  Gap junctions are channels in cell membranes allowing ions to pass directly
between cells. They connect cells throughout the body, including heart
myocytes, neurons, and astrocytes. Propagation mediated by gap junctions can be
passive or active. In passive propagation, the membrane potential of one cell
influences that of neighboring cells without triggering action potentials
(APs). In active propagation, an AP in one cell triggers APs in neighboring
cells; this occurs in cardiac tissue and throughout the nervous system. It is
known experimentally that there is an ideal gap junction conductance for AP
propagation -- weaker or stronger conductance can block propagation. We present
a theory explaining this phenomenon by analyzing an idealized model that
focuses exclusively on gap junctional and spike-generating currents. We also
find a novel type of behavior that we call semi-active propagation, in which
cells in the network are not excitable at rest, but still propagate action
potentials.
