The nonlinear mechanism for the same responses of neuronal bursting to opposite self-feedback modulations of autapse

In the traditional viewpoint, inhibitory and excitatory effects always induce opposite responses. In the present study, the enhanced bursting activities induced by excitatory autapses, which are consistent with the recent experimental observations, and those induced by inhibitory autapses, which is a paradoxical phenomenon, were simulated using the Chay model. The same bifurcations and different ionic currents for the same responses were acquired with fast-slow variable dissection and current decomposition, respectively. As the inhibitory or excitatory autaptic conductance increased, the ending phase of the burst related to a homoclinic bifurcation of the fast subsystem changed to widen the burst duration to contain more spikes, which was induced by an elevated minimal potential (Vmin) of spiking of the fast subsystem. Larger inhibitory and excitatory autaptic conductances induced smaller and larger maximal potentials (Vmax) of spiking, respectively. During the downstroke, a weaker potassium current induced by the smaller Vmax played a dominant role for the inhibitory autapse, and the stronger potassium current induced by the larger Vmax became weaker due to the opposite autaptic current of the excitatory autapse, which induced the Vmin elevated. The results present the nonlinear and biophysical mechanisms of the same responses to opposite effects, which extends nonlinear dynamics knowledge and provides potential modulation measures for the nervous system.