Using ephaptic coupling to estimate the synaptic cleft resistivity of the calyx of Held synapse

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Abstract
At synapses, the pre- and postsynaptic cell get so close that currents entering the cleft do not flow exclusively along its conductance, g cl . A prominent example is found in the calyx of Held synapse in the medial nucleus of the trapezoid body (MNTB), where the presynaptic action potential can be recorded in the postsynaptic cell in the form of a prespike. Here, we developed a theoretical framework for ephaptic coupling via the synaptic cleft, and we tested its predictions using the MNTB prespike recorded in voltage-clamp. The shape of the prespike is predicted to resemble either the first or the second derivative of the inverted, presynaptic action potential if cleft currents dissipate either mostly capacitively or resistively, respectively. We found that the resistive dissipation scenario provided a better description of the prespike shape. Its size is predicted to scale with the fourth power of the radius of the synapse, explaining why intracellularly recorded prespikes are uncommon in the central nervous system. We show that presynaptic calcium currents also contribute to the prespike shape. This calcium prespike resembled the first derivative of the inverted calcium current, again as predicted by the resistive dissipation scenario. Using this calcium prespike, we obtained an estimate for g cl of ~1 μS. We demonstrate that, for a circular synapse geometry, such as in conventional boutons or the immature calyx of Held, g cl is scale-invariant and only defined by extracellular resistivity, which was ~75 Ωcm, and by cleft height. During development the calyx of Held develops fenestrations. We show that these fenestrations effectively minimize the cleft potentials generated by the adult action potential, which might otherwise interfere with calcium channel opening. We thus provide a quantitative account of the dissipation of currents by the synaptic cleft, which can be readily extrapolated to conventional, bouton-like synapses. Author Summary: At chemical synapses two neurons are separated by a cleft, which is very narrow. As a result, the concentration of released neurotransmitter can rapidly peak, which is essential for fast synaptic transmission. At the same time, the currents that flow across the membranes that face the synaptic cleft are also substantial, and a fraction of these currents will enter the other cell. We made an electronic model of the synaptic cleft, which indicated that if the shape and fraction of these currents are known, the electrical resistance of the synaptic cleft can be inferred. We tested several of the predictions of our model by comparing the membrane currents during a presynaptic action potential in a giant terminal, the calyx of Held, with the much smaller prespike evoked by these currents in the postsynaptic cell. We estimate the cleft resistance to be about 1 MΩ, which means that the changes in the cleft potential due to the membrane currents can become large enough to have an impact on voltage-dependent calcium channels controlling neurotransmitter release.
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