The eukaryotic cell is organized in several compartments, named organelles, delimited by lipid membranes. The fission of these membranes is required for vesicular traffic between organelles. Endocytosis is the mechanism of vesicular traffic from the plasma membrane towards other organelles inside the cell. Dynamin is a guanosine triphosphatase (GTPase) implicated in vesicle scission during Clathrin-mediated endocytosis. It polymerizes into a helix at the neck of endocytic buds. Upon GTP hydrolysis, conformational changes modify the helical structure: the inner radius decreases from 10 to 5 nm and the helical pitch reduces from 13 to 9 nm. These modifications show that fission proceeds through a constriction mechanism. The dynamics of constriction is investigated by monitoring the rotations of microbeads attached along Dynamin-coated tubes after GTP addition. The deformation of Dynamin helices is highly concerted and damped by the friction between membrane and Dynamin. However constriction is not enough to trigger fission. To further understand fission, Dynamin polymerization and fission are studied on lipid tubes extruded from Giant Unilamellar Vesicles. It is shown that fission occurs at the edge of the helix, where the membrane is strongly curved. A statistical analysis of fission time reveals that the fission reaction can be modeled by a single step energy barrier. The fission time dependence on membrane tension, membrane rigidity and torque is established theoretically and validated experimentally. This work gives a quantitative picture of the energy landscape of Dynamin-mediated fission: the height of the energy barrier of fission is estimated around 70 kT.