Different dynamical behaviors induced by slow excitatory feedback for type II and III excitabilities

Abstract

Neuronal excitability is classified as type I, II, or III, according to the responses of electronic activities, which play different roles. In the present paper, the effect of an excitatory autapse on type III excitability is investigated and compared to type II excitability in the Morris-Lecar model, based on Hopf bifurcation and characteristics of the nullcline. The autaptic current of a fast-decay autapse produces periodic stimulations, and that of a slow-decay autapse highly resembles sustained stimulations. Thus, both fast- and slow-decay autapses can induce a resting state for type II excitability that changes to repetitive firing. However, for type III excitability, a fast-decay autapse can induce a resting state to change to repetitive firing, while a slow-decay autapse can induce a resting state to change to a resting state following a transient spike instead of repetitive spiking, which shows the abnormal phenomenon that a stronger excitatory effect of a slow-decay autapse just induces weaker responses. Our results uncover a novel paradoxical phenomenon of the excitatory effect, and we present potential functions of fast- and slow-decay autapses that are helpful for the alteration and maintenance of type III excitability in the real nervous system related to neuropathic pain or sound localization.

Excitability and Threshold Mechanism for Enhanced Neuronal Response Induced by Inhibition Preceding Excitation

“…No bifurcations or stable firing behaviors appear for type III excitability, as depicted in Figure 12(c) . In the present paper, more detailed descriptions of the bifurcations for 3 types of excitability are not described, which can be found in the previous investigations [ 15 , 16 ].…”

“…The ML model has been widely used to simulated type I, II, and III excitabilities [ 15 , 16 , 43 – 45 ]. We use the ML model in this study, which reads as …”

“…Neuronal excitability is one of the most important characteristics of the nervous system, which mainly describes the ability or activity of the generation of an action potential from the steady state [ 9 – 13 ]. Three types of excitability have been studied in the biological experiments and theoretical models, which are type I, II, and III excitabilities and are defined according to the responses of the resting state to the external stimulations [ 9 , 14 , 15 ]. For type II excitability, firing with nearly fixed period or frequency can be evoked from the resting state by the depolarization stimulation.…”

“…In the nonlinear theory, type I and II excitabilities correspond to the saddle-node bifurcation on an invariant cycle (SNIC) and Hopf bifurcation [ 10 , 12 , 16 , 17 ], respectively, and no bifurcation appears for the type III excitability [ 14 , 15 ]. In addition, three different kinds of excitability manifest very different dynamics in multiple aspects, for example, the phase responses to the pulse stimulation or self-feedback [ 15 , 18 ], the firing patterns to noise or stochastic stimulations [ 19 , 20 ], the phase resonance curve to the external periodic stimulations [ 11 ], and the synchronous behaviors [ 11 , 21 , 22 ], which are involved in different physiological functions. For example, type I excitability and type II excitability have been studied in many kinds of real neurons such as the hippocampal CA1 pyramidal neurons and Dopamine neuron [ 23 – 26 ].…”

“…Recently, it is discovered that for type II excitability or subcritical Hopf bifurcation in the HH model, the inhibitory or excitatory self-feedback can induce paradoxical phenomena, which is explained with the phase trajectory of the response [ 41 ]. For type III excitability, the weak excitatory stimulation with a suitable fast frequency (weak stimulation) can induce the resting state changed to firing behavior, while with a very slow frequency (strong stimulation) cannot induce the firing behavior [ 15 ]. The phase trajectory for 3 types of excitability maybe helpful for identification of the threshold mechanism for the PIF phenomenon.…”