基于抑制性突触可塑性的神经元放电率自稳态机制

神经元放电率自稳态是指大脑神经网络的放电率维持在相对稳定的状态.大量实验研究发现神经元放电率自稳态是神经电活动的重要特征,并且放电率自稳态是实现神经信息处理及维持正常脑功能的基础,因此放电率自稳态的研究是神经科学领域的重要科学问题.脑神经网络是一个高度复杂的动态系统,存在大量输入扰动信号及由于动态链接导致的参数摄动,因此如何建立并维持神经元放电率自稳态及其鲁棒性仍有待深入研究.反馈神经回路是皮层神经网络的典型连接模式,抑制性突触可塑性对神经元放电率自稳态具有重要的调控作用.本文通过构建包含抑制性突触可塑性的反馈神经回路模型对神经元放电率自稳态及其鲁棒性进行计算研究.结果表明:在抑制性突触可塑性的作用下,神经元放电率可自适应地跟踪目标放电率,从而取得放电率自稳态;在有外部输入干扰和参数摄动的情况下,神经元放电率具有良好的抗扰动性能,表明放电率自稳态具有很强的鲁棒性;理论分析揭示了抑制性突触可塑性学习规则是神经元放电率自稳态的神经机制;仿真分析进一步揭示了学习率及目标放电率对放电率自稳态建立过程具有重要影响.     

How Gibbs Distributions May Naturally Arise from Synaptic Adaptation Mechanisms. A Model-Based Argumentation

This paper addresses two questions in the context of neuronal networks dynamics, using methods from dynamical systems theory and statistical physics: (i) How to characterize the statistical properties of sequences of action potentials (“spike trains”) produced by neuronal networks? and; (ii) what are the effects of synaptic plasticity on these statistics? We introduce a framework in which spike trains are associated to a coding of membrane potential trajectories, and actually, constitute a symbolic coding in important explicit examples (the so-called gIF models). On this basis, we use the thermodynamic formalism from ergodic theory to show how Gibbs distributions are natural probability measures to describe the statistics of spike trains, given the empirical averages of prescribed quantities. As a second result, we show that Gibbs distributions naturally arise when considering “slow” synaptic plasticity rules where the characteristic time for synapse adaptation is quite longer than the characteristic time for neurons dynamics.     

Tomographic-probability description of solitons in Bose-Einstein condensates

The influence of a weight-dependent spike-timing dependent plasticity (STDP) rule on the temporal evolution and equilibrium state of a certain synapse is investigated. We show that under certain conditions, a spike-induced rate-learning scheme could be achieved. Through studying the situation when a single Hodgkin-Huxley neuron is driven by a large ensemble of input neurons, we find that synchronized firing of a sub population of input neurons may be important to information processing in the nervous system. Using simulations, we show that the temporal structure of the spike trains of these synchronized input neurons can be transmitted reliably; further, synapses from these neurons will increase stably due to the STDP rule and this may provide a mechanism for learning and information storage in biologically plausible network models. Received 12 September 2002 / Received in final form 12 December 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: huang_yue@netease.com     

Contrast Adaptation Decreases Complexity in Retinal Ganglion Cell Spike Train

The difference in temporal structures of retinal ganglion cell spike trains between spontaneous activity and firing activity after contrast adaptation is investigated. The Lempel-Ziv complexity analysis reveals that the complexity of the neural spike train decreases after contrast adaptation. This implies that the behaviour of the neuron becomes ordered, which may carry relevant information about the external stimulus. Thus, during the neuron activity after contrast adaptation, external information could be encoded in forms of some certain patterns in the temporal structure of spike train that is significantly different, compared to that of the spike train during spontaneous activity, although the firing rates in spontaneous activity and firing activity after contrast adaptation are sometime similar.     

Synchrony between orientation-selective neurons is modulated during adaptation-induced plasticity in cat visual cortex

Background  

Visual neurons respond essentially to luminance variations occurring within their receptive fields. In primary visual cortex, each neuron is a filter for stimulus features such as orientation, motion direction and velocity, with the appropriate combination of features eliciting maximal firing rate. Temporal correlation of spike trains was proposed as a potential code for linking the neuronal responses evoked by various features of a same object. In the present study, synchrony strength was measured between cells following an adaptation protocol (prolonged exposure to a non-preferred stimulus) which induce plasticity of neurons' orientation preference.     

Synaptic plasticity modulates autonomous transitions between waking and sleep states: insights from a Morris-Lecar model

The transitions between waking and sleep states are characterized by considerable changes in neuronal firing. During waking, neurons fire tonically at irregular intervals and a desynchronized activity is observed at the electroencephalogram. This activity becomes synchronized with slow wave sleep onset when neurons start to oscillate between periods of firing (up-states) and periods of silence (down-states). Recently, it has been proposed that the connections between neurons undergo potentiation during waking, whereas they weaken during slow wave sleep. Here, we propose a dynamical model to describe basic features of the autonomous transitions between such states. We consider a network of coupled neurons in which the strength of the interactions is modulated by synaptic long term potentiation and depression, according to the spike time-dependent plasticity rule (STDP). The model shows that the enhancement of synaptic strength between neurons occurring in waking increases the propensity of the network to synchronize and, conversely, desynchronization appears when the strength of the connections become weaker. Both transitions appear spontaneously, but the transition from sleep to waking required a slight modification of the STDP rule with the introduction of a mechanism which becomes active during sleep and changes the proportion between potentiation and depression in accordance with biological data. At the neuron level, transitions from desynchronization to synchronization and vice versa can be described as a bifurcation between two different states, whose dynamical regime is modulated by synaptic strengths, thus suggesting that transition from a state to an another can be determined by quantitative differences between potentiation and depression.     

兴奋性和抑制性自反馈压制靠近Hopf分岔的神经电活动比较

突触输入刺激神经元产生的电活动,在神经编码中发挥着重要作用.通常认为,兴奋性输入增强电活动,抑制性输入压制电活动.本文选取可调节电流衰减速度的突触模型,研究了兴奋性自突触在亚临界Hopf分岔附近压制神经元电活动的反常作用,与抑制性自突触的压制作用进行了比较,并采用相位响应曲线和相平面分析解释了压制作用的机制.对于单稳的峰放电,快速和中速衰减的兴奋性自突触分别可以诱发频率降低的峰放电和混合振荡(峰放电与阈下振荡的交替),而中速和慢速衰减的抑制性自突触也可以分别诱发频率降低的峰放电和混合振荡.对于与静息共存的峰放电,除上述两种行为外,中速衰减的兴奋性和慢速衰减的抑制性自突触还可以诱发静息.兴奋性和抑制性自突触电流在不同的衰减速度下,分别作用在峰放电的不同相位,才能诱发同类压制行为.结果丰富了兴奋性突触压制电活动反常作用的实例,获得了兴奋性和抑制性自突触压制作用机制的不同,给出了调控神经放电的新手段.     

Impact of network activity on noise delayed spiking for a Hodgkin-Huxley model

In a Hodgkin-Huxley neuron model driven just above threshold, external noise can increase both jitter and latency of the first spike, an effect called “noise delayed decay” (NDD). This phenomenon is important when considering how neuronal information is represented, thus by the precise timing of spikes or by their rate. We examine how NDD can be affected by network activity by varying the model's membrane time constant, τ_m. We show that NDD is significant for small τ_m or high network activity, and decreases for large τ_m, or low network activity. Our results suggest that for inputs just above threshold, the activity of the network constrains the neuronal coding strategy due to, at least in part, the NDD effect.     

动态突触、神经耦合与时间延迟对神经元发放的影响

神经元膜电位的受激发放在神经系统的信息传递中起着重要作用.基于一个受动态突触刺激的突触后神经元发放模型,采用数值模拟和傅里叶变换分析的方法研究了动态突触、神经耦合与时间延迟对突触后神经元发放的影响.结果发现:突触前神经元发放频率与Hodgkin-Huxley神经元的固有频率发生共振决定了突触后神经元发放的难易,特定频率范围内的电流刺激有利于神经元激发,动态突触输出的随机突触电流中这些电流刺激所占的比率在很大程度上影响了突触后神经元的发放次数;将突触后神经元换成神经网络后,网络中神经元之间的耦合可以促进神经元的发放,耦合中的时间延迟可以增强这种促进作用,但是不会改变神经耦合对神经元发放的促进模式.     

Plasticity-induced characteristic changes of pattern dynamics and the related phase transitions in small-world neuronal networks

Phase transitions widely exist in nature and occur when some control parameters are changed. In neural systems, their macroscopic states are represented by the activity states of neuron populations, and phase transitions between different activity states are closely related to corresponding functions in the brain. In particular, phase transitions to some rhythmic synchronous firing states play significant roles on diverse brain functions and disfunctions, such as encoding rhythmical external stimuli, epileptic seizure, etc. However, in previous studies, phase transitions in neuronal networks are almost driven by network parameters （e.g., external stimuli）, and there has been no investigation about the transitions between typical activity states of neuronal networks in a self-organized way by applying plastic connection weights. In this paper, we discuss phase transitions in electrically coupled and lattice-based small-world neuronal networks （LBSW networks） under spike-timing-dependent plasticity （STDP）. By applying STDP on all electrical synapses, various known and novel phase transitions could emerge in LBSW networks, particularly, the phenomenon of self-organized phase transitions （SOPTs）： repeated transitions between synchronous and asynchronous firing states. We further explore the mechanics generating SOPTs on the basis of synaptic weight dynamics.     

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.     

Inverse stochastic resonance induced by synaptic background activity with unreliable synapses

Inverse stochastic resonance (ISR) is a recently pronounced phenomenon that is the minimum occurrence in mean firing rate of a rhythmically firing neuron as noise level varies. Here, by using a realistic modeling approach for the noise, we investigate the ISR with concrete biophysical mechanisms. It is shown that mean firing rate of a single neuron subjected to synaptic bombardment exhibits a minimum as the spike transmission probability varies. We also demonstrate that the occurrence of ISR strongly depends on the synaptic input regime, where it is most prominent in the balanced state of excitatory and inhibitory inputs.     

The spike timing precision of FitzHugh--Nagumo neuron network coupled by gap junctions

It has been proved recently that the spike timing can play an important role in information transmission, so in this paper we develop a network with N-unit FitzHugh--Nagumo neurons coupled by gap junctions and discuss the dependence of the spike timing precision on synaptic coupling strength, the noise intensity and the size of the neuron ensemble. The calculated results show that the spike timing precision decreases as the noise intensity increases; and the ensemble spike timing precision increases with coupling strength increasing. The electric synapse coupling has a more important effect on the spike timing precision than the chemical synapse coupling.     

Model of a neuron trained to extract periodicity

In the auditory system, there should be elements that convert temporal parameters into spatial ones. To simulate such conversion, various neural networks are used. In this study, we modeled this conversion, carried out by one complex neuron on the basis of learning without a teacher. We postulate that conversion of the time code into a spatial code is observed at the input of the model. We admit that every aciculum of a complex neuron responds as a coincidence detector, and after each coincidence at any synapse, the neuron generates a spike. Every spike at the output of a neuron changes the weight of all acicula according to the Hebb principle. Training of the model is done without a teacher simply owing to model’s multiple perception of a certain type of signals. In the given case, such signals are the actual activity of the cochlear nucleus of frog, which arises as a response to an amplitude-modulated tone. After the action of such signals, the model behaved as a detector of the modulation frequency used during training. Such a situation existed up to modulation frequencies near 40 Hz. At higher modulation frequencies, the model even extracted signals with a doubled modulation period.     

电磁辐射诱发神经元放电节律转迁的动力学行为研究

本文首先根据能量转换理论建立了电磁辐射影响下神经元电流变量模型, 然后结合Hodgkin-Huxley(HH)神经元模型研究了电磁辐射对单个神经元以及耦合神经元放电行为的影响. 结果表明, 随着电磁辐射强度的增大, 神经元放电率逐渐减小, 最后达到一个比较稳定的值. 神经元原有的周期型放电由于辐射强度的增大而逐步过渡到簇放电状态, 并借助动态分岔理论解释了这种放电模式的转换. 同时证明了磁辐射对单个神经元放电的影响可以通过神经元间的耦合传递到临近其他神经元中.     

Coherence depression in stochastic excitable systems with two-frequency forcing

We study the response of two generic neuron models, the leaky integrate-and-fire (LIF) model and the leaky integrate-and-fire model with dynamic threshold (LIFDT) (i.e., with memory) to a stimulus consisting of two sinusoidal drives with incommensurate frequency, an amplitude modulation ("envelope") noise and a relatively weak additive noise. Spectral and coherence analysis of responses to such naturalistic stimuli reveals how the LIFDT model exhibits better correlation between modulation and spike train even in the presence of both noises. However, a resonance-induced synchrony, occurring when the beat frequency between the sinusoids is close to the intrinsic neuronal firing rate, decreases the coherence in the dynamic threshold case. Under suprathreshold conditions, the modulation noise simultaneously decreases the linear spectral coherence between the spikes and the whole stimulus, as well as between spikes and the stimulus envelope. Our study shows that the coefficient of variation of the envelope fluctuations is positively correlated with the degree of coherence depression. As the coherence function quantifies the linear information transmission, our findings indicate that under certain conditions, a transmission loss results when an excitable system with adaptive properties encodes a beat with frequency in the vicinity of its mean firing rate.     

Optical fiber synaptic sensor

Understanding neuron connections is a great challenge, which is needed to solve many important problems in neurobiology and neuroengineering for recreation of brain functions and efficient biorobotics. In particular, a design of an optical synapse capable to communicate with neuron spike sequences would be crucial to improve the functionality of neuromimmetic networks. In this work we propose an optical synaptic sensor based on an erbium-doped fiber laser driven by a FitzHung-Nagumo electronic neuron, to connect with another electronic neuron. Two possible optical synaptic configurations are analyzed for optoelectronic coupling between neurons: laser cavity loss modulation and pump laser modulation. The control parameters of the proposed optical synapse provide additional degrees of flexibility to the neuron connection traditionally controlled only by coupling strengths in artificial networks.     

Reducing Neuronal Networks to Discrete Dynamics

We consider a general class of purely inhibitory and excitatory-inhibitory neuronal networks, with a general class of network architectures, and characterize the complex firing patterns that emerge. Our strategy for studying these networks is to first reduce them to a discrete model. In the discrete model, each neuron is represented as a finite number of states and there are rules for how a neuron transitions from one state to another. In this paper, we rigorously demonstrate that the continuous neuronal model can be reduced to the discrete model if the intrinsic and synaptic properties of the cells are chosen appropriately. In a companion paper [W. Just, S. Ahn, D. Terman. Minimal attractors in digraph system models of neuronal networks (preprint)], we analyse the discrete model.     

Time-varying irregularities in multiple trial spike data

The measurement of neuronal firing rates has been a standard methodology for characterizing properties of neurons. The peri-stimulus time histogram (PSTH) is primarily used for visualizing changes of firing rates in relation to an external stimulus or an event. On the other hand, modulation of other statistics such as distribution and patterns of interspike intervals can be an important index for analysis of neuronal response and may provide insights into the neuronal codes. In particular, it is desirable to visualize the temporal modulation not only of the firing rates but also of the other statistics. In this study, we propose an analysis method for measuring irregularities in multiple trial spike data. The method calculates a local measure by extracting a short segment of data within a predefined time bin and connecting them each other. We compare the different data extraction methods in Poisson and gamma processes and show that our proposed method is effective for estimating the statistics of the irregular spike data.     

Bifurcation diagram globally underpinning neuronal firing behaviors modified by SK conductance

Neurons in the brain utilize various firing trains to encode the input signals they have received.Firing behavior of one single neuron is thoroughly explained by using a bifurcation diagram from polarized resting to firing,and then to depolarized resting.This explanation provides an important theoretical principle for understanding neuronal biophysical behaviors.This paper reports the novel experimental and modeling results of the modification of such a bifurcation diagram by adjusting small conductance potassium(SK)channel.In experiments,changes in excitability and depolarization block in nucleus accumbens shell and medium-spiny projection neurons are explored by increasing the intensity of injected current and blocking the SK channels by apamin.A shift of bifurcation points is observed.Then,a Hodgkin–Huxley type model including the main electrophysiological processes of such neurons is developed to reproduce the experimental results.The reduction of SK channel conductance also shifts the bifurcations,which is in consistence with experiment.A global bifurcation paradigm of this shift is obtained by adjusting two parameters,intensity of injected current and SK channel conductance.This work reveals the dynamics underpinning modulation of neuronal firing behaviors by biologically important ionic conductance.The results indicate that small ionic conductance other than that responsible for spike generation can modify bifurcation points and shift the bifurcation diagram and,thus,change neuronal excitability and adaptation.