急性大鼠癫痫模型海马神经元原发性单位后放电脉冲间隔特征

受到刺激后即刻出现的海马（hippocampus,HPC）原发性单位后放电是癫痫相关性细胞电活动的重要形式之一,其放电脉冲间隔（interspike interval,ISI）和串内平均频率（Hz）特征及其在网络癫痫形成中的作用值得探讨。实验用急性强直电刺激（60Hz,2S,0．4-0．6mA）大鼠右侧后背HPC（acute tetanization of the fight posterior dorsal hippocampus,以后简称ATPDH）或右侧尾壳核（acute tetanization of the fight caudate putamen nucleus,以后简称ATRC）诱导HPC或皮层网络癫痫,重点观察HPC神经元原发性单位后放电模式和上述的瞬时时间编码特征。结果表明：（1）HPC原发性单位后放电表现为两种不同的放电模式,即先易化后抑制或先抑制后易化,其ISI序列分别表现为先小后大的“头尾”式分布或先大后小的“尾头”式分布。（2）ATFDH主要引起“尾头”式（35／57串）、而ATRC主要引起“头尾”式（12／22串）ISI点分布的原发性单位后放电,串内“头”、“尾”平均持续时间均具有明显差异（P〈0．05）。（3）ATRC可以诱导双侧HPC单位后放电出现交互的“头尾”、‘呢头”式ISI点分布特征。（4）多串电刺激可以诱导HPC原发性单位后放电特征性ISI点分布重复显现。（5）特征性HPC原发性单位后放电伴随出现网络癫痫发作样高频电振荡。这提示：强直电刺激诱导的HPC神经元原发性单位后放电“头尾”或呢头”式ISI序列分布规律,可以较准确地反映所记录神经元的诱发性易化或抑制活动的程度,用于网络癫痫形成中单个成员细胞癫痫相关性电活动机制的分析。     

基于混沌降噪的神经元放电峰峰间期序列分析

围绕如何来消除神经元峰峰间期序列中随机噪声影响从而提取出决定不规则性的确定性动力学关系这个问题,本文首先简要介绍峰峰间期序列样本的制备,然后着重讨论一个简单可行的混沌时间序列降噪方法的原理和算法实现,最终将该方法运用到神经元放电活动数值模拟和实验记录到的峰峰间期时间序列样本分析中。本文分析结果再次证明神经放电活动中确实存在着不规则混沌运动,而且降噪结果进一步揭示了神经电生理实验中决定混沌放电的不连续但分段光滑的单峰函数关系     

豚鼠背侧海马锥体细胞自发放电特征

实验采用细胞外玻璃微电极采集豚鼠海马神经元放电信号,并将信号转化为峰峰间期(interspike interval,ISI)以研究麻醉和清醒状态海马锥体细胞自发放电线性和非线性特点。实验建立了豚鼠海马锥体细胞与中间神经元电生理鉴别标准;麻醉和清醒状态下豚鼠海马CA1和CA3区锥体细胞自发放电频率、时程、复杂度等无显著区别;麻醉组豚鼠海马锥体细胞ISI序列的复杂度小于清醒组,锥体细胞分型和ISI变异度等表现不同。实验表明,麻醉和清醒状态下豚鼠海马锥体细胞自发放电呈不同线性和非线性特征。传统和非线性研究手段的结合,可能较全面地反映海马锥体细胞自发放电特性。     

Fractal Stochastic Modeling of Spiking Activity in Suprachiasmatic Nucleus Neurons

Individual neurons in the suprachiasmatic nucleus (SCN), the master biological clock in mammals, autonomously produce highly complex patterns of spikes. We have shown that most (~90%) SCN neurons exhibit truly stochastic interspike interval (ISI) patterns. The aim of this study was to understand the stochastic nature of the firing patterns in SCN neurons by analyzing the ISI sequences of 150 SCN neurons in hypothalamic slices. Fractal analysis, using the periodogram, Fano factor, and Allan factor, revealed the presence of a 1/f-type power-law (fractal) behavior in the ISI sequences. This fractal nature was persistent after the application of the GABA_A receptor antagonist bicuculline, suggesting that the fractal stochastic activity is an intrinsic property of individual SCN neurons. Based on these physiological findings, we developed a computational model for the stochastic SCN neurons to find that their stochastic spiking activity was best described by a gamma point process whose mean firing rate was modulated by a fractal binomial noise. Taken together, we suggest that SCN neurons generate temporal spiking patterns using the fractal stochastic point process.Action Editor: Carson C. Chow     

Dynamics of On-Off Neural Firing Patterns and Stochastic Effects near a Sub-Critical Hopf Bifurcation

On-off firing patterns, in which repetition of clusters of spikes are interspersed with epochs of subthreshold oscillations or quiescent states, have been observed in various nervous systems, but the dynamics of this event remain unclear. Here, we report that on-off firing patterns observed in three experimental models (rat sciatic nerve subject to chronic constrictive injury, rat CA1 pyramidal neuron, and rabbit blood pressure baroreceptor) appeared as an alternation between quiescent state and burst containing multiple period-1 spikes over time. Burst and quiescent state had various durations. The interspike interval (ISI) series of on-off firing pattern was suggested as stochastic using nonlinear prediction and autocorrelation function. The resting state was changed to a period-1 firing pattern via on-off firing pattern as the potassium concentration, static pressure, or depolarization current was changed. During the changing process, the burst duration of on-off firing pattern increased and the duration of the quiescent state decreased. Bistability of a limit cycle corresponding to period-1 firing and a focus corresponding to resting state was simulated near a sub-critical Hopf bifurcation point in the deterministic Morris—Lecar (ML) model. In the stochastic ML model, noise-induced transitions between the coexisting regimes formed an on-off firing pattern, which closely matched that observed in the experiment. In addition, noise-induced exponential change in the escape rate from the focus, and noise-induced coherence resonance were identified. The distinctions between the on-off firing pattern and stochastic firing patterns generated near three other types of bifurcations of equilibrium points, as well as other viewpoints on the dynamics of on-off firing pattern, are discussed. The results not only identify the on-off firing pattern as noise-induced stochastic firing pattern near a sub-critical Hopf bifurcation point, but also offer practical indicators to discriminate bifurcation types and neural excitability types.     

Analysis of neural spike trains with interspike interval reconstruction

As a method for the analysis of neural spike trains, we examine fundamental characteristics of interspike interval (ISI) reconstruction theoretically with a leaky-integrator neuron model and experimentally with cricket wind receptor cells. Both the input to the leaky integrator and the stimulus to the wind receptor cells are the time series generated from the Rossler system. By numerical analysis of the leaky integrator, it is shown that, even if ISI reconstruction is possible, sometimes the entire structure of the R?ssler attractor may not be reconstructed with ISI reconstruction. For analysis of the in vivo physiological responses of cricket wind receptor cells, we apply ISI reconstruction, nonlinear prediction and the surrogate data method to the experimental data. As a result of the analysis, it is found that there is a significant deterministic structure in the spike trains. By this analysis of physiological data, it is also shown that, even if ISI reconstruction is possible, the entire attractor may not be reconstructed.     

A characterization of the time-rescaled gamma process as a model for spike trains

The occurrence of neuronal spikes may be characterized by not only the rate but also the irregularity of firing. We have recently developed a Bayes method for characterizing a sequence of spikes in terms of instantaneous rate and irregularity, assuming that interspike intervals (ISIs) are drawn from a distribution whose shape may vary in time. Though any parameterized family of ISI distribution can be installed in the Bayes method, the ability to detect firing characteristics may depend on the choice of a family of distribution. Here, we select a set of ISI metrics that may effectively characterize spike patterns and determine the distribution that may extract these characteristics. The set of the mean ISI and the mean log ISI are uniquely selected based on the statistical orthogonality, and accordingly the corresponding distribution is the gamma distribution. By applying the Bayes method equipped with the gamma distribution to spike sequences derived from different ISI distributions such as the log-normal and inverse-Gaussian distribution, we confirm that the gamma distribution effectively extracts the rate and the shape factor.     

周期激励下FHN模型的两种多峰分布放电节律

文章揭示了外界周期脉冲激励下神经元系统产生的随机整数倍和混沌多峰放电节律的关系.随机节律统计直方图呈多峰分布、峰值指数衰减、不可预报且复杂度接近1;混沌节律统计直方图呈不同的多峰分布,峰值非指数衰减、有一定的可预报性且复杂度小于1.混沌节律在激励脉冲周期小于系统内在周期且刺激强度较大时产生,参数范围较小;而随机节律在激励脉冲周期大于系统内在周期且脉冲刺激强度小时,可与随机因素共同作用而产生,产生的参数范围较大.上述结果揭示了两类节律的动力学特性,为区分两类节律提供了实用指标.     

Periodic and oscillatory firing patterns in identified nerve cells of Lymnaea stagnalis L

Firing patterns in identified neurons of Lymnaea stagnalis L. were analyzed by various mathematical methods including spike density function (SDF), interspike-interval histograms (ISI), Fourier transform and correlation analysis. Input-3 (IP3) events observed in most of the neurons of the respiratory regulatory system caused prominent changes in the firing frequency of the cells. Similarly, quasiperiodic firing patterns were observed in the neurons of buccal ganglia controlling feeding behavior. Apart from the known periodic patterns a fine oscillation of firing rate was observed in a large number of neurons in the visceral and parietal ganglia. The frequency of this oscillation varied between 0.2 and 0.4 Hz. The most obvious oscillatory patterns were found in the A-cells presumably resulted by periodically appearing synaptic excitation. Moderate intracellular hyperpolarizing current injection, low-Ca/high-Mg saline and application of d-tubocurarine failed to abolish the slow oscillations. Application of Ca-channel blocker cadmium, however, completely eliminated the oscillation in a reversible manner.     

大鼠视上核神经元自发放电节律的确定性机制

利用非线性动力学的方法,在多种生物数据中找到了确定性机制。大鼠下丘脑视上核（ｓｕｐｒａｏｐｔｉｃ ｎｕｃｌｅｕｓ,ＳＯＮ）神经元自发产生不规则的放电。为了研究这些不规则放电是否含有确定性机制,用电流钳对大鼠ＳＯＮ神经元进行全细胞纪录,取动作电位峰峰间期序列（ｉｎｔｅｒｓｐｉｋｅ ｉｎｔｅｒｖａｌ,ＩＳＩ）作为研究对象。采用一种新的检测时间序列非稳定周期轨道的方法分析ＩＳＩ序列,发现ＩＳＩ含有非稳定     

大鼠视上核神经元自发放电节律的确定性机制

利用非线性动力学的方法 ,在多种生物数据中找到了确定性机制。大鼠下丘脑视上核(supraopticnucleus,SON)神经元自发产生不规则的放电。为了研究这些不规则放电是否含有确定性机制 ,用电流钳对大鼠SON神经元进行全细胞纪录,取动作电位峰峰间期序列(interspikeinterval,ISI)作为研究对象。采用一种新的检测时间序列非稳定周期轨道的方法分析ISI序列 ,发现ISI含有非稳定周期轨道族 ,即周期1 ,周期2 ,和周期3存在。结果表明 ,SON神经元的自发放电序列存在确定性的动力学机制。     

Identifying type I excitability using dynamics of stochastic neural firing patterns

The stochastic firing patterns are simulated near saddle-node bifurcation on an invariant cycle corresponding to type I excitability in stochastic Morris–Lecar model. In absence of external periodic signal, the stochastic firing manifests continuous distribution in ISI histogram (ISIH), whose amplitude at first increases sharply and then decreases exponentially. In presence of the external periodic signal, stochastic firing patterns appear as two cases of integer multiple firing with multiple discrete peaks in ISIH. One manifests perfect exponential decay in all peaks and the other imperfect exponential decay except a lower first peak. These stochastic firing patterns simulated with or without external periodic signal can be demonstrated in the experiments on rat hippocampal CA1 pyramidal neurons. The exponential decay laws in the multiple peaks are also acquired using probability analysis method. The perfect decay law is determined by the independent characteristic within the firing while the imperfect decay law is from the inhibitory effect. In addition, the stochastic firing patterns corresponding to type I excitability are compared to those of type II excitability. The results not only reveal the dynamics of stochastic firing patterns with or without external signal corresponding to type I excitability, but also provide practical indicators to availably identify type I excitability.     

Processing of Auditory Midbrain Interspike Intervals by Model Neurons

A question central to sensory processing is how signal information is encoded and processed by single neurons. Stimulus features can be represented through rate coding (via firing rate), temporal coding (via firing synchronization to temporal periodicities), or temporal encoding (via intricate patterns of spike trains). Of the three, examples of temporal encoding are the least documented. One region in which temporal encoding is currently being explored is the auditory midbrain. Midbrain neurons in the plainfin midshipman generate different interspike interval (ISI) distributions depending on the frequencies of the concurrent vocal signals. However, these distributions differ only along certain lengths of ISIs, so that any neurons trying to distinguish the distributions would have to respond selectively to specific ISI ranges. We used this empirical observation as a realistic challenge with which to explore the plausibility of ISI-tuned neurons that could validate this form of temporal encoding. The resulting modeled cells—point neurons optimized through multidimensional searching—were successfully tuned to discriminate patterns in specific ranges of ISIs. Achieving this task, particularly with simplified neurons, strengthens the credibility of ISI coding in the brain and lends credence to its role in auditory processing.     

Dynamical Heterogeneity of Suprachiasmatic Nucleus Neurons Based on Regularity and Determinism

The suprachiasmatic nucleus (SCN) is known to be the master biological clock in mammals. Despite the periodic mean firing rate, interspike interval (ISI) patterns of SCN neurons are quite complex and irregular. The aim of the present study was to investigate the existence of nonlinear determinism in the complex ISI patterns of SCN neurons. ISI sequences were recorded from 173 neurons in rat hypothalamic slice preparations using a cell-attached patch recording technique. Their correlation dimensions (D₂) were estimated, and were then compared with those of the randomly-shuffled surrogate data. We found that only 16 neurons (16/173) exhibited deterministic ISI patterns of spikes. In addition, clustering analysis revealed that SCN neurons could be divided into two subgroups of neurons each having distinct values of coefficient of variation (CV) and skewness (SK). Interestingly, most deterministic SCN neurons (14/16) belonged to the group of irregularly spiking neurons having large CV and SK values. To see if the neuronal coupling mediated by the γ-aminobutyric acid (GABA), the major neurotransmitter in the SCN, contributed to the deterministic nature, we examined the effect of the GABA_A receptor antagonist bicuculline on D₂ values of 56 SCN neurons. 8 SCN neurons which were originally stochastic became to exhibit deterministic characteristics after the bicuculline application. This result suggests that the deterministic nature of the SCN neurons arises not from GABAergic synaptic interactions, but likely from properties inherent to neurons themselves.Action Editor: Barry J. Richmond     

A joint interspike interval difference stochastic spike train analysis: detecting local trends in the temporal firing patterns of single neurons

We introduce a stochastic spike train analysis method called joint interspike interval difference (JISID) analysis. By design, this method detects changes in firing interspike intervals (ISIs), called local trends, within a 4-spike pattern in a spike train. This analysis classifies 4-spike patterns that have similar incremental changes. It characterizes the higher-order serial dependence in spike firing relative to changes in the firing history. Mathematically, this spike train analysis describes the statistical joint distribution of consecutive changes in ISIs, from which the serial dependence of the changes in higher-order intervals can be determined. It is similar to the joint interspike interval (JISI) analysis, except that the joint distribution of consecutive ISI differences (ISIDs) is quantified. The graphical location of points in the JISID scatter plot reveals the local trends in firing (i.e., monotonically increasing, monotonically decreasing, or transitional firing). The trajectory of these points in the serial-JISID plot traces the time evolution of these trends represented by a 5-spike pattern, while points in the JISID scatter plot represent trends of a 4-spike pattern. We provide complete theoretical interpretations of the JISID analysis. We also demonstrate that this method indeed identifies firing trends in both simulated spike trains and spike trains recorded from cultured neurons. Received: 13 May 1997 / Accepted in revised form: 9 December 1998     

Interspike interval patterns of taste neurons in the hamster solitary nucleus

The central nervous system first processes taste informationin the solitary nucleus, which has been almost exclusively studiedin terms of average firing rate. We analyzed interspike intervals(ISI's) of 25 taste-responsive single units in the hamster (Mesocricetusauratus) solitary nucleus. ISI's were measured during spontaneousactivity and during stimulation with NaCl, KCl, sucrose, ora mixture of the three, and graphed on semi-logarithmic plots.Two different ISI patterns were evident: simple (13 units) andcomplex (12 units). Simple ISI patterns had a single broad peakat 284.7 ± 70.4 ms spontaneous and 78.8 ± 12.8ms stimulated. All complex ISI patterns had one distinct, sharppeak for an interval about 10 ms (11.3 ± 0.4 ms: spontaneous,9.3 ± 0.5 ms: stimulated), and a second, broader peakat 273.9 ± 45.9 ms spontaneous and 71.5 ± 14.6ms stimulated. As rate of firing increased peaks in ISI patternspredictably moved towards lower intervals, but ISI pattern-typedid not change. This constancy of ISI pattern held for responsesof a unit across all stimuli and did not depend upon the stimulusspecificity or location of the unit within the rostral poleof the solitary nucleus. Apparently, the pattern that a tasteneuron generates is intrinsic to the neuron and may relate tothe way it processes tast information.     

Exponential decay characteristics of the stochastic integer multiple neural firing patterns

Integer multiple neural firing patterns exhibit multi-peaks in inter-spike interval (ISI) histogram (ISIH) and exponential decay in amplitude of peaks, which results from their stochastic mechanisms. But in previous experimental observation that the decay in ISIH frequently shows obvious bias from exponential law. This paper studied three typical cases of the decay, by transforming ISI series of the firing to discrete binary chain and calculating the probabilities or frequencies of symbols over the whole chain. The first case is the exponential decay without bias. An example of this case was discovered on hippocampal CA1 pyramidal neuron stimulated by external signal. Probability calculation shows that this decay without bias results from a stochastic renewal process, in which the successive spikes are independent. The second case is the exponential decay with a higher first peak, while the third case is that with a lower first peak. An example of the second case was discovered in experiment on a neural pacemaker. Simulation and calculation of the second and third cases indicate that the dependency in successive spikes of the firing leads to the bias seen in decay of ISIH peaks. The quantitative expression of the decay slope of three cases of firing patterns, as well as the excitatory effect in the second case of firing pattern and the inhibitory effect in the third case of firing pattern are identified. The results clearly reveal the mechanism of the exponential decay in ISIH peaks of a number of important neural firing patterns and provide new understanding for typical bias from the exponential decay law.     

Firing rate of a retinal neuron are not predictable from interspike interval statistics.

The intervals between successive action potentials (impulses, or "spikes") produced the maintained firing of a neuron (ISIs) are often treated as if they were independent on each other; that is, an impulse train is considered as a stationary renewal process. If this is so, the variability of the mean rate of firing impulses in a sequence of temporal windows should be predictable from the distribution of ISIs. This was found not to be the case for the maintained firing of retinal ganglion cells in goldfish. Although some evident nonstationarity sometimes resulted in greater variability of the observed rate distributions than those predicted (for relatively long temporal windows), as a general rule the observed rate distributions were considerable less dispersed than would be predicted by sampling of the ISI distributions. This was taken as evidence of long-term serial dependency between successive ISIs; however, two standard test for dependency (autocorrelations and serial correlograms failed to to reveal structure of sufficiently long duration to account for the effect noted.     

Effect of brief inhibitory volley upon human firing motoneurons (experiment and model)

We investigated the effect of reciprocal inhibition upon single firing motoneurons of the human soleus and ex. carpus uln. A computer simulation of the effect of an inhibitory volley upon motoneuron impulse activity was carried out on the basis of our own data and data in the literature [3, 4]. It was shown that the duration of the silent period (SP), i.e., the period of complete cessation of firing as revealed on the peristimulus histogram (PSH), can be altered under the influence of the following factors: mean frequency of background firing (inverse dependence); variance of interspike intervals (ISIs) of background firing (inverse dependence); duration of that portion of an ISI of motoneuron activity during which an inhibitory volley causes a prolongation of the ISI (d); the maximum prolongation of the ISI (x_max). If _maxmax for the briefest ISI within the range of variability in background firing. If x_max>d, the duration of the SP is similar to the duration d of the briefest ISI. To a significant degree, the parameters of the peristimulus histogram thus determine the frequency and variance of ISIs in the background firing and possibly also the individual tendency of the motoneuron to respond to an inhibitory volley by prolongation of the ISI.L. A. Orbeli Institute of Biocybernetics and Biomedical Engineering PAS, Warsaw (Republic of Poland), Institute for Problems of Information Transmission, Academy of Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 23, No. 4, pp. 463–471, July–August, 1991.     

A basic bifurcation structure from bursting to spiking of injured nerve fibers in a two-dimensional parameter space

Two different bifurcation scenarios of firing patterns with decreasing extracellular calcium concentrations were observed in identical sciatic nerve fibers of a chronic constriction injury (CCI) model when the extracellular 4-aminopyridine concentrations were fixed at two different levels. Both processes proceeded from period-1 bursting to period-1 spiking via complex or simple processes. Multiple typical experimental examples manifested dynamics closely matching those simulated in a recently proposed 4-dimensional model to describe the nonlinear dynamics of the CCI model, which included most cases of the bifurcation scenarios. As the extracellular 4-aminopyridine concentrations is increased, the structure of the bifurcation scenario becomes more complex. The results provide a basic framework for identifying the relationships between different neural firing patterns and different bifurcation scenarios and for revealing the complex nonlinear dynamics of neural firing patterns. The potential roles of the basic bifurcation structures in identifying the information process mechanism are discussed.