PHASE-DIAGRAMS AND SHAPE TRANSFORMATIONS OF TOROIDAL VESICLES

Shapes of vesicles with toroidal topology are studied in the context o f curvature models for the membrane. For two simplified curvature mode ls, the spontaneous-curvature (SC) model and the bilayer-couple (BC) m odel, the structure of energy diagrams, sheets of stationary shapes an d phase diagrams are obtained by solving shape equations for axisymmet ric shapes. Three different sheets of axisymmetric shapes are investig ated systematically: i) discoid tori; ii) sickle-shaped tori and iii) toroidal stomatocytes. A stability analysis of axisymmetric shapes wit h respect to symmetry breaking conformal transformations reveals that large regions of the phase diagrams of toroidal vesicles are non-axisy mmetric, Non-axisymmetric shapes are determined approximately using co nformal transformations. To compare the theory with experiments, a gen eralization of the SC and BC model, the area-difference-elasticity-mod el (ADE-model), which is a more realistic curvature model for lipid bi layers, is discussed. Shapes of toroidal vesicles which have been obse rved recently can be located in the phase diagram of the ADE-model. We predict the effect of temperature changes on the observed shapes. The new class of shapes, the toroidal stomatocytes, have not yet been obs erved.