The effect of neuritic cables on conductance estimates for remote electrical synapses

The conductance of electrical synapses is usually estimated from voltage recordings at the neuronal somata under the assumption that each cell is isopotential. This approach neglects effects of intervening neurites. For a cell pair with unbranched neurites and an electrical synapse at their ends, we used cable theory to derive an analytical expression that relates the synaptic conductance to voltage recordings at the cell bodies and to the neurite properties. The equation implies that the conventional method significantly underestimates the actual synapse conductance if the neurite length is comparable to the electrotonic length constant and if the synaptic conductance is similar to the serial neurite conductance. For an experimental test we cultured pairs of snail neurons on protein patterns, resulting in a geometry that matched the theoretical model. Using the isopotential theory, we estimated the synapse conductances and found them to be rather weak. To obtain the cable properties we recorded spatio-temporal maps of signal propagation in the neurites using a voltagesensitive dye. Fits of these maps to a passive cable model showed that the snail neurons are electrotonically rather compact. Given these features of our experimental system, the synaptic conductances derived with the non-isopotential model deviated from the estimates of the isopotential theory by about 13 %. This discrepancy, although small, shows that even in electrotonically compact neurons coupled by weak synapses the impact of the neuritic cables on conductance estimates can not be neglected. When applied to less compact and more strongly coupled cell pairs in vivo, our approach can supply the realistic estimates of synaptic conductances that are necessary for a better understanding of the role of electrical coupling in neural systems.