The Spatial Variation of Membrane Potential Near a Small Source of Current in a Spherical Cell

A theoretical analysis is presented of the change in membrane potential produced by current supplied by a microelectrode inserted just under the membrane of a spherical cell. The results of the analysis are presented in tabular and graphic form for three wave forms of current: steady, step function, and sinusoidal. As expected from physical reasoning, we find that the membrane potential is nonuniform, that there is a steep rise in membrane potential near the current microelectrode, and that this rise is of particular importance when the membrane resistance is low, or the membrane potential is changing rapidly. The effect of this steep rise in potential on the interpretation of voltage measurements from spherical cells is discussed and practical suggestions for minimizing these effects are made: in particular, it is pointed out that if the current and voltage electrodes are separated by 60°, the change in membrane potential produced by application of current is close to that which would occur if there were no spatial variation of potential. We thus suggest that investigations of the electrical properties of spherical cells using two microelectrodes can best be made when the electrodes are separated by 60°.