Four different mechanisms for switching cell polarity
Fig 5
In the presence of the signal, the polarity system can display three qualitatively different phase space topologies, here denoted as ‘polarized’, ‘oscillatory’, and ‘symmetric’.
A For each case, the dynamics of the system is shown in the three-dimensional space (A1 − A2, B1 − B2, R1 − R2), in which the origin corresponds to a completely symmetric protein distribution. A In a polarized state, the system is bistable, with two stable fixed points, marked grey and blue, which correspond to the two polarities of the cell. Depending on the initial condition, the system approaches one or the other stable fixed point, as illustrated by the shown trajectories. B In an oscillatory state, all trajectories of the system run into a stable limit cycle, marked in black. C In a symmetric state, the system is monostable, with a single stable fixed point at the origin, corresponding to an unpolarized cell.