Tubulin is a GTPase (unrelated to ras and dynamin) whose activity is stimulated by polymerisation. This occurs when GTP-bound tubulin binds stably to the end of the microtubule. After hydrolysis the resulting GDP-tubulin is unstably attached. Polymerisation stimulates hydrolysis because GTP bound into the pocket of a beta-subunit needs to receive crucial residues from the alpha subunit from the next ring of the polymer. It seems likely that dynamin works in a similar way to stimulate its own hydrolysis by molecular interactions with the adjacent ring of dynamin.
It is interesting to note that dynamin was originally found as a GTPase associated with microtubules and was proposed to mediate microtubule sliding in vivo (Shpetner and Vallee, 1989). Although this observation did not stand the test of time, microtubule binding and stimulation of dynamin's GTPase activity has been a useful tool in mechanistic studies.