Cell membrane voltage during electrical cell fusion calculated by re-expansion method

In electrical cell fusion, two cells are first brought into contact by dielectrophoresis, and then a pulsed voltage is applied to induce reversible membrane breakdown at the contact point, by which the membranes of the two cells are reconnected to form a fusant cell. The prediction of the membrane voltage is a crucial issue for high fusion yield, however, its mathematical expression is known only for the case of an isolated cell in a uniform external field. In this paper, we employ the re-expansion method for the transient field analysis of such a multiple cell system. Each cell is modeled by an infinitesimally thin spherical insulating membrane in conducting media, on which accumulation of free charge occurs when an external field is applied. It is shown that the system has two time constants: (a) that governed by the conductivity and the permittivity of the media and (b) that of charging the membrane capacitance through the conducting media, and that the former is far shorter than the latter. Hence, the time variation due to the former is neglected to obtain a simplified expression for the membrane voltage. By expanding the potential into Legendre harmonic components and relating the coefficients for each cell based on the re-expansion method, a differential equation governing the membrane voltage buildup is obtained. The numerical calculation is performed for the axisymmetric case of two cells in contact, to which a step-wise voltage is applied. It is found that the maximum membrane voltage occurs initially at the contact point, but when the steady state is reached, it moves to the ends of the cell pair, and might lead to unsuccessful fusion. The analysis suggests that high-yield fusion may be achieved by an application of shorter pulse, or of a non-uniform field to concentrate the voltage drop at the contact point.