Inferring connection proximity in networks of electrically coupled cells by subthreshold frequency response analysis

Electrical synapses continuously transfer signals bi-directionally from one cell to another, directly or indirectly via intermediate cells. Electrical synapses are common in many brain structures such as the inferior olive, the subcoeruleus nucleus and the neocortex, between neurons and between glial cells. In the cortex, interneurons have been shown to be electrically coupled and proposed to participate in large, continuous cortical syncytia, as opposed to smaller spatial domains of electrically coupled cells. However, to explore the significance of these findings it is imperative to map the electrical synaptic microcircuits, in analogy with in vitro studies on monosynaptic and disynaptic chemical coupling. Since "walking" from cell to cell over large distances with a glass pipette is challenging, microinjection of (fluorescent) dyes diffusing through gap-junctions remains so far the only method available to decipher such microcircuits even though technical limitations exist. Based on circuit theory, we derive analytical descriptions of the AC electrical coupling in networks of isopotential cells. We then suggest an operative electrophysiological protocol to distinguish between direct electrical connections and connections involving one or more intermediate cells. This method allows inferring the number of intermediate cells, generalizing the conventional coupling coefficient, which provides limited information. We validate our method through computer simulations, theoretical and numerical methods and electrophysiological paired recordings.