自发和诱发神经放电序列的内在时序特性

运用Fano因子分析法,考察豚鼠听神经单纤维的自发放电序列、小鼠海马CAl区神经元的自发放电序列以及蟾蜍缝匠肌肌梭传入神经的诱发放电序列的时序特性,结果显示自发和诱发放电时间序列均存在Fano因子随计算窗口时间的增大而持续增长的特点,而原始数据的随机重排替代数据则没有这一特性,说明这些神经放电时间序列与一般的随机点过程不同,存在长时程相关性,在时序上具有某种结构特征。进一步的研究表明,这一时序结构特征可以通过将随机产生的一维正态分布序列数据,与神经放电时间序列数据进行跟随排序后而体现,提示这一特征与放电间隔的分布特点无关。     

神经放电节律加周期分岔序列中的簇放电到峰放电的转迁

含快慢子系统的神经元数学模型仿真预期,神经放电节律经历加周期分岔序列,可以进一步表现激变,并通过逆倍周期分岔级联进入周期1峰放电。实验调节胞外钙离子浓度,观察到从周期1簇放电开始的带有随机节律的加周期分岔到簇内有多个峰的簇放电,再经激变转迁到峰放电节律的分岔序列,提供了这种分岔序列模式实验证据。实验所见之激变表现为簇放电节律的休止期消失,放电节律变为混沌峰放电和周期峰放电。作者利用随机Chay模型更加逼真地仿真再现了实验所见的分岔序列。该实验结果验证了以前的确定性数学模型的理论预期,并利用随机理论模型仿真了其在现实神经系统的表现;揭示了一类完整的神经放电节律的转换规律。     

电突触耦合神经元的相位同步及放电节律的转化

研究了两个参数失配较大情况下,处于不同放电模式的两个电突触耦合Hindmarsh-rose(HR)神经元的相位同步问题,发现在适当耦合强度下可以实现相同步并呈现出复杂的放电节律.利用峰峰间期(Interspikeinterval,ISI)和平均放电频率证实了相同步的发生,给出并分析了不同放电状态的神经元在电突触耦合下实现相同步后的神经放电节律.从相同步的角度显示,神经元同步后呈现簇放电特征或峰放电特征,除与两耦合神经元独自放电模式有关外,还与电突触耦合强度有一定的内在关系.     

4-氨基吡啶敏感钾通道对神经自发放电节律转迁历程的调节作用

为进一步研究损伤神经放电节律的分岔转迁规律,以实验性神经起步点模型为研究对象,在联合改变胞外的钙离子和钾离子浓度的条件下,记录神经单纤维的放电节律转迁方式。选取4-氨基吡啶(4-aminopyridine,4-AP)作为条件参数,Ca2+浓度作为分岔参数,观察了实验性神经起步点自发放电节律的分岔规律。28例实验结果中,有21例神经对本文所取的条件参数变化不敏感,7例实验性神经起步点的自发放电节律会在不同的条件参数下出现不同类型的分岔序列结构。在不同的4-AP浓度下,随着Ca2+浓度的降低,同一实验性神经起步点会表现出不同的放电节律模式的分岔序列,不同实验性神经起步点,双参数分岔序列是不同的。以上结果说明,不同参数配置下的神经放电节律的变化规律是不同的,而且分岔序列结构是认识放电节律转迁规律的基础。     

用近似熵测量神经放电峰峰间期的复杂性

近似熵是用来测量信号复杂程度的非线性方法。为了研究神经放电序列的复杂性,用该方法及其改进方法对大鼠损伤坐崩神经模型、大鼠脑薄片视上核神经元自发放电模型、背根节自发放电模型峰峰间期以及Rose-Hindmarsh理论神经元模型分叉数据进行了动态测量。结果表明,近似熵可以定量反映多种神经放电序列复杂性的变化,是一种较为有效的复杂性序量方法。     

蛋白质序列的六维表示与相似性分析

给出了蛋白质序列的一种六维表示方法,根据这种表示方法有3种不同表示形式,利用这3种形式来构造距离矩阵的信息熵,然后通过信息熵向量的欧式距离、夹角来比较序列之间的相似性。     

神经放电节律转化的分岔序列模式

神经元接受到的外界信号是动态变化的,神经放电节律模式则会依据一定的规律动态转化来反映这种变化,以往确定性理论模型(如Chay模型和Rose-Hindmarsh模型)模拟出了部分神经放电模式转化的整体分岔规律。利用Chay模型仿真,通过调节具有生理学意义的参数,模拟出了神经元放电的一系列分岔序列,同时在神经起步点的实验中,应用与模型对应的参数进行调节,观察到了与仿真结果整体上一致的分岔序列,印证了数值模拟的结果,展现了真实的神经元放电整体分岔结构的基本规律,为理解具体的生理调节活动中神经放电节律的转化提供了理论基础。     

神经放电加周期分岔中由随机自共振引起一类新节律

当改变实验性神经起步点细胞外[Ca^2 ]时,放电节律表现出从周期1节律转换为周期4节律的加周期分岔序列。其中,周期n节律转换为周期n 1节律的过程中(n=1,2,3)存在一种新的具有交替特征的节律,该新节律为周期n簇与周期n 1簇放电的交替,并且周期n 1簇的时间间隔序列呈现出整数倍特征。确定性神经放电理论模型(chay模型)只能模拟周期n节律直接到周期n 1节律的加周期分岔序列;而随机chay模型可以模拟实验中的加周期分岔过程和新节律。进一步,新节律被确认是经随机自共振机制产生的。这不仅解释了实验现象,也将随机自共振的产生区间从以前认识到的Hopf分岔点附近扩大到加周期分岔点附近,同时扩大了噪声在神经放电和神经编码中起重要作用的参数区间。     

大鼠损伤神经的三种诱发簇放电节律

实验运用单纤维记录技术,观察了损伤神经起步点自发放电在改变[Ca^2 ]。和veratridine作用下放电节律的变化。结果表明：在每一标本上,记录到的相同背景的自发放电在低与高Ca^2 浓度和veratridine的作用下,转化为三种不同类型的簇放电。结果提示,神经元放电的节律形式与刺激的性质相关,不同的节律形式可能携带着不同的神经信息。     

使用伪氨基酸组成和模糊支持向量机预测蛋白质结构类

蛋白质结构类预测是生物信息和蛋白质科学中重要的研究领域.基于Chou提出的伪氨基酸离散模型框架,从蛋白质序列出发,设计一种新的伪氨基酸组成方法表示蛋白质序列样本.抽取氨基酸组合(10-D)在序列中出现的频率和疏水氨基酸模式(6-D)表示蛋白质序列的附加特征,用和传统的氨基酸组成(20-D)一起构成的36维的伪氨基酸组成向量来表示蛋白质序列的特征.使用遗传算法来优化附加特征的权重系数.伪氨基酸组成向量作为输入数据,模糊支持向量机作为预测工具.使用三个常用的标准数据集来验证算法的性能.Jack-knife检验结果说明本方法具有较高的准确率,有望成为潜在的预测蛋白质功能的工具.     

Chaos game representation of human pallidal spike trains

Many studies have demonstrated the presence of scale invariance and long-range correlation in animal and human neuronal spike trains. The methodologies to extract the fractal or scale-invariant properties, however, do not address the issue as to the existence within the train of fine temporal structures embedded in the global fractal organisation. The present study addresses this question in human spike trains by the chaos game representation (CGR) approach, a graphical analysis with which specific temporal sequences reveal themselves as geometric structures in the graphical representation. The neuronal spike train data were obtained from patients whilst undergoing pallidotomy. Using this approach, we observed highly structured regions in the representation, indicating the presence of specific preferred sequences of interspike intervals within the train. Furthermore, we observed that for a given spike train, the higher the magnitude of its scaling exponent, the more pronounced the geometric patterns in the representation and, hence, higher probability of occurrence of specific subsequences. Given its ability to detect and specify in detail the preferred sequences of interspike intervals, we believe that CGR is a useful adjunct to the existing set of methodologies for spike train analysis.     

Analyzing multiple spike trains with nonparametric granger causality

Simultaneous recordings of spike trains from multiple single neurons are becoming commonplace. Understanding the interaction patterns among these spike trains remains a key research area. A question of interest is the evaluation of information flow between neurons through the analysis of whether one spike train exerts causal influence on another. For continuous-valued time series data, Granger causality has proven an effective method for this purpose. However, the basis for Granger causality estimation is autoregressive data modeling, which is not directly applicable to spike trains. Various filtering options distort the properties of spike trains as point processes. Here we propose a new nonparametric approach to estimate Granger causality directly from the Fourier transforms of spike train data. We validate the method on synthetic spike trains generated by model networks of neurons with known connectivity patterns and then apply it to neurons simultaneously recorded from the thalamus and the primary somatosensory cortex of a squirrel monkey undergoing tactile stimulation.     

Reconstruction of Underlying Nonlinear Deterministic Dynamics Embedded in Noisy Spike Trains

An experimentally recorded time series formed by the exact times of occurrence of the neuronal spikes (spike train) is likely to be affected by observational noise that provokes events mistakenly confused with neuronal discharges, as well as missed detection of genuine neuronal discharges. The points of the spike train may also suffer a slight jitter in time due to stochastic processes in synaptic transmission and to delays in the detecting devices. This study presents a procedure aimed at filtering the embedded noise (denoising the spike trains) the spike trains based on the hypothesis that recurrent temporal patterns of spikes are likely to represent the robust expression of a dynamic process associated with the information carried by the spike train. The rationale of this approach is tested on simulated spike trains generated by several nonlinear deterministic dynamical systems with embedded observational noise. The application of the pattern grouping algorithm (PGA) to the noisy time series allows us to extract a set of points that form the reconstructed time series. Three new indices are defined for assessment of the performance of the denoising procedure. The results show that this procedure may indeed retrieve the most relevant temporal features of the original dynamics. Moreover, we observe that additional spurious events affect the performance to a larger extent than the missing of original points. Thus, a strict criterion for the detection of spikes under experimental conditions, thus reducing the number of spurious spikes, may raise the possibility to apply PGA to detect endogenous deterministic dynamics in the spike train otherwise masked by the observational noise.     

Regulation of spike timing in visual cortical circuits

A train of action potentials (a spike train) can carry information in both the average firing rate and the pattern of spikes in the train. But can such a spike-pattern code be supported by cortical circuits? Neurons in vitro produce a spike pattern in response to the injection of a fluctuating current. However, cortical neurons in vivo are modulated by local oscillatory neuronal activity and by top-down inputs. In a cortical circuit, precise spike patterns thus reflect the interaction between internally generated activity and sensory information encoded by input spike trains. We review the evidence for precise and reliable spike timing in the cortex and discuss its computational role.     

A cross-interval spike train analysis: the correlation between spike generation and temporal integration of doublets

A stochastic spike train analysis technique is introduced to reveal the correlation between the firing of the next spike and the temporal integration period of two consecutive spikes (i.e., a doublet). Statistics of spike firing times between neurons are established to obtain the conditional probability of spike firing in relation to the integration period. The existence of a temporal integration period is deduced from the time interval between two consecutive spikes fired in a reference neuron as a precondition to the generation of the next spike in a compared neuron. This analysis can show whether the coupled spike firing in the compared neuron is correlated with the last or the second-to-last spike in the reference neuron. Analysis of simulated and experimentally recorded biological spike trains shows that the effects of excitatory and inhibitory temporal integration are extracted by this method without relying on any subthreshold potential recordings. The analysis also shows that, with temporal integration, a neuron driven by random firing patterns can produce fairly regular firing patterns under appropriate conditions. This regularity in firing can be enhanced by temporal integration of spikes in a chain of polysynaptically connected neurons. The bandpass filtering of spike firings by temporal integration is discussed. The results also reveal that signal transmission delays may be attributed not just to conduction and synaptic delays, but also to the delay time needed for temporal integration. Received: 3 March 1997 / Accepted in revised form: 6 November 1997     

Variability and coding efficiency of noisy neural spike encoders

Encoding synaptic inputs as a train of action potentials is a fundamental function of nerve cells. Although spike trains recorded in vivo have been shown to be highly variable, it is unclear whether variability in spike timing represents faithful encoding of temporally varying synaptic inputs or noise inherent in the spike encoding mechanism. It has been reported that spike timing variability is more pronounced for constant, unvarying inputs than for inputs with rich temporal structure. This could have significant implications for the nature of neural coding, particularly if precise timing of spikes and temporal synchrony between neurons is used to represent information in the nervous system. To study the potential functional role of spike timing variability, we estimate the fraction of spike timing variability which conveys information about the input for two types of noisy spike encoders--an integrate and fire model with randomly chosen thresholds and a model of a patch of neuronal membrane containing stochastic Na(+) and K(+) channels obeying Hodgkin-Huxley kinetics. The quality of signal encoding is assessed by reconstructing the input stimuli from the output spike trains using optimal linear mean square estimation. A comparison of the estimation performance of noisy neuronal models of spike generation enables us to assess the impact of neuronal noise on the efficacy of neural coding. The results for both models suggest that spike timing variability reduces the ability of spike trains to encode rapid time-varying stimuli. Moreover, contrary to expectations based on earlier studies, we find that the noisy spike encoding models encode slowly varying stimuli more effectively than rapidly varying ones.     

An information-geometric framework for statistical inferences in the neural spike train space

Statistical inferences are essentially important in analyzing neural spike trains in computational neuroscience. Current approaches have followed a general inference paradigm where a parametric probability model is often used to characterize the temporal evolution of the underlying stochastic processes. To directly capture the overall variability and distribution in the space of the spike trains, we focus on a data-driven approach where statistics are defined and computed in the function space in which spike trains are viewed as individual points. To this end, we at first develop a parametrized family of metrics that takes into account different warpings in the time domain and generalizes several currently used spike train distances. These new metrics are essentially penalized L ^p norms, involving appropriate functions of spike trains, with penalties associated with time-warping. The notions of means and variances of spike trains are then defined based on the new metrics when p = 2 (corresponding to the “Euclidean distance”). Using some restrictive conditions, we present an efficient recursive algorithm, termed Matching-Minimization algorithm, to compute the sample mean of a set of spike trains with arbitrary numbers of spikes. The proposed metrics as well as the mean spike trains are demonstrated using simulations as well as an experimental recording from the motor cortex. It is found that all these methods achieve desirable performance and the results support the success of this novel framework.     

Studying spike trains using a van Rossum metric with a synapse-like filter

Spike trains are unreliable. For example, in the primary sensory areas, spike patterns and precise spike times will vary between responses to the same stimulus. Nonetheless, information about sensory inputs is communicated in the form of spike trains. A challenge in understanding spike trains is to assess the significance of individual spikes in encoding information. One approach is to define a spike train metric, allowing a distance to be calculated between pairs of spike trains. In a good metric, this distance will depend on the information the spike trains encode. This method has been used previously to calculate the timescale over which the precision of spike times is significant. Here, a new metric is constructed based on a simple model of synaptic conductances which includes binding site depletion. Including binding site depletion in the metric means that a given individual spike has a smaller effect on the distance if it occurs soon after other spikes. The metric proves effective at classifying neuronal responses by stimuli in the sample data set of electro-physiological recordings from the primary auditory area of the zebra finch fore-brain. This shows that this is an effective metric for these spike trains suggesting that in these spike trains the significance of a spike is modulated by its proximity to previous spikes. This modulation is a putative information-coding property of spike trains.     

A Pseudo-Markov Model for Series of Neuronal Spike Events

Spike trains of spontaneous neuronal activity in the rabbit brain are submitted to statistical analyses based on the following pseudo-Markov model. The nerve cell is supposed to alternate between a bursting and a resting state. The numbers of consecutive spikes within each state are assumed to be independent integer-valued random variables with discrete probability distributions. Given the state, the interspike intervals are independent real-valued random variables. The two state semi-Markov model is obtained as a special case when the discrete distributions are geometrical. Statistical second-order properties of recorded spike trains are compared with those predicted by the model on the basis of known first-order properties. For that purpose, serial correlation coefficients and intensity functions for spike trains produced by the model are computed. A comparison between observed and predicted results for the spontaneous activity of 17 brain cells yields a good fit in eight cells and discloses some salient features of the statistical structure in the activity of six other cells. By making it feasible to compute theoretical correlograms, the model may advance the understanding of empirical correlograms. The possibilities for integrating this statistical model of spike trains with a model of the mechanism of spike train production are discussed.     

A proposed mechanism for multiplication of neural signals

The probability of the joint occurrence of two statistically independent events is the product of the probabilities of the individual events. This fact is used to show that a neuron which detects coincident arrivals of spikes from two input neurons can function as a multiplier, i.e. its average output spike frequency is proportional to the product of the average input spike frequencies. The theoretical analysis is checked in two ways: (a) Computer simulations confirm the derived expressions for the output frequency and show that increasing the jitter in the input spike trains improves the operation of the multiplier by making the output spike train more regular (b) Experimentally recorded spike trains are used to demonstrate that the type and amount of jitter present in real spike trains is adequate for satisfactory operation of the proposed scheme for multiplication. The operating characteristics of the proposed multiplier make it an attractive candidate for the multiplicative mechanism that is involved in the optomotor response of insects.