Reverberation of excitation in neuronal networks interconnected through voltage-gated gap junction channels

We combined Hodgkin-Huxley equations and gating models of gap junction (GJ) channels to simulate the spread of excitation in two-dimensional networks composed of neurons interconnected by voltage-gated GJs. Each GJ channel contains two fast and slow gates, each exhibiting current-voltage (I-V) rectification and gating properties that depend on transjunctional voltage (V_j). The data obtained show how junctional conductance (g_j), which is necessary for synchronization of the neuronal network, depends on its size and the intrinsic firing rate of neurons. A phase shift between action potentials (APs) of neighboring neurons creates bipolar, short-lasting V_j spikes of approximately ±100 mV that induce V_j gating, leading to a small decay of g_j, which can accumulate into larger decays during bursting activity of neurons. We show that I-V rectification of GJs in local regions of the two-dimensional network of neurons can lead to unidirectional AP transfer and consequently to reverberation of excitation. This reverberation can be initiated by a single electrical pulse and terminated by a low-amplitude pulse applied in a specific window of reverberation cycle. Thus, the model accounts for the influence of dynamically modulatable electrical synapses in shaping the function of a neuronal network and the formation of reverberation, which, as proposed earlier, may be important for the development of short-term memory and its consolidation into long-term memory.