Effects of synaptic noise and filtering on the frequency response of spiking neurons

Noise can have a significant impact on the response dynamics of a nonlinear system. For neurons, the primary source of noise comes from background synaptic input activity. If this is approximated as white noise, the amplitude of the modulation of the firing rate in response to an input current oscillating at frequency omega decreases as 1/square root[omega] and lags the input by 45 degrees in phase. However, if filtering due to realistic synaptic dynamics is included, the firing rate is modulated by a finite amount even in the limit omega-->infinity and the phase lag is eliminated. Thus, through its effect on noise inputs, realistic synaptic dynamics can ensure unlagged neuronal responses to high-frequency inputs.     

Mechanism for propagation of rate signals through a 10-layer feedforward neuronal network

Using numerical simulations, we explore the mechanism for propagation of rate signals through a 10-layer feedforward network composed of Hodgkin--Huxley (HH) neurons with sparse connectivity. When white noise is afferent to the input layer, neuronal firing becomes progressively more synchronous in successive layers and synchrony is well developed in deeper layers owing to the feedforward connections between neighboring layers. The synchrony ensures the successful propagation of rate signals through the network when the synaptic conductance is weak. As the synaptic time constant τ_syn varies, coherence resonance is observed in the network activity due to the intrinsic property of HH neurons. This makes the output firing rate single-peaked as a function of τ_syn, suggesting that the signal propagation can be modulated by the synaptic time constant. These results are consistent with experimental results and advance our understanding of how information is processed in feedforward networks.     

Cingulate seizure-like activity reveals neuronal avalanche regulated by network excitability and thalamic inputs

Background

Cortical neurons display network-level dynamics with unique spatiotemporal patterns that construct the backbone of processing information signals and contribute to higher functions. Recent years have seen a wealth of research on the characteristics of neuronal networks that are sufficient conditions to activate or cease network functions. Local field potentials (LFPs) exhibit a scale-free and unique event size distribution (i.e., a neuronal avalanche) that has been proven in the cortex across species, including mice, rats, and humans, and may be used as an index of cortical excitability. In the present study, we induced seizure activity in the anterior cingulate cortex (ACC) with medial thalamic inputs and evaluated the impact of cortical excitability and thalamic inputs on network-level dynamics. We measured LFPs from multi-electrode recordings in mouse cortical slices and isoflurane-anesthetized rats.

Results

The ACC activity exhibited a neuronal avalanche with regard to avalanche size distribution, and the slope of the power-law distribution of the neuronal avalanche reflected network excitability in vitro and in vivo. We found that the slope of the neuronal avalanche in seizure-like activity significantly correlated with cortical excitability induced by γ-aminobutyric acid system manipulation. The thalamic inputs desynchronized cingulate seizures and affected the level of cortical excitability, the modulation of which could be determined by the slope of the avalanche size.

Conclusions

We propose that the neuronal avalanche may be a tool for analyzing cortical activity through LFPs to determine alterations in network dynamics.     

Aperiodic stochastic resonance in a hysteretic population of cardiac neurons

Aperiodic stochastic resonance (ASR) is studied for a densely interconnected population of excitatory and inhibitory neurons that exhibit hysteresis. Switching between states in the presence of noisy external forcing is represented as a "competition between averages" and this is further explained through a semianalytical model. In contrast to energy-based approaches where only the timing of a switch between states is represented, the competition between averages also identifies the input history responsible for a switch. This last point leads to some interesting conclusions regarding cause and effect in the presence of noisy forcing of a hysteretic system. For example, at subthreshold inputs, it is found that the input history causing a switch between states is primarily dependent upon the noise level even though the corresponding time to switch is sensitive to both the distance from the threshold and the noise level. Since the application considered here is to cardiac neuronal control, control performance is considered over the full input range. Noise tuning for adequate control performance is found to be unnecessary if the noise level is high enough. This is consistent with studies of ASR for sensory neurons. Another observation made here that may be of clinical significance is that at higher noise levels, constraints placed upon inputs to ensure adequate control performance are likely to depend upon the switching direction.     

双耳幅值差确定声源方向的神经信息处理机理研究

神经信息系统实质上是定量系统, 应引起足够重视. 关于神经系统的定量研究方面的报道比较少见. 这一问题将会影响进一步的研究, 如双耳声音定向. 双耳定向是定量测量, 用定性分析的方法无法满足要求. 已有的生理实验发现声音输入信号强度与听觉神经的输出频率存在单调递增关系, 所以本文中声音强度的变化被简化成神经脉冲频率的变化. 本文基于圆映射和符号动力学原理, 建立了神经回路定量模型, 模型中对同侧输入回路采用兴奋性耦合, 对侧输入回路采用抑制性耦合, 并考虑神经元间突触连接的量子释放特征, 采用化学耦合模型实现连接, 用耦合系数表示神经元间的耦合程度. 采用Hodgkin-Huxley模型仿真研究听觉神经回路的输入/输出脉冲序列关系. 在已经仿真过的参数范围, 模型在输入信号变化与输出脉冲频率变化间存在单调递增/递减的关系. 对于单输入单输出的神经元, 采用符号动力学方法进行符号化; 对于多输入单输出的神经元, 采用分析各输出脉冲的产生时间, 判断其变化位置, 从神经脉冲序列中得到对应的两耳声音幅值差变化, 以此定位声源. 随着输出脉冲数的增加, 符号序列的长度增加, 符号序列对输入信号变化敏感, 能够得到较高的测量精度. 仿真结果表明这个模型是定量的, 神经脉冲序列能够区分信号的大小.     

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.     

Stochastic resonance in hybrid scale-free neuronal networks

We study the phenomenon of stochastic resonance in a system of coupled neurons that are globally excited by a weak periodic input signal. We make the realistic assumption that the chemical and electrical synapses interact in the same neuronal network, hence constituting a hybrid network. By considering a hybrid coupling scheme embedded in the scale-free topology, we show that the electrical synapses are more efficient than chemical synapses in promoting the best correlation between the weak input signal and the response of the system. We also demonstrate that the average degree of neurons within the hybrid scale-free network significantly influences the optimal amount of noise for the occurrence of stochastic resonance, indicating that there also exists an optimal topology for the amplification of the response to the weak input signal. Lastly, we verify that the presented results are robust to variations of the system size.     

Fisher information for spike-based population decoding

We evaluate the Fisher information of a population of model neurons that receive dynamical input and interact via spikes. With spatially independent threshold noise, the spike-based Fisher information that summarizes the information carried by individual spike timings has a particularly simple analytical form. We calculate the loss of information caused by abandoning spike timing and study the effect of synaptic connections on the Fisher information. For a simple spatiotemporal input, we derive the optimal recurrent connectivity that has a local excitation and global inhibition structure. The optimal synaptic connections depend on the spatial or temporal feature of the input that the system is designed to code.     

Propagation of spiking regularity and double coherence resonance in feedforward networks

We investigate the propagation of spiking regularity in noisy feedforward networks (FFNs) based on FitzHugh-Nagumo neuron model systematically. It is found that noise could modulate the transmission of firing rate and spiking regularity. Noise-induced synchronization and synfire-enhanced coherence resonance are also observed when signals propagate in noisy multilayer networks. It is interesting that double coherence resonance (DCR) with the combination of synaptic input correlation and noise intensity is finally attained after the processing layer by layer in FFNs. Furthermore, inhibitory connections also play essential roles in shaping DCR phenomena. Several properties of the neuronal network such as noise intensity, correlation of synaptic inputs, and inhibitory connections can serve as control parameters in modulating both rate coding and the order of temporal coding.     

Spiking sychronization regulated by noise in three types of Hodgkin—Huxley neuronal networks

In this paper,we study spiking synchronization in three different types of Hodgkin-Huxley neuronal networks,which are the small-world,regular,and random neuronal networks.All the neurons are subjected to subthreshold stimulus and external noise.It is found that in each of all the neuronal networks there is an optimal strength of noise to induce the maximal spiking synchronization.We further demonstrate that in each of the neuronal networks there is a range of synaptic conductance to induce the effect that an optimal strength of noise maximizes the spiking synchronization.Only when the magnitude of the synaptic conductance is moderate,will the effect be considerable.However,if the synaptic conductance is small or large,the effect vanishes.As the connections between neurons increase,the synaptic conductance to maximize the effect decreases.Therefore,we show quantitatively that the noise-induced maximal synchronization in the Hodgkin-Huxley neuronal network is a general effect,regardless of the specific type of neuronal network.     

FitzHugh-Nagumo神经元网络的联想记忆与分割

以广泛讨论的Fitz Hugh-Nagumo神经元节点组成脉动神经元网络,从神经系统空时模式编码理论研究网络的记忆(或模式)存储与时间分割问题.给定一个输入模式,它是几种模式的叠加,网络能够以一部分神经元同步发放的形式一个接一个地分割出每一种模式.如果输入的模式有缺损,系统能够把它们恢复成原型,即神经网络的联想记忆功能.模拟需要调节耦合强度和噪声强度等参数使得网络在特定的参数值和中等强度噪声达到最优的时间分割,与广泛讨论的随机共振现象一致.     

Models of the temporal dynamics of visual processing

Single unit recordings of neurons in primary visual cortex have demonstrated complex temporal patterns in the interspike interval return maps when presented with periodic input. Two models are tested to account for these patterns. An integrate-and-fire model is only able to replicate thein vivo data if its synaptic input is a chaotic function of time (such as a time series derived from the sinusoidally driven Duffing equation). Simpler purely periodic inputs are insufficient to replicate the experimental data. A Hodgkin-Huxley ionic model with a periodic input can replicate some of the features of the neural data, however it seems to be lacking as a complete model. These results indicate that thein vivo dynamics are not a result of the intrinsic properties of the neuron, but arise from a chaotic input to the neuron.     

Travelling waves in a model of quasi-active dendrites with active spines

Dendrites, the major components of neurons, have many different types of branching structures and are involved in receiving and integrating thousands of synaptic inputs from other neurons. Dendritic spines with excitable channels can be present in large densities on the dendrites of many cells. The recently proposed Spike-Diffuse-Spike (SDS) model that is described by a system of point hot-spots (with an integrate-and-fire process) embedded throughout a passive tree has been shown to provide a reasonable caricature of a dendritic tree with supra-threshold dynamics. Interestingly, real dendrites equipped with voltage-gated ion channels can exhibit not only supra-threshold responses, but also sub-threshold dynamics. This sub-threshold resonant-like oscillatory behaviour has already been shown to be adequately described by a quasi-active membrane. In this paper we introduce a mathematical model of a branched dendritic tree based upon a generalisation of the SDS model where the active spines are assumed to be distributed along a quasi-active dendritic structure. We demonstrate how solitary and periodic travelling wave solutions can be constructed for both continuous and discrete spine distributions. In both cases the speed of such waves is calculated as a function of system parameters. We also illustrate that the model can be naturally generalised to an arbitrary branched dendritic geometry whilst remaining computationally simple. The spatio-temporal patterns of neuronal activity are shown to be significantly influenced by the properties of the quasi-active membrane. Active (sub- and supra-threshold) properties of dendrites are known to vary considerably among cell types and animal species, and this theoretical framework can be used in studying the combined role of complex dendritic morphologies and active conductances in rich neuronal dynamics.     

Dynamical Mean-Field Equations for a Neural Network with Spike Timing Dependent Plasticity

We study the discrete dynamics of a fully connected network of threshold elements interacting via dynamically evolving synapses displaying spike timing dependent plasticity. Dynamical mean-field equations, which become exact in the thermodynamical limit, are derived to study the behavior of the system driven with uncorrelated and correlated Gaussian noise input. We use correlated noise to verify that our model gives account to the fact that correlated noise provides stronger drive for synaptic modification. Further we find that stochastic independent input leads to a noise dependent transition to the coherent state where all neurons fire together, most notably there exists an optimal noise level for the enhancement of synaptic potentiation in our model.     

Analysis of pulsed-signal transmission in a system of interacting neural oscillators with frequency-dependent connections

In this paper, we study the influence of the frequency-dependent connection on the signal transmission in a system of two interacting pulsed neural oscillators. The system is a model of two neurons with synaptic connection having the synaptic-plasticity feature, i.e., synaptic-parameter variation as a function of the frequency characteristics of the signal. It is shown that plastic connection can control the signal-transmission efficiency depending on the pulse-repetition rate and ensures stable synchronization modes of the pulse trains with different ratios between the frequencies of the output and input pulses. Analytical estimates for the parameter ranges corresponding to generation of the pulse response at the detector neuron depending on the pulse-repetition rate at the oscillator neuron were obtained.     

Self-organized criticality occurs in non-conservative neuronal networks during Up states

During sleep, under anesthesia and in vitro, cortical neurons in sensory, motor, association and executive areas fluctuate between Up and Down states (UDS) characterized by distinct membrane potentials and spike rates [1, 2, 3, 4, 5]. Another phenomenon observed in preparations similar to those that exhibit UDS, such as anesthetized rats [6], brain slices and cultures devoid of sensory input [7], as well as awake monkey cortex [8] is self-organized criticality (SOC). This is characterized by activity "avalanches" whose size distributions obey a power law with critical exponent of about [Formula: see text] and branching parameter near unity. Recent work has demonstrated SOC in conservative neuronal network models [9, 10], however critical behavior breaks down when biologically realistic non-conservatism is introduced [9]. We here report robust SOC behavior in networks of non-conservative leaky integrate-and-fire neurons with short-term synaptic depression. We show analytically and numerically that these networks typically have 2 stable activity levels corresponding to Up and Down states, that the networks switch spontaneously between them, and that Up states are critical and Down states are subcritical.     

Coherence resonance in globally coupled neuronal networks with different neuron numbers

Because a brain consists of tremendous neuronal networks with different neuron numbers ranging from tens to tens of thousands, we study the coherence resonance due to ion channel noises in globally coupled neuronal networks with different neuron numbers. We confirm that for all neuronal networks with different neuron numbers there exist the array enhanced coherence resonance and the optimal synaptic conductance to cause the maximal spiking coherence. Furthermoremore, the enhancement effects of coupling on spiking coherence and on optimal synaptic conductance are almost the same, regardless of the neuron numbers in the neuronal networks. Therefore for all the neuronal networks with different neuron numbers in the brain, relative weak synaptic conductance (0.1 mS/cm²) is sufficient to induce the maximal spiking coherence and the best sub-threshold signal encoding.     

神经系统中随机和混沌感知信号的联想记忆与分割

为了模拟人与动物感知信息的真实环境，以脉动神经元节点组成神经元网络，研究在随机刺激和混沌刺激等极端条件下的记忆模式存储与时间分割问题.研究表明：网络对于若干种模式的叠加输入，能够以一部分神经元同步发放的形式在时间域上分割出每一模式. 如果输入模式是缺损的，系统能够把它们恢复到原型，即具有联想记忆功能.通过调节耦合强度和噪声强度等参数使得网络在中等强度噪声达到最优的时间分割，与广泛讨论的随机共振现象一致. 关键词： 神经网络 空时模式 联想记忆 随机共振     

A multichannel shot noise approach to describe synaptic background activity in neurons

Systems driven by Poisson-distributed quantal inputs can be described as “shot noise” stochastic processes. This formalism can apply to neurons which receive a large number of Poisson-distributed synaptic inputs of similar quantal size. However, the presence of temporal correlations between these inputs destroys their quantal nature, and such systems can no longer be described by classical shot noise processes. Here, we show that explicit expressions for various statistical properties, such as the amplitude distribution and the power spectral density, can be deduced and investigated as functions of the correlation between input channels. The monotonic behavior of these expressions allows an one-to-one relation between temporal correlations and the statistics of fluctuations. Multi-channel shot noise processes, therefore, open a way to deduce correlations in input patterns by analyzing fluctuations in experimental systems. We discuss applications such as detecting correlations in networks of neurons from intracellular recordings of single neurons.     

Nonlinear transfer function encodes synchronization in a neural network from the mammalian brain

Synchronization is one of the mechanisms by which the brain encodes information. The observed synchronization of neuronal activity has, however, several levels of fluctuations, which presumably regulate local features of specific areas. This means that biological neural networks should have an intrinsic mechanism able to synchronize the neuronal activity but also to preserve the firing capability of individual cells. Here, we investigate the input-output relationship of a biological neural network from developing mammalian brain, i.e., the hippocampus. We show that the probability of occurrence of synchronous output activity (which consists in stereotyped population bursts recorded throughout the hippocampus) is encoded by a sigmoidal transfer function of the input frequency. Under this scope, low-frequency inputs will not produce any coherent output while high-frequency inputs will determine a synchronous pattern of output activity (population bursts). We analyze the effect of the network size (N) on the parameters of the transfer function (threshold and slope). We found that sigmoidal functions realistically simulate the synchronous output activity of hippocampal neural networks. This outcome is particularly important in the application of results from neural network models to neurobiology.