one and the same. Let us now discuss the typical time and velocity scales obtained in our simulations. A typical vesicle size is approximately 10 µ m, and for liposomes κ ≈ 10 − 19 Nm. Except for very curved vesicles, the typical radius of curvature r$_{0}$ is approximately 10 µ m as well, leading to a velocity scale of 10 µ m/s. This gives calculated mean velocities on the order of 0 . 1 µ m/s for the sponta- neous curvature model, and 0 . 5 µ m/s for the bilayer coupling model. Translational and rotational diffusion constants for vesicles this size at room temperature are D ≈ 10 − 14 m $^{2}$/s and D$_{r}$ ≈ 10 − 3 s − $^{1}$, respectively. This implies a time scale for translational diffusion of approximately 104 s, and a time scale for diffusive reorientation of approximately 10 3 s. Since the actuation proposed in this paper can be implemented faster than both of these time scales, significant diffusion will take place only after many actuation cycles. For time scales much larger than D − 1 r , the effective vesicle diffu- sion will then be given by D$_{eff}$ ≈ U $^{2}$/D$_{r}$ [47], which accounts for both swimming and orientation loss. The ratio D$_{eff}$/D ≈ 10 3 is large, which implies that locomotion will lead to a substantially enhanced diffusion of the vesicles over long time scales. We have considered only two minimal models for vesicle shape change, and many possible av- enues exist to expand upon this basic model, including a study non-axisymmetric vesicles, more advanced curvature models, and arc length-dependent spontaneous curvature. Since we have as- sumed a quasi-static deformation, non-equilibrium effects would also have to be taken into account for fast deformations, and the shape should be fully determined as a balance between elastic and fluid forces. In addition, swimming is just one example of behavior that could be exhibited by a membrane that is actively deformed. It is perhaps the simplest transduction of geometrical defor- mation into mechanical work, and one that we hope provides further inspiration for the combined study of membrane physics and low Reynolds number fluid mechanics. This research was funded in part by the NSF (grant CBET-0746285). The swimming velocity is computed at each time by solving a standard boundary integral formulation of the Stokes equations. As an application of the Lorentz reciprocal identity, the Acknowledgements Appendix: Velocity and Stress Computation 20