  A model of vesicle electrodeformation is described which obtains a
parametrized vesicle shape by minimizing the sum of the membrane bending energy
and the energy due to the electric field. Both the vesicle membrane and the
aqueous media inside and outside the vesicle are treated as leaky dielectrics,
and the vesicle itself is modelled as a nearly spherical shape enclosed within
a thin membrane. It is demonstrated (a) that the model achieves a good
quantitative agreement with the experimentally determined prolate-to-oblate
transition frequencies in the kHz range, and (b) that the model can explain a
phase diagram of shapes of giant phospholipid vesicles with respect to two
parameters: the frequency of the applied AC electric field and the ratio of the
electrical conductivities of the aqueous media inside and outside the vesicle,
explored in a recent paper (S. Aranda et al., Biophys. J. 95:L19--L21, 2008). A
possible use of the frequency-dependent shape transitions of phospholipid
vesicles in conductometry of microliter samples is discussed.
