The morphogenesis of liposomes viewed from the aspect of bending energy

It is known that liposomes transform their shapes sequentially through one of several transformation pathways. Using the mechanical principle of the least bending energy of membranes, we investigate the stability and shape transformation of liposomes with geometrical symmetry. We have done this by computer simulations and theoretical analyses, in which three-dimensional liposome shapes have been generated by the modified Cassini equation. We show first that there are energetically stable liposome shapes having intrinsic geometrical symmetry. We find that by reducing the volume, the stable shape can change from a circular biconcave shape as in red blood cells, to elliptical, triangular, square, and other polygonal shapes. It is also found that the preceding two results hold true irrespective of the overall surface area of liposome.