Multistability and noise-induced transitions in the model of bidirectionally coupled neurons with electrical synaptic plasticity

We systematically study the effects of synaptic plasticity in the model describing dynamics of electrically coupled neuron cells. Neurotransmission through electrical synapses plays an important role in the spike synchrony among neurons in the neural network. Synaptic plasticity is known to arise from the transjunction voltage-dependent conductance of channels formed, for instance, by Connexin-36 (Cx36), the principal gap junction protein of electrical synapses between inhibitory interneurons in vertebrates. A coupling strength between neurons is modulated in a complex manner, and the significance of this regulation in the presence of a stimulus that changes the firing properties of the coupled neurons, is still unknown. The neuron model based on the FitzHung–Nagumo equations exhibits multistability when two neurons are linearly bidirectionally coupled, i.e., two new resting states emerge in addition to the original either resting or spiking state depending on the ionic currents, observed in the solitary neuron. Synaptic plasticity of electrical neurotransmission is accounted in the model by making the coupling strength a linear function of the transjunction current so that the coupling becomes quadratic. This nonlinearity in synaptic transmission results in very rich dynamics leading to chaos in the neuron spikes via a cascade of period-doubling bifurcations as the external current is changed, as well as to amplitude-dependent signal attenuation similar to a low-pass signal filtering effect. The latter property of electrical synapses is consistent with experimental data involving Cx36-mediated electrical communication. In the presence of multiplicative noise, inherent to neural systems, intermittent transitions between the coexisting states occur. In the case of linear coupling, the transjunctional current switches between three states, whereas nonlinearity in coupling destroys one of the coexisting states so that multistate intermittency is converted into on-off intermittency. These results are consistent with physiological experiments on random switches between different states of a single gap junction channel