A single-shell model for biological cells extended to account for the dielectric anisotropy of the plasma membrane

For modeling the polarization of biological cells in electric fields and related AC electrokinetical phenomena, such as electrorotation, dielectrophoresis, etc., dielectric isotropy of the plasma membrane and other cellular compartments is usually assumed. However, this traditional assumption is no longer valid in the case of cell membranes containing mobile charges introduced by the adsorbed hydrophobic ions, such as dipicrylamine, tetraphenylborate, etc. Once partitioned into the membrane, the hydrophobic ions can move freely in the plane of the membrane thus increasing the tangential component of membrane conductivity σmt. On the contrary, only finite charge displacement, i.e. translocation of hydrophobic ions between the two membrane boundaries, can be induced by the field component normal to the plasma membrane plane. This relaxational effect causes a dielectric dispersion (e.g. in the kHz–MHz range) with a marked increase of the radial membrane permittivity εmr at low field frequencies. In this study we extended the single-shell spherical model of cells in order to account for the dielectrically anisotropic plasma membrane. In contrast to the usual approach, where the plasma membrane permittivity and conductivity are viewed as scalar quantities, these membrane parameters are treated as tensors in the anisotropic membrane model. Calculations based on the new model showed that the tangential conductivity of hydrophobic ions can induce noticeable changes in the low-frequency part of the electrokinetic spectra of cells.