Effect of Neuritic Cables on Conductance Estimates for Remote Electrical Synapses

Abstract

Prinz, Astrid A. and Peter Fromherz. Effect of neuritic cables on conductance estimates for remote electrical synapses. J Neurophysiol 89: 2215-2224, 2003. First published December 18, 2002 10.1152/jn.00956.2002. 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 spatiotemporal maps of signal propagation in the neurites using a voltage-sensitive 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 nonisopotential 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 cannot 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.

The robustness of phase-locking in neurons with dendro-dendritic electrical coupling

“…With this in mind, we re-examine the stability and robustness of phase-locking using a fixed value of the experimentally measured coupling coefficient rather than a fixed g c . Specifically, we take CC = 0.05 (Amitai et al 2004) and use ball-and-stick model neurons to derive the corresponding g c (Prinz and Fromherz 2002). As expected, we find that the phase-locked states are less robust for more proximal coupling positions and more robust for more distal coupling positions for fixed CC = 0.05 as compared to the corresponding phase-locked states for a fixed g c = 400 pS.…”

“…These studies use singlecompartment models to estimate g c from the experimentally measured coupling coefficient (CC). By neglecting the spatial properties of the neurons, the estimates resulting from this model will substantially underestimate g c for coupling on distal dendrites (Prinz and Fromherz 2002). This, in turn, could substantially affect the estimates of the robustness of phase-locking.…”

“…Estimating g c in this manner omits the effect of dendritic filtering. The value of the coupling coefficient for two identical electrically-coupledball-and-stick neurons was derived by Prinz and Fromherz (2002). In the Appendix B we present an alternate derivation that allows for heterogeneity in the dendritic parameters of the two neurons.…”

“…However, it is important to note that the published estimates of g c (as cited above) are calculated from the experimentally measured coupling coefficient (CC) based on a single-compartment description of a neuron (Bennett 1977), which neglects spatial properties. As such, g c = 400 pS may be a severe underestimate of the actual value of the electrical coupling conductance when it is located on the distal dendrites (Prinz and Fromherz 2002). With this in mind, we re-examine the stability and robustness of phase-locking using a fixed value of the experimentally measured coupling coefficient rather than a fixed g c .…”

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

“…A full characterization of the impact of morphological anatomical complexity to the frequency-dependent signal transduction of gap-junctions (Prinz and Fromherz 2003) was beyond our goals. However, as a first step, we considered the Rall's multicompartmental model (Dayan and Abbott 2001) to explore limitations of our assumptions.…”