Primož Peterlin, Saša Svetina and Boštjan Žekš
Experiments show that phospholipid vesicles exposed to alternating external electric fields undergo a shape transition from prolate to oblate ellipsoidal shape when the frequency of the field is increased. The theoretical models proposed so far have failed to explain the existence of oblate shape at higher frequencies at conditions when the internal and external aqueous medium have identical electrical properties.
First, the Laplace equation is solved for the electric potential around a nearly-spherical shape, taking into account its periodic time dependence. The electric field strength and ultimately the Maxwell stress tensor are then calculated from the expression for the electric potential. The Maxwell stress tensor, evaluated on the membrane-water boundaries in the direction perpendicular to the boundary is the surface density of the force with which the electric field is acting on the membrane. Its scalar product with the membrane displacement, integrated over the total membrane area, amounts to the contribution of the electric field to the total free energy of the vesicle. The other terms in the free energy are the local and the non-local bending energies. Minimizing the total free energy yields the vesicle shape, thus depending on the frequency of the applied electric field.
The solution predicts three regimes of vesicle behaviour: a conducting one at low frequencies, a dielectric one at high frequencies, and an intermediate one between the two. The boundary frequencies delimiting them depend on the electric properties of both the aqueous medium and the phospholipid membrane, as well as the vesicle size.
Institute of Biophysics, Medical Faculty, University of
Ljubljana, Lipičeva 2, 1000 Ljubljana, Slovenia;
primoz.peterlin@biofiz.mf.uni-lj.si.