Influence of temporal correlation of synaptic input on the rate and variability of firing in neurons

The spike trains that transmit information between neurons are stochastic. We used the theory of random point processes and simulation methods to investigate the influence of temporal correlation of synaptic input current on firing statistics. The theory accounts for two sources for temporal correlation: synchrony between spikes in presynaptic input trains and the unitary synaptic current time course. Simulations show that slow temporal correlation of synaptic input leads to high variability in firing. In a leaky integrate-and-fire neuron model with spike afterhyperpolarization the theory accurately predicts the firing rate when the spike threshold is higher than two standard deviations of the membrane potential fluctuations. For lower thresholds the spike afterhyperpolarization reduces the firing rate below the theory's predicted level when the synaptic correlation decays rapidly. If the synaptic correlation decays slower than the spike afterhyperpolarization, spike bursts can occur during single broad peaks of input fluctuations, increasing the firing rate over the prediction. Spike bursts lead to a coefficient of variation for the interspike intervals that can exceed one, suggesting an explanation of high coefficient of variation for interspike intervals observed in vivo.     

Interspike interval dependency from arterial chemoreceptors

The carotid body impulse generator has been previously characterized as a Poisson-type random process. We examined the validity of this characterization by analyzing sinus nerve spike trains for interspike interval dependency. Fifteen single chemoreceptive afferents were recorded in vivo under hypoxic-hypercapnic conditions, and approximately 1,000 consecutive interspike intervals for each fiber were timed and analyzed for serial dependence. The same set of intervals placed in shuffled order served as a control series without serial dependence. The original spike interval trains showed significantly negative first-order serial correlation coefficients and less variability in joint interval distributions than did the shuffled interval trains. These results suggest that the chemoreceptor afferent train is not random and may reflect a negative feedback system operating within the carotid body that limits variation about a mean frequency.     

Enhanced specificity of information in axons with negatively correlated adjacent interspike intervals

A model is formulated for the conversion of a motoneuron's spike train to tension in a muscle. This model demonstrates that a spike train whose adjacent interspike intervals are negatively correlated results in a steady-state tension which fluctuates less about its mean value than if the interspike intervals are randomly arranged. The ability of a spike train to develop more distinguishable levels of tension by negative correlation between adjacent interspike intervals is more significant for interspike interval distributions with greater dispersion. The number of distinguishable tension levels increases by about 33 percent when a typical set of neuromuscular parameters are used. These results may be generalized to the smoothing of postsynaptic potentials and the regulation of blood pressure.     

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.     

Extra spike formation in sensory neurons and the disruption of afferent spike patterning

The peculiar pseudounipolar geometry of primary sensory neurons can lead to ectopic generation of "extra spikes" in the region of the dorsal root ganglion potentially disrupting the fidelity of afferent signaling. We have used an explicit model of myelinated vertebrate sensory neurons to investigate the location and mechanism of extra spike formation, and its consequences for distortion of afferent impulse patterning. Extra spikes originate in the initial segment axon under conditions in which the soma spike becomes delayed and broadened. The broadened soma spike then re-excites membrane it has just passed over, initiating an extra spike which propagates outwards into the main conducting axon. Extra spike formation depends on cell geometry, electrical excitability, and the recent history of impulse activity. Extra spikes add to the impulse barrage traveling toward the spinal cord, but they also travel antidromically in the peripheral nerve colliding with and occluding normal orthodromic spikes. As a result there is no net increase in afferent spike number. However, extra spikes render firing more staccato by increasing the number of short and long interspike intervals in the train at the expense of intermediate intervals. There may also be more complex changes in the pattern of afferent spike trains, and hence in afferent signaling.     

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.     

Discharge patterns of tonically firing human motoneurones

We have attempted to reconcile the different patterns of distribution of interspike intervals that are found in motoneurones made to discharge by intracellular injection of constant current in reduced animal preparations and by voluntary control in human subjects. We recorded long spike trains from single motor units in three human muscles made to discharge at constant mean frequencies with the help of auditory and visual feedback. The distribution of interspike intervals in each spike train was analysed quantitatively. We found that the different pattern of discharge of the human motor units could be accounted for when due allowance was made for the variability of the drive to the human motoneurone which arose because of the feedback process used to maintain the target frequency. A model testing this hypothesis gave results that were qualitatively consistent with the human data.     

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.     

STDP allows fast rate-modulated coding with Poisson-like spike trains

Spike timing-dependent plasticity (STDP) has been shown to enable single neurons to detect repeatedly presented spatiotemporal spike patterns. This holds even when such patterns are embedded in equally dense random spiking activity, that is, in the absence of external reference times such as a stimulus onset. Here we demonstrate, both analytically and numerically, that STDP can also learn repeating rate-modulated patterns, which have received more experimental evidence, for example, through post-stimulus time histograms (PSTHs). Each input spike train is generated from a rate function using a stochastic sampling mechanism, chosen to be an inhomogeneous Poisson process here. Learning is feasible provided significant covarying rate modulations occur within the typical timescale of STDP (~10-20 ms) for sufficiently many inputs (~100 among 1000 in our simulations), a condition that is met by many experimental PSTHs. Repeated pattern presentations induce spike-time correlations that are captured by STDP. Despite imprecise input spike times and even variable spike counts, a single trained neuron robustly detects the pattern just a few milliseconds after its presentation. Therefore, temporal imprecision and Poisson-like firing variability are not an obstacle to fast temporal coding. STDP provides an appealing mechanism to learn such rate patterns, which, beyond sensory processing, may also be involved in many cognitive tasks.     

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     

Statistical characteristics of unit activity in spinal locomotor centers

A statistical analysis of unit activity in spinal locomotor centers was undertaken on immobilized thalamic cats at rest and during generation of efferent discharges. Activation of the spinal locomotor generator was accompanied by shortening of interspike intervals in the spike sequences of neurons and a decrease in their fluctuations. Histograms of interspike intervals became more symmetrical under these circumstances and there was a considerable increase in the number of neurons whose activity showed regular fluctuations on autocorrelation histograms. Spike trains at rest were characterized by dependence of successive intervals, which increased during efferent discharge generation. The possible mechanisms of modification of the time structure of unit activity in spinal locomotor centers during their activation are discussed.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 12, No. 2, pp. 192–198, March–April, 1980.     

Static response of infrared neurons of crotaline snakes—normal distribution of interspike intervals

Background discharges (static responses) of warm fibers in the pit organs (infrared receptive organs) of two species of crotaline snakes were recorded at various temperatures (water, 18-33 degrees C; air, 19-28 degrees C). Mean interspike intervals (means), standard deviations (SD), and coefficients of variation (CV) were calculated, and the goodness of fit of interspike interval histograms to a corresponding normal distribution (i.e., one having the same mean and SD) were tested. Means, SD, and CV were smallest at a certain temperature, which might be the optimum receptor temperature for the species. More than half of the histograms (22/42 for water, 7/10 for air) showed a normal distribution at a significance level of 0.01. This suggests that the spike intervals generated at the spike initiation site are constant, with some random error. Background discharges of three pure infrared secondary neurons from the lateral descending nucleus were analyzed in the same way and compared to the peripheral discharges. There were no histograms with a normal distribution in these central neurons, which might indicate that the constant interspike intervals which appear in the primary afferent fibers are not utilized for information processing at this level but occur only as part of a receptor mechanism which is still unknown. The discharge patterns of primary afferent fibers are also discussed in relation to the known discharge patterns of cold fibers in other animals.     

Fast coding of orientation in primary visual cortex

Understanding how populations of neurons encode sensory information is a major goal of systems neuroscience. Attempts to answer this question have focused on responses measured over several hundred milliseconds, a duration much longer than that frequently used by animals to make decisions about the environment. How reliably sensory information is encoded on briefer time scales, and how best to extract this information, is unknown. Although it has been proposed that neuronal response latency provides a major cue for fast decisions in the visual system, this hypothesis has not been tested systematically and in a quantitative manner. Here we use a simple 'race to threshold' readout mechanism to quantify the information content of spike time latency of primary visual (V1) cortical cells to stimulus orientation. We find that many V1 cells show pronounced tuning of their spike latency to stimulus orientation and that almost as much information can be extracted from spike latencies as from firing rates measured over much longer durations. To extract this information, stimulus onset must be estimated accurately. We show that the responses of cells with weak tuning of spike latency can provide a reliable onset detector. We find that spike latency information can be pooled from a large neuronal population, provided that the decision threshold is scaled linearly with the population size, yielding a processing time of the order of a few tens of milliseconds. Our results provide a novel mechanism for extracting information from neuronal populations over the very brief time scales in which behavioral judgments must sometimes be made.     

The relationship of post-stimulus time and interval histograms to the timming characteristics of spike trains.

PST (post-stimulus time) and interval histograms computed from recorded spike trains are related to an average timing characteristics of the spike train. The exact nature of this relationship varies with recording parameters, interfering signals, the histogram bin width, and the duration of the measurement interval. This work describes the conditions under which a PST histogram can serve as an unbiased estimate of the ensemble average of a spike train's intensity and an interval histogram can serve as an unbiased estimate of the probability density function of the interspike intervals. Simulation studies are used to confirm the validity of the theoretical results. As an example of an application, these results are used to analyze recordings of singleunit activity in the eight cranial nerve.     

Dependence of different spike sequences on the mean neuronal firing rate in the neocortex in vivo and in vitro

Neuronal spikes were recorded extracellularly in rabbit visual cortex in vivo (88 cells) and in surviving slices of guinea pig sensorimotor cortex in vitro (50 cells). Spike sequences (SS) with monotonically increasing (SS+) and decreasing (SS-) interspike intervals were detected. Relative number of spikes of SS in the recording was closely associated with SS generation. The relative number of spikes was plotted against the average firing rate, this function had a biphasic character with the critical point around 7 Hz. The rate of change in interspike duration (the slope) was virtually independent of the firing rate, but was significantly different in vivo and in vitro conditions for both SS+ (325 and 180 ms/s, respectively) and SS- (270 and 160 ms/s, respectively). By and large, in vivo and in vitro the spike sequence parameters depended in the average firing rate in the same manner. The role of the spike sequences in rhythmic and information processes in neocortex is discussed.     

Model of spike propagation reliability along the myelinated axon corrupted by axonal intrinsic noise sources

We investigated how selected electromorphological parameters of myelinated axons influence the preservation of interspike intervals when the propagation of action potentials is corrupted by axonal intrinsic noise. Hereby we tried to determine how the intrinsic axonal noise influences the performance of axons serving as carriers for temporal coding. The strategy of this coding supposes that interspike intervals presented to higher order neurons would minimally be deprived of information included in interspike intervals at the axonal initial segment. Our experiments were conducted using a computer model of the myelinated axon constructed in a software environment GENESIS (GEneral NEural SImulation System). We varied the axonal diameter, myelin sheath thickness, axonal length, stimulation current and channel distribution to determine how these parameters influence the role of noise in spike propagation and hence in preserving the interspike intervals. Our results, expressed as the standard deviation of spike travel times, showed that by stimulating the axons with regular rectangular pulses the interspike intervals were preserved with a microsecond accuracy. Stimulation with pulses imitating postsynaptic currents, greater changes of interspike intervals were found, but the influence of implemented noise on the jitter of interspike intervals was approximately the same.     

Model of spike propagation reliability along the myelinated axon corrupted by axonal intrinsic noise sources

We investigated how selected electromorphological parameters of myelinated axons influence the preservation of interspike intervals when the propagation of action potentials is corrupted by axonal intrinsic noise. Hereby we tried to determine how the intrinsic axonal noise influences the performance of axons serving as carriers for temporal coding. The strategy of this coding supposes that interspike intervals presented to higher order neurons would minimally be deprived of information included in interspike intervals at the axonal initial segment. Our experiments were conducted using a computer model of the myelinated axon constructed in a software environment GENESIS (GEneral NEural SImulation System). We varied the axonal diameter, myelin sheath thickness, axonal length, stimulation current and channel distribution to determine how these parameters influence the role of noise in spike propagation and hence in preserving the interspike intervals. Our results, expressed as the standard deviation of spike travel times, showed that by stimulating the axons with regular rectangular pulses the interspike intervals were preserved with a microsecond accuracy. Stimulating the axons with pulses imitating postsynaptic currents, greater changes of interspike intervals were found, but the influence of implemented noise on the jitter of interspike intervals was approximately the same.     

基于复杂性度量的心率变异信号非线性分析

假设心率变异信号是累积－发放模型（Ｉｎｔｅｇｒａｔｅ－ｆｉｒｅ）与非线性动力学系统耦合产生的峰电位链（ＳｐｉｋｅＴｒａｉｎ）。以符号动力学为基础,提出利用峰电位间隔（ｉｎｔｅｒｓｐｉｋｅｉｎｔｅｒｖａｌ,ＩＳＩ）及其随机替代数据的Ｃ１、Ｃ２复杂度来定量刻划非线性动力学系统特性。结果表明：确定性驱动产生的峰电位间隔序列可以与随机性驱动产生的峰电位间隔序列区分开。因此,在噪声干扰较强的生理信号中,尤其是在不清楚非线性动力系统变量和峰电位间隔序列之间是否存在微分同胚的情况下,以复杂性度量来代替以Ｔａｋｅｎｓ嵌入定理为基础的关联维数、Ｌｙａｐｎｏｖ指数等描述动力系统特征的方法是合适的。最后通过２类共３７个个体,每个个体的心电数据为１０００个Ｒ－Ｒ间期的微分序列检验心率变异信号的非线性结构。