Paradoxical roles of inhibitory autapse and excitatory synapse in formation of counterintuitive anticipated synchronization

Different from the common delayed synchronization(DS)in which response appears after stimulation,anticipated synchronization(AS)in unidirectionally coupled neurons denotes a counterintuitive phenomenon in which response of the receiver neuron appears before stimulation of the sender neuron,showing an interesting function of brain to anticipate the future.The dynamical mechanism for the AS remains unclear due to complex dynamics of inhibitory and excitatory modulations.In this article,the paradoxical roles of excitatory synapse and inhibitory autapse in the formation of AS are acquired.Firstly,in addition to the common roles such that inhibitory modulation delays and excitatory modulation advances spike,paradoxical roles of excitatory stimulation to delay spike via type-II phase response and of inhibitory autapse to advance spike are obtained in suitable parameter regions,extending the dynamics and functions of the excitatory and inhibitory modulations.Secondly,AS is related to the paradoxical roles of the excitatory and inhibitory modulations,presenting deep understandings to the AS.Inhibitory autapse induces spike of the receiver neuron advanced to appear before that of the sender neuron at first,and then excitatory synapse plays a delay role to prevent the spike further advanced,resulting in the AS as the advance and delay effects realize a dynamic balance.Lastly,inhibitory autapse with strong advance,middle advance,and weak advance and delay effects induce phase drift(spike of the receiver neuron advances continuously),AS,and DS,respectively,presenting comprehensive relationships between AS and other behaviors.The results present potential measures to modulate AS related to brain function.

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

Post-inhibitory rebound(PIR)spike,which has been widely observed in diverse nervous systems with different physiological functions and simulated in theoretical models with class-2 excitability,presents a counterintuitive nonlinear phenomenon in that the inhibitory effect can facilitate neural firing behavior.In this study,a PIR spike induced by inhibitory stimulation from the resting state corresponding to class-3 excitability that is not related to bifurcation is simulated in the Morris–Lecar neuron.Additionally,the inhibitory self-feedback mediated by an autapse with time delay can evoke tonic/repetitive spiking from phasic/transient spiking.The dynamical mechanism for the PIR spike and the tonic/repetitive spiking is acquired with the phase plane analysis and the shape of the quasi-separatrix curve.The result extends the counterintuitive phenomenon induced by inhibition to class-3 excitability,which presents a potential function of inhibitory autapse and class-3 neuron in many neuronal systems such as the auditory system.