Transmembrane voltage induced on a cell membrane in suspensions exposed to an alternating field: a theoretical analysis

We present analytical equations for the transmembrane voltage (DeltaPsi) induced by an alternating field on spherical cells arranged in orderly suspensions. For physiologically normal cells, the cell membrane was assumed to be non-conductive. With increasing alternating field frequency, capacitive property of the cytoplasm and the external medium become increasingly important and thus must be accounted for. Considering the symmetry of the arrayed cells and the tiny volume of the unit cell compared to that of the suspensions, the influence exerted on a unit cell by other cells was posited to be approximately symmetrical with respect to the symmetrical axis. This implies that the shape of the equipotential plane of spherical cells in the suspensions is similar to that of the single cell exposed to the external field, though the value of the potential of both cells should be different. Therefore, the internal field of the cytoplasm and the equivalent body of a unit cell in the suspensions should be approximately constant. This allows for calculating the effective average field in the equivalent body with Maxwell-Wagner and Bruggeman-Hanai equations for low and high cell concentrations, respectively. We investigated the conditions, under which the local electric field of a unit cells in suspension is approximately equal to that of a single cell. Under these conditions the analytical solution for DeltaPsi induced by alternating fields on cells in suspensions can be derived from that of the single cell.