Polarizability of spherical biological cells in the presence of localized surface charge distributions at the membrane interfaces

The electrical polarizability alpha(omega) of a biological cell in the presence of a layer of localized, partially bounded, charges at the two cell membrane interfaces has been calculated within the dipolar approximation. The cell is modeled in the light of the single-shell spherical model, but the results can be easily extended to shelled particles of more complex shape. Under the influence of an external electric field, the presence of these charge distributions, which added to the ones originated by the mismatch of the complex dielectric constants of the different media, produces a further dielectric relaxation, besides the one due to the usual Maxwell-Wagner effect. We explicitly find the contribution that must be added to the electrical polarizability alpha(omega) in order to take into account the surface electrical currents originated by the localized charges free to move on the membrane surfaces. Our results, maintaining their validity whatsoever the values of the surface charge distributions and, moreover, whatsoever the values of the membrane conductivity are, extend the applicability of the model recently proposed by Prodan et al. [Biophys. J. 95, 4174 (2008)], who developed an analytical solution which offers reliable results only in the case of weak surface charge distributions and, moreover, for negligible small values of the membrane conductivity. Our approach, removing these constrains, represents a valuable improvement toward more realistic biological cell models and widens the use of dielectric relaxation methods to a larger class of biological systems.