Signal transmission between gap-junctionally coupled passive cables is most effective at an optimal diameter

We analyze simple morphological configurations that represent gap-junctional coupling between neuronal processes or between muscle fibers. Specifically, we use cable theory and simulations to examine the consequences of current flow from one cable to other gap-junctionally coupled passive cables. When the proximal end of the first cable is voltage clamped, the amplitude of the electrical signal in distal portions of the second cable depends on the cable diameter. However, this amplitude does not simply increase if cable diameter is increased, as expected from the larger length constant; instead, an optimal diameter exists. The optimal diameter arises because the dependency of voltage attenuation along the second cable on cable diameter follows two opposing rules. As cable diameter increases, the attenuation decreases because of a larger length constant yet increases because of a reduction in current density arising from the limiting effect of the gap junction on current flow into the second cable. The optimal diameter depends on the gap junction resistance and cable parameters. In branched cables, dependency on diameter is local and thus may serve to functionally compartmentalize branches that are coupled to other cells. Such compartmentalization may be important when periodic signals or action potentials cause the current flow across gap junctions.