Exploration of the shapes of double-walled vesicles with a confined inner membrane

We investigate double-walled vesicles as a simple model system for multi-vesicular structures, where the inner membrane is confined within the outer membrane. Various shapes of double-walled vesicles in two dimensions are obtained by means of our recently-developed discrete space variation method, and the shapes of each layer are found to be interdependent. Confined within the outer membrane, an inner membrane with a larger surface area always shows a cristae shape. As previous simulations and theoretical analyses of a single-walled vesicle have been done before, the geometric properties of double-walled vesicles, including the mean square radius of gyration and volume within the vesicle membrane, are studied in detail as functions of the pressure and surface area. It is found that due to the inter-space restriction of each layer, double-walled vesicles exhibit different behaviors compared with the previously-observed scaling laws of single-walled vesicles. It is straightforward to extend this study to more complicated and realistic biological systems, such as those including electrostatic interactions between membranes and solvent, phase separation, and cooperative interactions between multicomponent membranes.