Schwan equation and transmembrane potential induced by alternating electric field

Abstract

The transmembrane potential generated by an alternating electric field (ac) depends strongly on the frequency of the field and can be calculated using the Schwan Equation. We have measured the critical electric breakdown potential, delta psi crit, of the plasma membrane of murine myeloma cell line (Tib9) using ac fields, by monitoring the entry of a fluorescence probe, propidium iodide, into the cells. This dye is weakly fluorescent in solution but becomes strongly fluorescent when it binds to DNA. Experiments were done under a microscope by direct visual examination of single cells or by examining photographic prints. When an ac field reached the intensity, Ecrit, that generated a maximal membrane potential delta psi max, equal to or greater than the delta psi crit, the membrane was perforated at the two loci facing the electrodes. The dye diffused into the cell, giving rise to two bright, narrow bands, which expanded to the whole cell in 1-3 min. delta psi crit's were measured in three media of different resistivities, rho ext, (52,600, 7,050, and 2,380 omega cm), over the range of 0.1-300 kHz, with the field duration of 200 ms. Regression analysis based on the Schwan Equation showed that in a medium of given resistivity, the delta psi crit was constant over the frequency range studied. When the capacitance of the membrane, Cmembr, was taken to be 0.90 microF cm-2, the resistivity of the cytoplasmic medium, rho int, was determined to be 910-1,100 omega cm. The delta psi crit were 0.33, 0.48, and 0.53 V, respectively, for the three media in decreasing resistivities. The good fit of these data to the curves calculated using the Schwan Equation indicates that the equation may be used to describe the transmembrane potential of a living cell generated by an oscillating electric field.