Abstract
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.
Highlights
Neuronal electronic activities, such as firing and resting states, play basic and important roles in achieving biological functions of the nervous system[1, 2]
Class I excitability corresponds to a resting state changed to firing via saddle-node on invariant circle (SNIC) bifurcation as the depolarization current increases; class II excitability corresponds to Andronov-Hopf bifurcations[1,2,3], which have been widely investigated in the classical 2-dimensional Morris-Lecar (ML) model with variables (V, w)[3, 16, 19,20,21]
If the firing or spiking is changed to resting state via an SNIC as the depolarization current is decreased, the spiking is named as class I since the spiking exhibits a nearly zero frequency
Summary
Neuronal electronic activities, such as firing and resting states, play basic and important roles in achieving biological functions of the nervous system[1, 2] (for example, information encoding, transmission, and processing[2,3,4,5]). Class I excitability corresponds to a resting state (stable equilibrium) changed to firing (limit cycle) via saddle-node on invariant circle (SNIC) bifurcation as the depolarization current increases; class II excitability corresponds to Andronov-Hopf bifurcations[1,2,3], which have been widely investigated in the classical 2-dimensional Morris-Lecar (ML) model with variables (V, w)[3, 16, 19,20,21]. If the firing or spiking is changed to resting state via an SNIC as the depolarization current is decreased, the spiking is named as class I since the spiking exhibits a nearly zero frequency. The current mediated by the autapse may induce transition between the 2 classes of excitability through changes in competition between outward and inward currents, the position relationship between nullclines, bifurcations, as well as firing frequency
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