) cells take up a circular shape, so p ^∗ and a ^∗ are trivially related; for J<68,584, p ^∗ and a ^∗ vary independently of each other. Solid and dashed lines represent stable and unstable equilibria, respectively. Dots refer to the equilibria at simulation parameter settings, which can be stable (blue circles), unstable with respect to size (open circles), or unstable with respect to shape (open diamonds). Boundaries between the four parameter regions are defined by black dashed lines. (Note the discontinuity in the p ^∗-axis.) (C1–F1) Snapshots of single cell simulations in different regions: Region I with initial radius r=50(C1); Region II with initial r=50(D1); region III with initial r={30, 36}(E1); Region IV with initial r=150(F1). (C2–F2) Time evolution of the perimeter (top) and radius (bottom) of simulated cells for different initial conditions with variable initial cell radius. Blue line(s) correspond to the individual cell dynamics shown in the snapshots (C1–F1). Black solid lines indicate the analytically derived stable equilibria, dashed lines the unstable equilibria. Further parameter details are given in Appendix C.