  Recent in vitro experiments with FtsZ polymers show self-organization into
different dynamic patterns, including structures reminiscent of the bacterial
Z-ring. We model FtsZ polymers as active particles moving along chiral,
circular paths by Brownian dynamics simulations and a Boltzmann approach. Our
two conceptually different methods point to a generic phase behavior. At
intermediate particle densities, we find self-organization into vortex
structures including closed rings. Moreover, we show that the dynamics at the
onset of pattern formation is described by a generalized complex
Ginzburg-Landau equation.
