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

TL;DR

This study explains the prolate-to-oblate shape transition of phospholipid vesicles under varying AC electric field frequencies using a theoretical model that incorporates dielectric anisotropy of the membrane.

Contribution

The paper introduces a novel theoretical model accounting for dielectric anisotropy to explain vesicle shape transitions under electric fields, improving upon previous low-frequency approximations.

Findings

Vesicle deformation depends on frequency, transitioning from prolate to oblate.

The model requires the tangential permittivity to be about three times the radial permittivity.

Membrane conductivity must be roughly 10% of the external medium's conductivity.

Abstract

The external electric field deforms flaccid phospholipid vesicles into spheroidal bodies, with the rotational axis aligned with its direction. Deformation is frequency dependent: in the low frequency range (~ 1 kHz), the deformation is typically prolate, while increasing the frequency to the 10 kHz range changes the deformation to oblate. We attempt to explain this behaviour with a theoretical model, based on the minimization of the total free energy of the vesicle. The energy terms taken into account include the membrane bending energy and the energy of the electric field. The latter is calculated from the electric field via the Maxwell stress tensor, where the membrane is modelled as anisotropic lossy dielectric. Vesicle deformation in response to varying frequency is calculated numerically. Using a series expansion, we also derive a simplified expression for the deformation, which retains the frequency dependence of the exact expression and may provide a better substitute for the series expansion used by Winterhalter and Helfrich, which was found to be valid only in the limit of low frequencies. The model with the anisotropic membrane permittivity imposes two constraints on the values of material constants: tangential component of dielectric permittivity tensor of the phospholipid membrane must exceed its radial component by approximately a factor of 3; and the membrane conductivity has to be relatively high, approximately one tenth of the conductivity of the external aqueous medium.