  The tubulin-like protein FtsZ is crucial for cytokinesis in bacteria and many
archaea, forming a ring-shaped structure called the Z-ring at the site of cell
division. Despite extensive research, the formation of Z-rings is not entirely
understood. We propose a theoretical model based on FtsZ's known filament
structures, treating them as semiflexible polymers with specific mechanical
properties and lateral inter-segment attraction that can stabilize ring
formations. Our Langevin dynamics simulations reveal various morphological
phases, including open helices, chains, rings, and globules, capturing
experimental observations in the fission yeast model using FtsZ from different
bacterial species or mutants of Escherichia coli. Using the theoretical model,
we explore how treadmilling activity affects Z-ring stability and identify a
spooling mechanism of ring formation. The active ring produces contractile,
shear, and rotational stresses, which intensify before the Z-ring transitions
to an open helix at high activity.
