The prolate-to-oblate shape transition of phospholipid vesicles in response to frequencyvariation of an AC electric field can be explained by the dielectric anisotropy of aphospholipid bilayer

Abstract

An external electric field deforms flaccid phospholipid vesicles into spheroidal bodies, with therotational axis aligned with its direction. Deformation is frequency dependent: in the low-frequencyrange (∼1 kHz), the deformation is typically prolate, while increasing the frequency to the 10 kHz rangechanges the deformation to oblate. We attempt to explain this behaviour with a theoreticalmodel, based on the minimization of the total free energy of the vesicle. The energy termstaken into account include the membrane bending energy and the energy of the electricfield. The latter is calculated from the electric field via the Maxwell stress tensor, where themembrane is modelled as anisotropic lossy dielectric. Vesicle deformation in response tovarying frequency is calculated numerically. Using a series expansion, we also derive asimplified expression for the deformation, which retains the frequency dependence of theexact expression and may provide a better substitute for the series expansion used byWinterhalter and Helfrich, which was found to be valid only in the limit of lowfrequencies. The model with anisotropic membrane permittivity imposes two constraintson the values of material constants: the tangential component of the dielectricpermittivity tensor of the phospholipid membrane must exceed its radial component byapproximately a factor of 3; and the membrane conductivity has to be relatively high,approximately one tenth of the conductivity of the external aqueous medium.