Electrical properties of spherical syncytia

Syncytial tissues consist of many cells whose intracellular spaces are electrically coupled one to another. Such tissues typically include narrow, tortuous extracellular space and often have specialized membranes at their outer surface. We derive differential equations to describe the potentials induced when a sinusoidal or steady current is applied to the intracellular space with a microelectrode. We derive solutions for spherical preparations with isotropic properties or with a particular anisotropy in effective extracellular and intracellular resistivities. Solutions are presented in an approximate form with a simple physical interpretation. The leading term in the intracellular potential describes an "isopotential" cell in which there is no spatial variation of intracellular potential. The leading term in the extracellular potential, and thus the potential across the inner membranes, varies with radial position, even at zero frequency. The next term of the potentials describes the direct effects of the point source of current and, for the parameters given here, acts as a series resistance producing a large local potential drop essentially independent of frequency. A lumped equivalent circuit describes the "low frequency" behavior of the syncytium, and a distributed circuit gives a reasonably accurate general description. Graphs of the spatial variation and frequency dependence of intracellular, extracellular, and transmembrane potential are given, the response to sinusoidal currents is used to calculate numerically the response to a step function of current