Spike-timing-dependent plasticity enhanced synchronization transitions induced by autapses in adaptive Newman-Watts neuronal networks

Blinking coupling enhances network synchronization

This paper studies the synchronization of a network with linear diffusive coupling, which blinks between the variables periodically. The synchronization of the blinking network in the case of sufficiently fast blinking is analyzed by showing that the stability of the synchronous solution depends only on the averaged coupling and not on the instantaneous coupling. To illustrate the effect of the blinking period on the network synchronization, the Hindmarsh-Rose model is used as the dynamics of nodes. The synchronization is investigated by considering constant single-variable coupling, averaged coupling, and blinking coupling through a linear stability analysis. It is observed that by decreasing the blinking period, the required coupling strength for synchrony is reduced. It equals that of the averaged coupling model times the number of variables. However, in the averaged coupling, all variables participate in the coupling, while in the blinking model only one variable is coupled at any time. Therefore, the blinking coupling leads to an enhanced synchronization in comparison with the single-variable coupling. Numerical simulations of the average synchronization error of the network confirm the results obtained from the linear stability analysis.

Contribution of AMPA and NMDA receptors in the spontaneous firing patterns of single neurons in autaptic culture

Single neurons in an autaptic culture exhibit various types of firing pattern with different firing durations and rhythms. However, a neuron with autapses has often been modeled as an oscillator providing a monotonic firing pattern with a constant periodicity because of the lack of a mathematical model. In the work described in this study, we use computational simulation and whole-cell patch-clamp recording to elucidate and model the mechanism by which such neurons generate various firing pattens. In the computational simulation, three types of spontaneous firing pattern, i.e., short, long-lasting, and periodic burst firing patterns are realized by changing the combination ratio of N-methyl-d-aspartate (NMDA) to α-amino-3-hydroxyl-5-methyl-4-isoxazole-propionate (AMPA) conductance. These three types of firing patterns are also observed in the experiments where neurons are cultured in isolation on micropatterned substrates. Using the AMPA and NMDA current models, we discuss that, in principle, autapses can regulate rhythmicity and information selection in neuronal networks.

Transitions between classes of neuronal excitability and bifurcations induced by autapse

Neuronal excitabilities behave as the basic and important dynamics related to the transitions between firing and resting states, and are characterized by distinct bifurcation types and spiking frequency responses. Switches between class I and II excitabilities induced by modulations outside the neuron (for example, modulation to M-type potassium current) have been one of the most concerning issues in both electrophysiology and nonlinear dynamics. In the present paper, we identified switches between 2 classes of excitability and firing frequency responses when an autapse, which widely exists in real nervous systems and plays important roles via self-feedback, is introduced into the Morris-Lecar (ML) model neuron. The transition from class I to class II excitability and from class II to class I spiking frequency responses were respectively induced by the inhibitory and excitatory autapse, which are characterized by changes of bifurcations, frequency responses, steady-state current-potential curves, and nullclines. Furthermore, we identified codimension-1 and -2 bifurcations and the characteristics of the current-potential curve that determine the transitions. Our results presented a comprehensive relationship between 2 classes of neuronal excitability/spiking characterized by different types of bifurcations, along with a novel possible function of autapse or self-feedback control on modulating neuronal excitability.