Polarization of a spherical cell in a nonuniform extracellular electric field

Polarization of cells by extracellular fields is relevant to neural stimulation, cardiac pacing, cardiac defibrillation, and electroporation. The electric field generated by an extracellular electrode may be nonuniform, and highly nonuniform fields are produced by microelectrodes and near the edges of larger electrodes. We solved analytically for the transmembrane voltage (phi(m)) generated in a spherical cell by a nonuniform extracellular field, as would arise from a point electrode. Phi(m) reached its steady state value with a time constant much shorter than the membrane time constant in both uniform and nonuniform fields. The magnitude of phi(m) generated in the hemisphere of the cell toward the electrode was larger than in the other hemisphere in the nonuniform field, while symmetric polarization occurred in the uniform field. The transmembrane potential in oocytes stained with the voltage sensitive dye Di-8-ANEPPS was measured in a nonuniform field at three different electrode-to-cell distances. Asymmetric biphasic polarization and distance-dependent patterns of membrane voltage were observed in the measurements, as predicted from the analytical solution. These results highlight the differences in cell polarization in uniform and nonuniform electric fields, and these differences may impact excitation and poration by extracellular fields.