Dielectric anisotropy of the phospholipid bilayer determined from the frequency-dependent prolate-to-oblate shape transition of phospholipid vesicles in an external electric field

Primož Peterlin1, Saša Svetina1,2 and Boštjan Žekš1,2

1University of Ljubljana, Faculty of Medicine, Institute of Biophysics, 2Jožef Stefan Institute, Ljubljana, Slovenia

External AC electric field tends to deform flaccid phospholipid vesicles in aqueous solution into approximately spheroidal shapes. Their axis of symmetry is aligned with the direction of the applied field. At low frequencies, the deformation is prolate. If the frequency is increased, the shape changes into oblate spheroid. We tried to find a suitable theoretical explanation for this phenomenon. Both the aqueous solution and the vesicle membrane are modeled as lossy dielectrics, the latter also being characterized by an anisotropic dielectric tensor. The electric potential inside and outside the vesicle is obtained by solving the Laplace equation for a spherical shell immersed in a medium with different electrical properties. A differential equation similar to Laplace equation is obtained and solved for the spherical shell. Maxwell stress tensor is then calculated from the electric potential. The Maxwell stress tensor, evaluated on both the inner and the outer membrane-water boundary in the direction perpendicular to the boundary, amounts to the surface density of the force with which the electric field is acting on the membrane. Its scalar product with the local membrane displacement, integrated over the total membrane area, yields the work of electric forces acting on the vesicle. Equilibrium vesicle shape at given external parameters (vesicle size, electric field strength, frequency and the material constants) is then finally calculated by minimizing the total free energy, consisting of the membrane bending energy and the energy of the electric field. Described theoretical model predicts that the vesicle shape depends on the frequency in the same manner as was observed in the experiment. The transition frequency between the prolate and the oblate shape shows most pronounced dependency on two parameters: it increases with the conductivity of the aqueous medium and decreases with the vesicle size.

Email: primoz.peterlin@biofiz.mf.uni-lj.si

Address: University of Ljubljana, Faculty of Medicine, Institute of Biophysics, Lipičeva 2, SI-1000 Ljubljana, Slovenia