Delayed excitatory self-feedback-induced negative responses of complex neuronal bursting patterns*

Abstract

In traditional viewpoint, excitatory modulation always promotes neural firing activities. On contrary, the negative responses of complex bursting behaviors to excitatory self-feedback mediated by autapse with time delay are acquired in the present paper. Two representative bursting patterns which are identified respectively to be “Fold/Big Homoclinic” bursting and “Circle/Fold cycle” bursting with bifurcations are studied. For both burstings, excitatory modulation can induce less spikes per burst for suitable time delay and strength of the self-feedback/autapse, because the modulation can change the initial or termination phases of the burst. For the former bursting composed of quiescent state and burst, the mean firing frequency exhibits increase, due to that the quiescent state becomes much shorter than the burst. However, for the latter bursting pattern with more complex behavior which is depolarization block lying between burst and quiescent state, the firing frequency manifests decrease in a wide range of time delay and strength, because the duration of both depolarization block and quiescent state becomes long. Therefore, the decrease degree of spike number per burst is larger than that of the bursting period, which is the cause for the decrease of firing frequency. Such reduced bursting activity is explained with the relations between the bifurcation points of the fast subsystem and the bursting trajectory. The present paper provides novel examples of paradoxical phenomenon that the excitatory effect induces negative responses, which presents possible novel modulation measures and potential functions of excitatory self-feedback/autapse to reduce bursting activities.

Bifurcations for counterintuitive post-inhibitory rebound spike related to absence epilepsy and Parkinson disease

“…Nonlinear physical concepts such as threshold and bifurcation are widely used in neuroscience to study the dynamics of firing behaviors in neurons. [1][2][3][4][5][6][7][8] These concepts play important roles in understanding brain functions and diseases, such as information coding, locomotion, and seizure. [9][10][11][12][13][14][15] The threshold is a basic conception to represent neuronal excitation property to external stimulation.…”

Negative self-feedback induced enhancement and transition of spiking activity for class-3 excitability

“…[39,48] In particular, recent research has shown some paradoxical results for the inhibitory and excitatory autapses, which can enhance and reduce neuronal firing, respectively. Specifically, excitatory autapse can reduce the spike number of a bursting neuron [49] and change from repetitive spiking near the subcritical Hopf bifurcation (corresponds to class-2 excitability) to the resting state or mixedmode oscillations. [50] Inhibitory autapse can enhance the spike number of bursting patterns [51] and change the resting state near the Hopf bifurcation as repetitive spiking by modulating the time delay in the inhibitory autapse.…”

Inferring interactions of time-delayed dynamic networks by random state variable resetting

“…[1][2][3][4][5][6] Due to the limited propagation speed of signals, time delays play a significant role and exist extensively in real systems. [7][8][9][10][11] Detecting the interactions in networks is helpful for understanding the collective behaviors of complex systems. However, due to systematic nonlinearity, noises, a lack of information, time delays, and so on, inferring the interactions in dynamic networks is complicated and challenging.…”