Microtubules formed from pure tubulin undergo subunit uptake and loss at ends by both random exchange diffusion, and by a directional (treadmilling) element.  Treadmilling is inefficient, and for microtubules at steady state: the Wegner s-value (the reciprocal of the number of molecular events required for the net uptake of a subunit) is equal to 0.0005-0.001; i.e., it requires >1000 events. Microtubule treadmilling with pure tubulin also occurs with growing microtubules and is enhanced by proteins that bind to ends.  Rapid treadmilling occurs in cells.
FtsZ treadmilling
The bacterial tubulin homolog FtsZ is one of the best documented treadmilling polymers. FtsZ assembles into protofilaments that are one subunit thick, which can further associate into small patches of parallel protofilaments. Single filaments and/or patches have been demonstrated to treadmill in vitro and inside bacterial cells. A Monte Carlo model of FtsZ treadmilling has been designed, based on a conformational change of subunits upon polymerization and GTP hydrolysis.