Figure 5.

Simulation on a cylinder and the problem of ring formation. (A) Assuming a more realistic cylindrical geometry for the bacterium, a simple activator-depletion mechanism can lead to unpredictable patterns. Several maxima may emerge, preferentially at opposite positions of the cylinder. The simulation corresponds to the static MinE pattern formation as shown in Fig. 1C. (B–F) In the mechanism proposed, the diffusion of MinE leads to a synchronization of the wave and to ring-shaped bands. Shown are the MinD (green) and MinE (red) distributions in one full MinD cycle. (G–I) Patterning of the FtsZ ring. (G) The FtsZ ring also would decay into individual patches. (H) By a saturation of the F autocatalysis (κ_F = 0.2), this decay can be avoided. Nevertheless, the position of the ring(s) would be unpredictable. (I) The elaborate mechanism proposed is able to generate one central band as required. Simulations are made of the surface of a cylinder; the diffusion within the cylinder is not considered (cell length = 19 space elements, circumference = 9 space elements). Except for a diffusion term generalized for two dimensions, the same equations and parameters as in Figs. 1–4 are used. For animated simulations, see the supporting information.