Measuring spike pattern reliability with the Lempel-Ziv-distance

Spike train distance measures serve two purposes: to measure neuronal firing reliability, and to provide a metric with which spike trains can be classified. We introduce a novel spike train distance based on the Lempel-Ziv complexity that does not require the choice of arbitrary analysis parameters, is easy to implement, and computationally cheap. We determine firing reliability in vivo by calculating the deviation of the mean distance of spike trains obtained from multiple presentations of an identical stimulus from a Poisson reference. Using both the Lempel-Ziv-distance (LZ-distance) and a distance focussing on coincident firing, the pattern and timing reliability of neuronal firing is determined for spike data obtained along the visual information processing pathway of macaque monkey (LGN, simple and complex cells of V1, and area MT). In combination with the sequential superparamagnetic clustering algorithm, we show that the LZ-distance groups together spike trains with similar but not necessarily synchronized firing patterns. For both applications, we show how the LZ-distance gives additional insights, as it adds a new perspective on the problem of firing reliability determination and allows neuron classifications in cases, where other distance measures fail.     

Spike trains in rat periaqueductal gray depend on the stochastic properties of interacting electrical stimulation trains

Spike trains flowing into the periaqueductal gray (PAG) might be discriminated from one another by PAG neurons on the basis of the distribution or sequence of their respective interspike intervals. The various sequences of interspike intervals characteristic of spontaneous PAG unit activities were assessed in a preliminary experiment. These sequences were then simulated by means of appropriate mathematical functions. These functions allowed the production of stimulation trains that were applied to two PAG sites to induce spike trains with similar sequences in order to reveal the sensitivity of PAG neurons to the stochastic structure of afferent spike trains. We placed emphasis on parameters of the spike train that proved to be altered independently of any alteration of the corresponding parameters in the stimulation train. The mean pulse rate is the simplest example of such a parameter as it was never altered in the stimulation train. Alterations of either the distribution or sequence of pulses in the stimulation train were found to affect the mean discharge rate in a number of cases (30-40% of the cases). Despite their moderate degree (20-30% mean rate alteration) such differential effects could correspond to stimulation-induced differential behavioral effects as was shown in a previous study. Furthermore, a specific dependence of the generated spike trains on the sequential structure of the stimulation train was observed in some cases when appropriate stimulation trains were simultaneously applied to another PAG stimulation site. This fact is worth considering in relation to the integrative function of the PAG neuronal network.     

Optimization of population decoding with distance metrics

Recent advances in multi-electrode recording and imaging techniques have made it possible to observe the activity of large populations of neurons. However, to take full advantage of these techniques, new methods for the analysis of population responses must be developed. In this paper, we present an algorithm for optimizing population decoding with distance metrics. To demonstrate the utility of this algorithm under experimental conditions, we evaluate its performance in decoding both population spike trains and calcium signals with different correlation structures. Our results demonstrate that the optimized decoder outperforms other simple population decoders and suggest that optimization could serve as a tool for quantifying the potential contribution of individual cells to the population code.     

A nonparametric approach for detection of bursts in spike trains

In spike-train data, bursts are considered as a unit of neural information and are of potential interest in studies of responses to any sensory stimulus. Consequently, burst detection appears to be a critical problem for which the Poisson-surprise (PS) method has been widely used for 20 years. However, this method has faced some recurrent criticism about the underlying assumptions regarding the interspike interval (ISI) distributions. In this paper, we avoid such assumptions by using a nonparametric approach for burst detection based on the ranks of ISI in the entire spike train. Similar to the PS statistic, a “Rank surprise” (RS) statistic is extracted. A new algorithm performing an exhaustive search of bursts in the spike trains is also presented. Compared to the performances of the PS method on realizations of gamma renewal processes and spike trains recorded in cat auditory cortex, we show that the RS method is very robust for any type of ISI distribution and is based on an elementary formalization of the definition of a burst. It presents an alternative to the PS method for non-Poisson spike trains and is simple to implement.     

Fast algorithm for the metric-space analysis of simultaneous responses of multiple single neurons

Spike train metrics quantify the notion of dissimilarity, or distance, between spike trains and between multineuronal responses (J. Neurophysiol. 76 (1996) 1310, Network 8 (1997) 127). We present a new algorithm for the implementation of a metric based on the timing of individual spikes and on their neurons of origin. This algorithm surpasses the earlier approach in speed by a factor that grows exponentially with the number of neurons, substantially extending the applicability of metric space methods to the study of coding in larger neuronal populations.     

Statistical technique for analysing functional connectivity of multiple spike trains

A new statistical technique, the Cox method, used for analysing functional connectivity of simultaneously recorded multiple spike trains is presented. This method is based on the theory of modulated renewal processes and it estimates a vector of influence strengths from multiple spike trains (called reference trains) to the selected (target) spike train. Selecting another target spike train and repeating the calculation of the influence strengths from the reference spike trains enables researchers to find all functional connections among multiple spike trains. In order to study functional connectivity an "influence function" is identified. This function recognises the specificity of neuronal interactions and reflects the dynamics of postsynaptic potential. In comparison to existing techniques, the Cox method has the following advantages: it does not use bins (binless method); it is applicable to cases where the sample size is small; it is sufficiently sensitive such that it estimates weak influences; it supports the simultaneous analysis of multiple influences; it is able to identify a correct connectivity scheme in difficult cases of "common source" or "indirect" connectivity. The Cox method has been thoroughly tested using multiple sets of data generated by the neural network model of the leaky integrate and fire neurons with a prescribed architecture of connections. The results suggest that this method is highly successful for analysing functional connectivity of simultaneously recorded multiple spike trains.     

Wavelet-based processing of neuronal spike trains prior to discriminant analysis

Investigations of neural coding in many brain systems have focused on the role of spike rate and timing as two means of encoding information within a spike train. Recently, statistical pattern recognition methods, such as linear discriminant analysis (LDA), have emerged as a standard approach for examining neural codes. These methods work well when data sets are over-determined (i.e., there are more observations than predictor variables). But this is not always the case in many experimental data sets. One way to reduce the number of predictor variables is to preprocess data prior to classification. Here, a wavelet-based method is described for preprocessing spike trains. The method is based on the discriminant pursuit (DP) algorithm of Buckheit and Donoho [Proc. SPIE 2569 (1995) 540-51]. DP extracts a reduced set of features that are well localized in the time and frequency domains and that can be subsequently analyzed with statistical classifiers. DP is illustrated using neuronal spike trains recorded in the motor cortex of an awake, behaving rat [Laubach et al. Nature 405 (2000) 567-71]. In addition, simulated spike trains that differed only in the timing of spikes are used to show that DP outperforms another method for preprocessing spike trains, principal component analysis (PCA) [Richmond and Optican J. Neurophysiol. 57 (1987) 147-61].     

A simple indicator of nonstationarity of firing rate in spike trains

The assessment of stationarity of firing rate in neural spike trains is important but is often performed only visually. Facing the growing amount of neural data generated by multi-electrode recording, there is a need for an automatic method to identify and disqualify spike trains with highly nonstationary firing rates. In this report, we propose a simple test of nonstationarity, associated with an indicator quantifying the degree of nonstationary in a spike train. This method is compared to the Mann-Kendall test of trend detection and the Runs test on simulated and real spike trains.     

Testing a neural coding hypothesis using surrogate data

Determining how a particular neuron, or population of neurons, encodes information in their spike trains is not a trivial problem, because multiple coding schemes exist and are not necessarily mutually exclusive. Coding schemes generally fall into one of two broad categories, which we refer to as rate and temporal coding. In rate coding schemes, information is encoded in the variations of the average firing rate of the spike train. In contrast, in temporal coding schemes, information is encoded in the specific timing of the individual spikes that comprise the train. Here, we describe a method for testing the presence of temporal encoding of information. Suppose that a set of original spike trains is given. First, surrogate spike trains are generated by randomizing each of the original spike trains subject to the following constraints: the local average firing rate is approximately preserved, while the overall average firing rate and the distribution of primary interspike intervals are perfectly preserved. These constraints ensure that any rate coding of information present in the original spike trains is preserved in the members of the surrogate population. The null-hypothesis is rejected when additional information is found to be present in the original spike trains, implying that temporal coding is present. The method is validated using artificial data, and then demonstrated using real neuronal data.     

Dynamic programming algorithms for comparing multineuronal spike trains via cost-based metrics and alignments

Cost-based metrics formalize notions of distance, or dissimilarity, between two spike trains, and are applicable to single- and multineuronal responses. As such, these metrics have been used to characterize neural variability and neural coding. By examining the structure of an efficient algorithm [Aronov D, 2003. Fast algorithm for the metric-space analysis of simultaneous responses of multiple single neurons. J Neurosci Methods 124(2), 175-79] implementing a metric for multineuronal responses, we determine criteria for its generalization, and identify additional efficiencies that are applicable when related dissimilarity measures are computed in parallel. The generalized algorithm provides the means to test a wide range of coding hypotheses.     

Information trains. The technique and its uses in spike train and network analysis, with examples taken from the nucleus parabrachialis medialis during sleep-waking states

We describe an analytical procedure for assessing functional interactions between neuronal spike trains based on the outcome of cross-correlation procedures. Subsets of a reference cell spike train in a two-train recording are extracted, based on their time-locked relationship to spikes in the dependent train. Such timing relationships comprise the significant primary structures in the cross-correlogram. Different subsets can be extracted for different primary structures in the same correlogram (i.e. a subset responsible for an interaction effect, a subset responsible for a shared input effect, etc.) These new spike trains represent an information transfer process across synapses. These ‘information trains’ may be compared and correlated to different cells of the network across different functional conditions such as sleep-waking states, and may also be subjected to conventional spike train analysis techniques such as rate histogram, auto-correlation and cross-correlation procedures. We illustrate the information train procedures with a network analysis of a set of cells recorded in the nucleus parabrachialis medialis during different sleep-waking states.     

Single unit analysis of the human ventral thalamic nuclear group: correlation of thalamic "tremor cells" with the 3-6 Hz component of parkinsonian tremor

Although cells firing at tremor frequency, called "tremor cells" (Guiot et al., 1962), have often been recorded in the thalamus of parkinsonian patients, the extent of correlation between these spike trains and tremor has rarely been assessed quantitatively. This paper describes spectral cross-correlation functions calculated between the activity of "tremor cells" and electromyogram (EMG) signals recorded from several muscles in the contralateral arm. The power occurring in the spike train at tremor frequency was described in absolute terms by the spike autopower, and in relation to the average for all spectral components by the spike autopower signal-to-noise ratio (spike autopower SNR). The probability of significant cross-correlation between the thalamic spike train and EMG at tremor frequency was assessed by the coherence at tremor frequency. Autopower spectra of the activity of many of these cells exhibited a concentration of power at tremor frequency, indicated by spike autopower SNRs as high as 18. Of the EMG signals studied, signals recorded from finger flexors were most often significantly correlated at tremor frequency. Significant correlation between the thalamic spike train and finger flexor EMG activity was found in 34% of cells analyzed. Tremor frequency coherence was significantly correlated with tremor frequency spike autopower (r = 0.46, p less than 0.0001) and spike autopower SNR (r = 0.533, p less than 0.0001). The proportion of cells with a spike autopower SNR greater than 2 that were significantly correlated with finger flexor EMG activity was greater than that of cells with a spike autopower SNR of less than 2 (p less than 0.001; chi-square). Therefore, cells exhibiting a large amount of power at tremor frequency were those best correlated with EMG activity during tremor. Some of these cells may be involved in the generation of tremor.     

Cerebellar units show several types of long-lasting posttetanic responses to telencephalic stimulation in catfish

Extracellular spikes from Purkinje and eurydendroid cells as well as evoked field potentials were recorded from the cerebellum in a catfish following trains of 50-100 stimuli at 2-10 Hz delivered to the area dorsalis centralis (Dc) of the telencephalon. Forty out of 48 Purkinje cells tested showed some response, either an increase or a decrease in the level of ongoing spike discharge following the 10- to 25-second tetanic pulse trains. The altered level lasted for greater than 3 min. Four out of 16 eurydendroid cells showed an increase in posttrain ongoing discharge; none showed a decrease. In those Purkinje cells responding to single pulse stimulation with early excitation, that response was converted to early inhibition during the later cycles of a tetanic pulse train. When tested with posttrain stimulation, they resumed the pretrain early excitation about 100 s after the train; before that, the recovery stages are complex, neither a simple continuation of, nor a simple rebound from, the later cycles of the stimulus train. Bursting discharge of Purkinje cells is often induced or, if already present, enhanced and regularized, typically at approximately 3/s, by train stimulation of Dc. This pattern begins during the train but continues for tens of seconds after its end. The effects of a stimulus train on the mean frequency and on the pattern of ongoing discharge depend on the train parameters: intensity, duration and stimulus rate within the train; 4-5 Hz is most effective. Higher rates or repeated trains produce a more intense but shorter-lasting effect. Evoked field potentials change during a train, and posttrain test stimuli show a slow recovery, especially after longer pulse trains. The cerebrocerebellar influence in a teleost is nontrivial, widespread, differentiated and shows long-lasting posttetanic plasticity.     

Single-trial estimation of neuronal firing rates: from single-neuron spike trains to population activity

We present a method to estimate the neuronal firing rate from single-trial spike trains. The method, based on convolution of the spike train with a fixed kernel function, is calibrated by means of simulated spike trains for a representative selection of realistic dynamic rate functions. We derive rules for the optimized use and performance of the kernel method, specifically with respect to an effective choice of the shape and width of the kernel functions. An application of our technique to the on-line, single-trial reconstruction of arm movement trajectories from multiple single-unit spike trains using dynamic population vectors illustrates a possible use of the proposed method.     

Identification of bursts in spike trains.

A computer algorithm to identify 'bursts' in trains of spikes is described. The algorithm works by constructing a histogram of interspike intervals, then analyzing the histogram to detect the critical interval value in the distribution that represents the break between short intervals within a burst and the longer intervals between bursts. When such a value is found, it is used as the 'threshold' to determine those intervals in the spike train that lie within a burst and those that lie between bursts and, thereby, to identify the beginning and end of each burst in the train. The validity of the bursts is evaluated with a chi-square test. The performance of the algorithm and how it can be assessed is discussed.     

Functional significance of the apamin-sensitive conductance in rat locus coeruleus neurons

The effects of apamin on rat locus coeruleus (LC) neurons were studied in a brain slice preparation with intracellular recording. Bath application of apamin (2–500 nM) reduced the amplitude of an intermediate component of the afterhyperpolarization (AHP) following single spontaneous action potentials, but did not change the size or time-course of fast and slow components of the AHP, spike amplitude or duration. Apamin blocked the early component of the post-stimulus hyperpolarization (PSH) which follows a train of action potentials. The size of the late component of PSH was sometimes augmented by apamin. Apamin increased the number of spikes evoked by a depolarizing current pulse and increased the slope of the spike frequency-current intensity relation. Accommodation of firing during long depolarizing pulses showed a biexponential time-course indicating 2 distinct components. Apamin specifically reduced the contribution of the fast component of accommodation and increased its time constant. These data indicate that the apamin-sensitive conductance is functionally important in accommodation at faster firing rates such as those seen during evoked spike trains in the present experiments, and which may occur in vivo during behavioral arousal and in anxiety or drug withdrawal syndromes.     

An efficient algorithm for continuous time cross correlogram of spike trains

We propose an efficient algorithm to compute the smoothed correlogram for the detection of temporal relationship between two spike trains. Unlike the conventional histogram-based correlogram estimations, the proposed algorithm operates on continuous time and does not bin either the spike train nor the correlogram. Hence it can be more precise in detecting the effective delay between two recording sites. Moreover, it can take advantage of the higher temporal resolution of the spike times provided by the current recording methods. The Laplacian kernel for smoothing enables efficient computation of the algorithm. We also provide the basic statistics of the estimator and a guideline for choosing the kernel size. This new technique is demonstrated by estimating the effective delays in a neuronal network from synthetic data and recordings of dissociated cortical tissue.     

Contribution of Ca2+-activated K+ channels to hyperpolarizing after-potentials and discharge pattern in rat supraoptic neurones

The contribution of Ca(2+)-activated K(+) channels to hyperpolarizing after-potentials (HAP) of action potentials, to spike-frequency adaptation and thus to the shaping of discharge pattern, was examined in rat supraoptic magnocellular neurosecretory cells. In addition, the expression of BK channels and SK3 subunits of SK channels was studied using double immunofluorescence detection. The presence of BK channels and SK3 subunits was detected in many supraoptic neurones containing either vasopressin or oxytocin. Current-clamp recordings of current-induced spike trains revealed that HAPs comprise a fast and a slow HAP (fHAP and sHAP). Correlation analyses revealed that the increase of the fHAP in amplitude and spike broadening were correlated to a moderate gradual increase of the interspike interval and thus to weak spike-frequency adaptation. By contrast, marked prolongation of the interspike interval and strong spike-frequency adaptation depended on the appearance and on the amplitude of the sHAP. The sHAP and spike-frequency adaptation were blocked by cadmium, as well as by the SK channel antagonist apamin. The fHAP was attenuated by the BK channel antagonist iberiotoxin (IbTX), by the BK/IK channel antagonist charybdotoxin (ChTX) and by apamin. ChTX attenuated fHAPs throughout the entire spike train. By contrast, the IbTX-induced attenuation of the fHAP was restricted to the initial part of the spike train, while the apamin-induced attenuation slowly increased with the progression of the spike train. These results suggest that strong spike-frequency adaptation in supraoptic neurones essentially depends on the generation of the sHAP by activation of SK channels. Comparison of effects of IbTX, ChTX and apamin suggests a complementary contribution of SK-, BK- and IK-channels to fHAPs.     

Developments in understanding neuronal spike trains and functional specializations in brain regions.

Understanding information processing at the neuronal level would provide valuable insights to computational intelligence research and computational neuroscience. In particular, understanding constraints on neuronal spike trains would provide indication about the type of syntactic rules used by neurons when processing information. A recent discovery, reported here, was made through analyzing microelectrode recordings (MER) made during surgical procedure in humans. Analysis of MERs of extracellular neuronal activity has gained increasing interest due to potential improvements to surgical techniques involving ablation or placement of deep brain stimulators, done in the treatment of advanced Parkinson's disease. Important to these procedures is the identification of different brain structures such as the globus pallidus internus from the spike train being recorded from the intracranial probe tip during surgery. Spike train data gathered during surgical procedure from multiple patients were processed using a novel feature extraction method reported here. Distinct structures within the spike trains were identified and used to build an effective brain region classifier. The extracted features upon analysis provide some insight into the 'syntactic' constraint on spike trains.