Vesicular instabilities: The prolate-to-oblate transition and other shape instabilities of fluid bilayer membranes

The equilibrium shapes of fluid-phase phospholipid vesicles in an aqueous solution are controlled by bending elasticity. The regime of nonvesiculated shapes at reduced volume v≥1/ √2 involves the interplay of five branches of distinct stationary shapes: pears, prolates, oblates, stomatocytes, plus a branch of nonaxisymmetric shapes with the symmetry ${\mathit{D}}_{2\mathit{h}}$. We exploit a method for calculating explicitly the stability of arbitrary axisymmetric shapes to map out in a numerically exact way both the stable phases and the metastability of the low-lying shape branches. To obtain additional required information about nonaxisymmetric shapes, we calculate these by numerical minimization of the curvature energy on a triangulated surface. Combining these two methods allows us to construct the full (shape) phase diagram and the full stability diagram in this region. We provide explicit results for values of the bending constants appropriate to stearoyl-oleoyl-phosphatidylcholine; generalization to other values is straightforward. (c) 1995 The American Physical Society