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 . We explore different mechanisms for ring breaking and hydrolysis.
After 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 filaments. In this stochastic model, we explore different mechanisms for ring breaking and hydrolysis.