We investigate equilibrium shapes of vesicles composed of a mixture of partially miscible amphiphiles embedded in two- and three-dimensional space. The amphiphilic molecules can diffuse within the membrane and undergo an intramembrane phase separation below a critical temperature. We assume a simple phenomenological coupling between the local relative composition of the amphiphiles and the local curvature of the membrane shape. A linear stability analysis in the vicinity of the critical temperature indicates that a shape instability is induced by the coupling. Using a single mode approximation, we obtained phase diagrams for : (i) two-dimensional vesicles and (ii) three-dimensional axisymmetric vesicles. The equilibrium shape deformations are shown to depend on the phenomenological parameters of our model yielding highly non-trivial vesicle shapes which deviate from spherical-like objects.
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Taniguchi et al. (1994) studied this question.