Before revision:  In this work, we present a minimal stochastic model that qualitatively reproduces {\it  observations of polymerization, of formation of dynamic contractile ring that is stable for a long time and of depolymerization shown by FtsZ polymer .
After revision:  In this work, we present a minimal stochastic model that qualitatively reproduces {\it in vitro observations of polymerization, of formation of dynamic contractile ring that is stable for a long time and of depolymerization shown by FtsZ polymer .