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 (Vj). The data obtained show how junctional conductance (gj), 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 Vj spikes of approximately ±100 mV that induce Vj gating, leading to a small decay of gj, 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.
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