Primož
Peterlin1, Saša Svetina1,2 and
Boštjan Žekš1,2
1Institute of Biophysics, Medical Faculty, University of
Ljubljana, Lipičeva 2, 1000 Ljubljana, and 2Jožef
Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
Alternating electric field tends to deform flaccid phospholipid vesicles in aqueous solution into approximately rotational ellipsoids. The rotational axis is aligned with the direction of the applied field. At low frequencies, the deformation is prolate. If the frequency is increased, the deformation changes into oblate deformation.
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. 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. The other term in the vesicle free energy is the membrane bending energy. Equilibrium vesicle shape is then finally calculated by minimizing the total free energy.
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 shapes increases with the increased conductivity of the aqueous medium and decreases with the vesicle size.