perimental methods, not only these examples in no way constitute the full set of possibilities, but also they might be difficult to implement experimentally. Other experimental techniques already exist (see Refs. [19, 38]), or may be developed in the near future that could be more suited for controlled two-parameter change. Rather than suggest specific experimental methodology whose specifics would depend not only on the particular material of the bilayer vesicles, but also on the parameter alternation methods, we adopt in this paper a simplified modeling approach that highlights the qualitative pieces that are required in order to transform a motionless vesicle into a locomotive cargo-carrier. In parallel to the the various practical mechanisms that could be used to implement such shape changes experimentally, it is of fundamental interest to ask theoretically the question of prediction and performance. Would shape change indeed lead to locomotion of the vesicle? How efficient would it be? Can we quantitatively predict the resulting swimming speed and the work done against the fluid to achieve it? This is the approach taken in this paper. Considering two simplified vesicle models, and for slow modulations of the vesicle shapes, we introduce below a computational framework able to quantitatively predict swimming kinematics and performance. While real biological membranes have multiple constituents, all interacting in non-trivial ways, minimal models can still help to illuminate the fundamental physics of such systems. For length scales on which a membrane is approximately flat a Monge parameterization can be employed [40– 42], but for a closed bilayer vesicle the curvatures can become very large and the small geometric gradient assumption may break down. In order to characterize the shapes of such objects, an enthalpy must be extremized and the full nonlinear shape equations so generated must be solved. There are many models that could be used to describe the physics of curvature-mediated vesicle morphology. In this paper we will consider two classical models as case studies. These formulations, known respectively as the spontaneous curvature and bilayer coupling models, have both been used in classical work [43] and correspond to different interaction dynamics between the membrane monolayers. Both of these models also include exactly two free parameters, which enable us to explore the breaking of the Scallop theorem, and the generation of locomotion via a change in morphology. III. DYNAMICS OF COUPLED FLUID-BODY SYSTEM A. Vesicle physics 6