Multi-scale detection of rate changes in spike trains with weak dependencies

The statistical analysis of neuronal spike trains by models of point processes often relies on the assumption of constant process parameters. However, it is a well-known problem that the parameters of empirical spike trains can be highly variable, such as for example the firing rate. In order to test the null hypothesis of a constant rate and to estimate the change points, a Multiple Filter Test (MFT) and a corresponding algorithm (MFA) have been proposed that can be applied under the assumption of independent inter spike intervals (ISIs). As empirical spike trains often show weak dependencies in the correlation structure of ISIs, we extend the MFT here to point processes associated with short range dependencies. By specifically estimating serial dependencies in the test statistic, we show that the new MFT can be applied to a variety of empirical firing patterns, including positive and negative serial correlations as well as tonic and bursty firing. The new MFT is applied to a data set of empirical spike trains with serial correlations, and simulations show improved performance against methods that assume independence. In case of positive correlations, our new MFT is necessary to reduce the number of false positives, which can be highly enhanced when falsely assuming independence. For the frequent case of negative correlations, the new MFT shows an improved detection probability of change points and thus, also a higher potential of signal extraction from noisy spike trains.     

Analysis of point process signals applied to motor unit firing patterns: II. Superposition of phase-locked spike trains

The different possibilities of cross-constraints between the firing patterns of a number of motor units are laid out. Correlated phasic activity is defined, and the effect of phase locking on the superposition of event sequences is being investigated by the simulation model. For superposition of four spike trains, the two cases of phase locking investigated by the model, φ=0.25 and φ=0.0 may represent an asynchroneous and synchroneous motor unit activity, respectively. A filtering method for estimation of the phase, in cases of phase-locked activity, is described.     

A Superposition Model of the Spontaneous Activity of Cerebellar Purkinje Cells

Based on physiological evidence for multiple firing zones in the dendritic arborizations of cerebellar Purkinje cells, a superposition model is proposed for spike triggering in these cells. Spike trains from 10 Purkinje cells were analyzed in terms of independence of interspike intervals and the properties of their variance-time curves. The results of this analysis were found consistent with the hypothesis that the spike train of a cerebellar Purkinje cell is the pooled output of a relatively large number of independent component processes. Simplifying assumptions as to the statistical nature of these processes lead to a very rough estimate of the number of firing zones.     

Neural coding in antennal olfactory cells of tsetse flies (Glossina spp.)

Spike trains from individual antennal olfactory cells of tsetse flies (Glossina spp.) obtained during steady-state conditions (spontaneous as well as during stimulation with 1-octen-3-ol) and dynamic stimulation with repetitive pulses of 1-octen-3-ol were investigated by studying the spike frequency and the temporal structure of the trains. In general, stimulation changes the intensity of the spike activity but leaves the underlying stochastic structure unaffected. This structure turns out to be a renewal process. The only independently varying parameter in this process is the mean interspike interval length, suggesting that olfactory cells of tsetse flies may transmit information via a frequency coding. In spike records with high firing rates, however, the stationary records had significant negative first- order serial correlation coefficients and were non-renewal. Some cells in this study were capable of precisely encoding the onset of the odour pulses at frequencies up to at least 3 Hz. Cells with a rapid return to pre-stimulus activity at the end of stimulation responded more adequately to pulsed stimuli than cells with a long increased spike frequency. While short-firing cells process information via a frequency code, long-firing cells responded with two distinctive phases: a phasic, non-renewal response and a tonic, renewal response which may function as a memory of previous stimulations.      

Neuronal spike trains and stochastic point processes. I. The single spike train

In a growing class of neurophysiological experiments, the train of impulses (“spikes”) produced by a nerve cell is subjected to statistical treatment involving the time intervals between spikes. The statistical techniques available for the analysis of single spike trains are described and related to the underlying mathematical theory, that of stochastic point processes, i.e., of stochastic processes whose realizations may be described as series of point events occurring in time, separated by random intervals. For single stationary spike trains, several orders of complexity of statistical treatment are described; the major distinction is that between statistical measures that depend in an essential way on the serial order of interspike intervals and those that are order-independent. The interrelations among the several types of calculations are shown, and an attempt is made to ameliorate the current nomenclatural confusion in this field. Applications, interpretations, and potential difficulties of the statistical techniques are discussed, with special reference to types of spike trains encountered experimentally. Next, the related types of analysis are described for experiments which involve repeated presentations of a brief, isolated stimulus. Finally, the effects of nonstationarity, e.g. long-term changes in firing rate, on the various statistical measures are discussed. Several commonly observed patterns of spike activity are shown to be differentially sensitive to such changes. A companion paper covers the analysis of simultaneously observed spike trains.     

Statistical Analysis of Motor Unit Firing Patterns in a Human Skeletal Muscle

A statistical analysis of the firing pattern of single motor units in the human brachial biceps muscle is presented. Single motor unit spike trains are recorded and analyzed. The statistical treatment of these spike trains is as stochastic point processes, the theory of which is briefly discussed. Evidence is presented that motor unit spike trains may be modelled by a renewal process with an underlying gaussian probability density. Statistical independence of successive interspike intervals is shown using scatter diagrams; the hypothesis of a gaussian distribution is accepted at the 99th percentile confidence limit, chi-square test, in 90% of the units tested. A functional relationship between the mean and standard deviation is shown and discussed; its implications in obtaining sample size are presented in an appendix.The results of higher order analysis in the form of autocorrelograms and grouped interval histograms are presented. Grouped interval histograms are discussed in the context of motor unit data, and used to confirm the hypothesis that a stable probability density function does not represent a good model of the data at this level of analysis.     

Dynamical features of higher-order correlation events: impact on cortical cells

Cortical neurons receive signals from thousands of other neurons. The statistical properties of the input spike trains substantially shape the output response properties of each neuron. Experimental and theoretical investigations have mostly focused on the second order statistical features of the input spike trains (mean firing rates and pairwise correlations). Little is known of how higher order correlations affect the integration and firing behavior of a cell independently of the second order statistics. To address this issue, we simulated the dynamics of a population of 5000 neurons, controlling both their second order and higher-order correlation properties to reflect physiological data. We then used these ensemble dynamics as the input stage to morphologically reconstructed cortical cells (layer 5 pyramidal, layer 4 spiny stellate cell), and to an integrate and fire neuron. Our results show that changes done solely to the higher-order correlation properties of the network’s dynamics significantly affect the response properties of a target neuron, both in terms of output rate and spike timing. Moreover, the neuronal morphology and voltage dependent mechanisms of the target neuron considerably modulate the quantitative aspects of these effects. Finally, we show how these results affect sparseness of neuronal representations, tuning properties, and feature selectivity of cortical cells. An erratum to this article can be found at     

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     

The stochastic properties of input spike trains control neuronal arithmetic

In the nervous system, the representation of signals is based predominantly on the rate and timing of neuronal discharges. In most everyday tasks, the brain has to carry out a variety of mathematical operations on the discharge patterns. Recent findings show that even single neurons are capable of performing basic arithmetic on the sequences of spikes. However, the interaction of the two spike trains, and thus the resulting arithmetic operation may be influenced by the stochastic properties of the interacting spike trains. If we represent the individual discharges as events of a random point process, then an arithmetical operation is given by the interaction of two point processes. Employing a probabilistic model based on detection of coincidence of random events and complementary computer simulations, we show that the point process statistics control the arithmetical operation being performed and, particularly, that it is possible to switch from subtraction to division solely by changing the distribution of the inter-event intervals of the processes. Consequences of the model for evaluation of binaural information in the auditory brainstem are demonstrated. The results accentuate the importance of the stochastic properties of neuronal discharge patterns for information processing in the brain; further studies related to neuronal arithmetic should therefore consider the statistics of the interacting spike trains.     

Motor unit activity and surface electromyogram power spectrum during increasing force of contraction

Twelve male subjects were tested to determine the relationship between motor unit (MU) activities and surface electromyogram (EMG) power spectral parameters with contractions increasing linearly from zero to 80% of maximal voluntary contraction (MVC). Intramuscular spike and surface EMG signals recorded simultaneously from biceps brachii were analyzed by means of a computer-aided intramuscular MU spike amplitude-frequency (ISAF) histogram and an EMG frequency power spectral analysis. All measurements were made in triplicate and averaged. Results indicate that there were highly significant increases in surface EMG amplitude (71 +/- 31.3 to 505 +/- 188 microV, p less than 0.01) and mean power frequency (89 +/- 13.3 to 123 +/- 23.5 Hz, p less than 0.01) with increasing force. These changes were accompanied by progressive increases in the firing frequency of MU's initially recruited, and of newly recruited MU's with relatively larger spike amplitudes. The group data in the ISAF histograms revealed significant increases in mean spike amplitude (412 +/- 79 to 972 +/- 117 microV, p less than 0.01) and mean firing frequency (17.8 +/- 5.4 to 24.7 +/- 4.1 Hz, p less than 0.01). These data suggest that surface EMG spectral analysis can provide a sensitive measure of the relative changes in MU activity during increasing force output.     

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。     

Use of `relative-phase' analysis to assess correlation between neuronal spike trains

 We propose a new method of studying the correlation between neuronal spike trains. This technique is based on the analysis of relative phase between two point processes. Relative phase here is defined as the relative timing difference between two spike trains normalized by the associated interspike interval of one cell. This phase measurement is intended to reveal the relative timing relationship between spike trains atdifferent firing rates. We apply this method to a numerical example and an example from two cerebellar neuronal spike trains of a behaving rat. The results are compared with classical cross-correlation analysis. We show that the technique can avoid some of the limitations of cross-correlation methods, reveal certain statistical dependencies that cannot be shown by cross correlation, and provide information as to the direction of influence between two spike trains. Received: 8 November 2001 / Accepted: 30 September 2002 / Published online: 24 January 2003 Correspondence to: Y. Chen (e-mail: chen@nsi.edu, Fax: + 1-858-626-2099) Acknowledgements. Research for this paper was supported by the Alafi Family Foundation and the Neurosciences Research Foundation.     

Establishing a Statistical Link between Network Oscillations and Neural Synchrony

Pairs of active neurons frequently fire action potentials or “spikes” nearly synchronously (i.e., within 5 ms of each other). This spike synchrony may occur by chance, based solely on the neurons’ fluctuating firing patterns, or it may occur too frequently to be explicable by chance alone. When spike synchrony above chances levels is present, it may subserve computation for a specific cognitive process, or it could be an irrelevant byproduct of such computation. Either way, spike synchrony is a feature of neural data that should be explained. A point process regression framework has been developed previously for this purpose, using generalized linear models (GLMs). In this framework, the observed number of synchronous spikes is compared to the number predicted by chance under varying assumptions about the factors that affect each of the individual neuron’s firing-rate functions. An important possible source of spike synchrony is network-wide oscillations, which may provide an essential mechanism of network information flow. To establish the statistical link between spike synchrony and network-wide oscillations, we have integrated oscillatory field potentials into our point process regression framework. We first extended a previously-published model of spike-field association and showed that we could recover phase relationships between oscillatory field potentials and firing rates. We then used this new framework to demonstrate the statistical relationship between oscillatory field potentials and spike synchrony in: 1) simulated neurons, 2) in vitro recordings of hippocampal CA1 pyramidal cells, and 3) in vivo recordings of neocortical V4 neurons. Our results provide a rigorous method for establishing a statistical link between network oscillations and neural synchrony.     

Intramuscular and surface electromyogram changes during muscle fatigue

Twelve male subjects were tested to determine the effects of motor unit (MU) recruitment and firing frequency on the surface electromyogram (EMG) frequency power spectra during sustained maximal voluntary contraction (MVC) and 50% MVC of the biceps brachii muscle. Both the intramuscular MU spikes and surface EMG were recorded simultaneously and analyzed by means of a computer-aided intramuscular spike amplitude-frequency histogram and frequency power spectral analysis, respectively. Results indicated that both mean power frequency (MPF) and amplitude (rmsEMG) of the surface EMG fell significantly (P less than 0.001) together with a progressive reduction in MU spike amplitude and firing frequency during sustained MVC. During 50% MVC there was a significant decline in MPF (P less than 0.001), but this decline was accompanied by a significant increase in rmsEMG (P less than 0.001) and a progressive MU recruitment as evidenced by an increased number of MUs with relatively large spike amplitude. Our data suggest that the surface EMG amplitude could better represent the underlying MU activity during muscle fatigue and the frequency powers spectral shift may or may not reflect changes in MU recruitment and rate-coding patterns.     

大鼠初级传入纤维与脊髓背角神经元间的动作电序列的突触传递

外周感觉神经元通过动作电位序列对信号进行编码,这些动作电位序列经过突触传递最终到达脑部。但是各种脉冲序列如何通过神经元之间的化学突触进行传递依然是一个悬而未决的问题。研究了初级传入A6纤维与背角神经元之间各种动作电位序列的突触传递过程。用于刺激的规则,周期、随机脉冲序列由短簇脉冲或单个脉冲构成。定义“事件”(event)为峰峰问期(intefspike interval)小于或等于规定阈值的最长动作电位串,然后从脉冲序列中提取事件间间期(interevent interval,IEI)。用时间,IEI图与回归映射的方法分析IEI序列,结果表明在突触后输出脉冲序列中可以检测到突触前脉冲序列的主要时间结构特征,特别是在短簇脉冲作为刺激单位时。通过计算输入与输出脉冲序列的互信息,发现短簇脉冲可以更可靠地跨突触传递由输入序列携带的神经信息。这些结果表明外周输入脉冲序列的主要时间结构特征可以跨突触传递,在突触传递神经信息的过程中短簇脉冲更为有效。这一研究在从突触传递角度探索神经信息编码方面迈出了一步。     

Estimating summary statistics in the spike-train space

Estimating sample averages and sample variability is important in analyzing neural spike trains data in computational neuroscience. Current approaches have focused on advancing the use of parametric or semiparametric probability models of the underlying stochastic process, where the probabilistic distribution is characterized at each time point with basic statistics such as mean and variance. To directly capture and analyze the average and variability in the observation space of the spike trains, we focus on a data-driven approach where statistics are defined and computed in a function space in which the spike trains are viewed as individual points. Based on the definition of a “Euclidean” metric, a recent paper introduced the notion of the mean of a set of spike trains and developed an efficient algorithm to compute it under some restrictive conditions. Here we extend this study by: (1) developing a novel algorithm for mean computation that is quite general, and (2) introducing a notion of covariance of a set of spike trains. Specifically, we estimate the covariance matrix using the geometry of the warping functions that map the mean spike train to each of the spike trains in the dataset. Results from simulations as well as a neural recording in primate motor cortex indicate that the proposed mean and covariance successfully capture the observed variability in spike trains. In addition, a “Gaussian-type” probability model (defined using the estimated mean and covariance) reasonably characterizes the distribution of the spike trains and achieves a desirable performance in the classification of the spike trains.     

Computing Complex Visual Features with Retinal Spike Times

Neurons in sensory systems can represent information not only by their firing rate, but also by the precise timing of individual spikes. For example, certain retinal ganglion cells, first identified in the salamander, encode the spatial structure of a new image by their first-spike latencies. Here we explore how this temporal code can be used by downstream neural circuits for computing complex features of the image that are not available from the signals of individual ganglion cells. To this end, we feed the experimentally observed spike trains from a population of retinal ganglion cells to an integrate-and-fire model of post-synaptic integration. The synaptic weights of this integration are tuned according to the recently introduced tempotron learning rule. We find that this model neuron can perform complex visual detection tasks in a single synaptic stage that would require multiple stages for neurons operating instead on neural spike counts. Furthermore, the model computes rapidly, using only a single spike per afferent, and can signal its decision in turn by just a single spike. Extending these analyses to large ensembles of simulated retinal signals, we show that the model can detect the orientation of a visual pattern independent of its phase, an operation thought to be one of the primitives in early visual processing. We analyze how these computations work and compare the performance of this model to other schemes for reading out spike-timing information. These results demonstrate that the retina formats spatial information into temporal spike sequences in a way that favors computation in the time domain. Moreover, complex image analysis can be achieved already by a simple integrate-and-fire model neuron, emphasizing the power and plausibility of rapid neural computing with spike times.     

Multifractal analysis of wide dynamic range neuron discharge profiles in normal rats and in rats with sciatic nerve constriction

Using normal rats and rats with a chronic constriction injury of the sciatic nerve (injured, model of Bennett-Xie) we investigated the possibility of classifying, by statistical tools, the temporal sequences of neuronal discharges during different noxious and non-noxious stimuli. An analysis was made of both the distribution of the inter-spike intervals and the temporal density of spike trains, the latter being studied within the framework of stochastic universal multifractals, to allow the identification of different random processes involved in the discharge distributions through the Levy index alpha. The statistical analysis shows that the parametrization based on the Levy index seems able to discriminate between different noxious stimuli (mechanical pinching and thermal), both in normal and injured animals. Furthermore, comparing normal and injured animals, although the spontaneous basal and non-noxious stimuli (brushing) evoked activities presented different frequencies, these seem to have the same multifractal structure, while the corresponding statistics of the inter-spike intervals are quite different. This information might be relevant to the understanding of a code of neuronal firing and to the modelling of temporal patterns in acute and chronic noxious signals.     

Changes in interspike interval during propagation: Quantitative description

The intervals between nerve impulses can change substantially during propagation because of conduction velocity aftereffects of previous impulse activity. Effects of such changes on interval histograms and on statistical parameters of spike trains were evaluated for Poisson spike trains and for trains generated by a clock with added random delays. The distribution of short intervals was significantly changed during propagation for these spike trains. Substantial changes in serial correlation coefficients were found in trains with certain initial interval distributions. The relevance of these effects to neural coding is discussed.