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.

Enhanced vibrational resonance in a single neuron with chemical autapse for signal detection

Many animals can detect the multi-frequency signals from their external surroundings.The understanding for underlying mechanism of signal detection can apply the theory of vibrational resonance,in which the moderate high frequency driving can maximize the nonlinear system's response to the low frequency subthreshold signal.In this work,we study the roles of chemical autapse on the vibrational resonance in a single neuron for signal detection.We reveal that the vibrational resonance is strengthened significantly by the inhibitory autapse in the neuron,while it is weakened typically by the excitatory autapse.It is generally believed that the inhibitory synapse has a suppressive effect in neuronal dynamics.However,we find that the detection of the neuron to the low frequency subthreshold signal can be improved greatly by the inhibitory autapse.Our finding indicates that the inhibitory synapse may act constructively on the detection of weak signal in the brain and neuronal system.

Control of firing activities in thermosensitive neuron by activating excitatory autapse

Temperature has distinct influence on the activation of ion channels and the excitability of neurons,and careful change in temperature can induce possible mode transition in the neural activities.The formation and development of autapse connection to neuron can enhance its self-adaption to external stimulus,and thus the firing patterns in neuron can be controlled effectively.The autapse is activated to drive a thermosensitive neuron,which is developed from the FitzHugh-Nagumo neural circuit by incorporating a thermistor,and the dynamics in the neural activities is explored to find mode dependence on the temperature and autaptic current.It is found that the firing modes can be controlled by temperature,and the neuron is wakened from resting state to periodic oscillation with the increase of temperature.Furthermore,the intensity and the intrinsic time delay in the autapse are respectively adjusted to control the neural activities,and it is confirmed that appropriate setting for autaptic current can balance and enhance the temperature effect on the neural activities.

Effect of stochastic electromagnetic disturbances on autapse neuronal systems

With the help of a magnetic flux variable, the effects of stochastic electromagnetic disturbances on autapse Hodgkin–Huxley neuronal systems are studied systematically. Firstly, owing to the autaptic function, the inter-spike interval series of an autapse neuron not only bifurcates, but also presents a quasi-periodic characteristic. Secondly, an irregular mixed-mode oscillation induced by a specific electromagnetic disturbance is analyzed using the coefficient of variation of inter-spike intervals. It is shown that the neuronal discharge activity has certain selectivity to the noise intensity, and the appropriate noise intensity can induce the significant mixed-mode oscillations. Finally, the modulation effects of electromagnetic disturbances on a ring field-coupled neuronal network with autaptic structures are explored quantitatively using the average spiking frequency and the average coefficient of variation. The electromagnetic disturbances can not only destroy the continuous and synchronous discharge state, but also induce the resting neurons to generate the intermittent discharge mode and realize the transmission of neural signals in the neuronal network. The studies can provide some theoretical guidance for applying electromagnetic disturbances to effectively control the propagation of neural signals and treat mental illness.

Functional Autapses Form in Striatal Parvalbumin Interneurons but not Medium Spiny Projection Neurons

Autapses selectively form in specific cell types in many brain regions.Previous studies have also found putative autapses in principal spiny projection neurons(SPNs)in the striatum.However,it remains unclear whether these neurons indeed form physiologically functional autapses.We applied whole-cell recording in striatal slices and identified autaptic cells by the occurrence of prolonged asynchronous release(AR)of neurotransmitters after bursts of high-frequency action potentials(APs).Surprisingly,we found no autaptic AR in SPNs,even in the presence of Sr^(2+).However,robust autaptic AR was recorded in parvalbumin(PV)-expressing neurons.The autaptic responses were mediated by GABA_(A) receptors and their strength was dependent on AP frequency and number.Further computer simulations suggest that autapses regulate spiking activity in PV cells by providing self-inhibition and thus shape network oscillations.Together,our results indicate that PV neurons,but not SPNs,form functional autapses,which may play important roles in striatal functions.

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(V_(min)) of spiking of the fast subsystem.Larger inhibitory and excitatory autaptic conductances induced smaller and larger maximal potentials(V_(max)) of spiking,respectively.During the downstroke,a weaker potassium current induced by the smaller V_(max) played a dominant role for the inhibitory autapse,and the stronger potassium current induced by the larger V_(max) became weaker due to the opposite autaptic current of the excitatory autapse,which induced the V_(min) 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.

Effect of autaptic delay signal on spike-timing precision of single neuron

Experimental and theoretical studies have reported that the precise firing of neurons is crucial for sensory representation.Autapse serves as a special synapse connecting neuron and itself,which has also been found to improve the accuracy of neuronal response.In current work,the effect of autaptic delay signal on the spike-timing precision is investigated on a single autaptic Hodgkin–Huxley neuron in the present of noise.The simulation results show that both excitatory and inhibitory autaptic signals can effectively adjust the precise spike time of neurons with noise by choosing the appropriate coupling strength g and time delay of autaptic signalτ.The g–τparameter space is divided into two regions:one is the region where the spike-timing precision is effectively regulated;the other is the region where the neuronal firing is almost not regulated.For the excitatory and inhibitory autapse,the range of parameters causing the accuracy of neuronal firing is different.Moreover,it is also found that the mechanisms of the spike-timing precision regulation are different for the two kinds of autaptic signals.

Firing dynamics of an autaptic neuron

Autapses are synapses that connect a neuron to itself in the nervous system. Previously, both experimental and theoretical studies have demonstrated that autaptic connections in the nervous system have a significant physiological function. Autapses in nature provide self-delayed feedback, thus introducing an additional timescale to neuronal activities and causing many dynamic behaviors in neurons. Recently, theoretical studies have revealed that an autapse provides a control option for adjusting the response of a neuron： e.g., an autaptic connection can cause the electrical activities of the Hindmarsh–Rose neuron to switch between quiescent, periodic, and chaotic firing patterns; an autapse can enhance or suppress the mode-locking status of a neuron injected with sinusoidal current; and the firing frequency and interspike interval distributions of the response spike train can also be modified by the autapse. In this paper, we review recent studies that showed how an autapse affects the response of a single neuron.

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

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.

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.