Analysis of discharges recorded simultaneously from pairs of auditory nerve fibers.

Spike trains were recorded simultaneously from pairs of auditory nerve fibres in anesthetized cats. Tests for correlation between spike trains were developed for spontaneous activity and for discharge patterns resulting from single-tone stimuli. The application of these tests to the recordings indicates that the responses of auditory nerve fibers to a tone and to silence can be described as statistically independent point processes. This result implies that the initiation of spikes in these fibers is governed by localized processes specific for each fiber.     

Reconstruction of Underlying Nonlinear Deterministic Dynamics Embedded in Noisy Spike Trains

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

The role of individual spikes and spike patterns in population coding of stimulus location in rat somatosensory cortex

This report addresses the nature of population coding in sensory cortex by applying information theoretic analysis to data recorded simultaneously from neuron pairs located in primary somatosensory cortex of anaesthetised rats. We studied how cortical spike trains code for the location of a whisker stimulus on the rat's snout. We found that substantially more information was conveyed by 10 ms precision spike timing compared with that conveyed by the number of spikes counted over a 40 ms response interval. Most of this information was accounted for by the timing of individual spikes. In particular, it was the first post-stimulus spikes that were crucial. Spike patterns within individual cells played a smaller role; spike patterns across cells were negligible. This pattern of results was robust both to the exact nature of the stimulus set and to the precision at which spikes were binned.     

Recurrence plots of neuronal spike trains

The recently developed qualitative method of diagnosis of dynamical systems — recurrence plots has been applied to the analysis of dynamics of neuronal spike trains recorded from cerebellum and red nucleus of anesthetized cats. Recurrence plots revealed robust and common changes in the similarity structure of interspike interval sequences as well as significant deviations from randomness in serial ordering of intervals. Recurring episodes of alike, quasi-deterministic firing patterns suggest the spontaneous modulation of the dynamical complexity of the trajectories of observed neurons. These modulations are associated with changing dynamical properties of a neuronal spike-train-generating system. Their existence is compatible with the information processing paradigm of attractor neural networks.     

Cross-intensity functions and the estimate of spike-time jitter

Correlation measures are important tools for the analysis of simultaneously recorded spike trains. A well-known measure with probabilistic interpretation is the cross-intensity function (CIF), which is an estimate of the conditional probability that a neuron spikes as a function of the time lag to spikes in another neuron. The non-commutative nature of the CIF is particularly useful when different neuron classes are studied that can be distinguished based on their anatomy or physiology. Here we explore the utility of the CIF for estimating spike-time jitter in synaptic interactions between neuron pairs of connected classes. When applied to spike train pairs from sleeping songbirds, we are able to distinguish fast synaptic interactions mediated primarily by AMPA receptors from slower interactions mediated by NMDA receptors. We also find that spike jitter increases with the time lag between spikes, reflecting the accumulation of noise in neural activity sequences, such as in synfire chains. In conclusion, we demonstrate some new utility of the CIF as a spike-train measure.     

Spike sequences and their consequences

Spatio-temporal patterns of spikes have an advantage of representing information by their spike composition similar to words of languages. First we review the models of neuronal coding, then we discuss technical aspects of detecting spatio-temporal spike patterns. We argue by presenting data from rat hippocampus that spike trains recorded simultaneously from multiple pyramidal cells are not independent. Their hidden dependency structure can be revealed by spike 'sequences', defined as a set of neurons which fire in a specific temporal order with certain delay between successive spikes. The only way to prove their existence in vivo is to show that they recur with higher than by-chance frequency. We observed that 'sequences' possess 'compositional' features and that a given spike composition is time scale invariant. We illustrate that the same neuron can be a part of different 'sequences' and 'sequences' recur in a temporally compressed fashion during slow wave sleep. The statistical significance of 'sequences' is testable. Their biological significance has been implicated by experiments where recurrence rate of the sequences during different behavioral sessions were compared. As consistent with the 'replay hypothesis' of memory consolidation, new sequences generated during the wake state are persistent during the subsequent sleep. Thus, information acquired during the wake state and represented by spatio-temporal patterns of spikes may transfer to the neocortex during sleep. Our results suggest that 'sequences' reflect the activation of specific but configurable circuitries during exploratory behavior, followed by spontaneous re-activation of the same circuitry during sleep. Whether the delay structure of spikes as a combination is an effective input to single neurons downstream or 'sequence' components are being processed in parallel pathways and evaluated independently is an open question.     

Reliability of spike and burst firing in thalamocortical relay cells

The reliability and precision of the timing of spikes in a spike train is an important aspect of neuronal coding. We investigated reliability in thalamocortical relay (TCR) cells in the acute slice and also in a Morris-Lecar model with several extensions. A frozen Gaussian noise current, superimposed on a DC current, was injected into the TCR cell soma. The neuron responded with spike trains that showed trial-to-trial variability, due to amongst others slow changes in its internal state and the experimental setup. The DC current allowed to bring the neuron in different states, characterized by a well defined membrane voltage (between ?80 and ?50 mV) and by a specific firing regime that on depolarization gradually shifted from a predominantly bursting regime to a tonic spiking regime. The filtered frozen white noise generated a spike pattern output with a broad spike interval distribution. The coincidence factor and the Hunter and Milton measure were used as reliability measures of the output spike train. In the experimental TCR cell as well as the Morris-Lecar model cell the reliability depends on the shape (steepness) of the current input versus spike frequency output curve. The model also allowed to study the contribution of three relevant ionic membrane currents to reliability: a T-type calcium current, a cation selective h-current and a calcium dependent potassium current in order to allow bursting, investigate the consequences of a more complex current-frequency relation and produce realistic firing rates. The reliability of the output of the TCR cell increases with depolarization. In hyperpolarized states bursts are more reliable than single spikes. The analytically derived relations were capable to predict several of the experimentally recorded spike features.     

The correlation grid: analysis of synchronous spiking in multi-dimensional spike train data and identification of feasible connection architectures

This paper presents a visualization technique specifically designed to support the analysis of synchronous firings in multiple, simultaneously recorded, spike trains. This technique, called the correlation grid, enables investigators to identify groups of spike trains, where each pair of spike trains has a high probability of generating spikes approximately simultaneously or within a constant time shift. Moreover, the correlation grid was developed to help solve the following reverse problem: identification of the connection architecture between spike train generating units, which may produce a spike train dataset similar to the one under analysis. To demonstrate the efficacy of this approach, results are presented from a study of three simulated, noisy, spike train datasets. The parameters of the simulated neurons were chosen to reflect the typical characteristics of cortical pyramidal neurons. The schemes of neuronal connections were not known to the analysts. Nevertheless, the correlation grid enabled the analysts to find the correct connection architecture for each of these three data sets.     

Estimation of the individual firing frequencies of two neurons recorded with a single electrode

When monitoring neurons with a single extracellular electrode, it is common to record action potentials from different neurons. A recurring problem with such recordings is to identify which neuron is active. Sorting spikes into separate classes is possible if each neuron discharge spikes differing by their shapes and sizes. However, this approach is not applicable when the spikes are indistinguishable. In this paper, we develop a method for estimating the respective firing frequencies of two neurons, producing indistinguishable spikes. It is based on the fact that, when a neuron fires a spike, there is an interval of time during which the probability of generating a second spike is very low. If a spike occurs during this 'silent period', it is likely to be generated from another neuron and the number of occurrences of such 'doublets' can be used to estimate the respective frequencies of two spike trains. We demonstrate here that a simple relation holds between the frequency of doublets d, the respective frequencies of the two neurons A and B, fA and fB, and a chosen value Delta shorter than the silent period, d=2fAfBDelta. This relation holds for a wide class of firing processes. We used this method to analyze responses from Drosophila taste sensilla. We first checked if the method was consistent with results obtained with stimuli that elicit responses of two taste neurons firing distinguishable spikes. We then applied this method to the study of a pair of taste neurons involved in the coding for salt taste in Drosophila melanogaster.     

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.     

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.     

Single unit activity of dopaminergic neurons in freely moving cats

Single unit activity was recorded from the area of the substantia nigra in freely moving cats. A sub-population of these neurons had the following characteristics: long action potential durations (2–4 msec); relatively slow discharge rates (2–6 spikes/sec); firing as single spikes along with periods of bursting activity in which spike amplitude successively decreased; suppression of unit activity by systemic injection of apomorphine and increased activity after systemic injection of haloperidol. These characteristics are similar to those of identified dopamine neurons recorded in chloral hydrate anesthetized or peripherally paralyzed rats. Therefore, based upon these physiological and pharmacological similarities, this study represents the first systematic report providing evidence for recording the activity of dopaminergic neurons in freely moving cats. In addition, when these cells were studied across the sleep-waking cycle they displayed little variation in firing rates between waking, slow wave sleep and REM sleep.     

Functional sites in protein families uncovered via an objective and automated graph theoretic approach

We report a method for detection of recurring side-chain patterns (DRESPAT) using an unbiased and automated graph theoretic approach. We first list all structural patterns as sub-graphs where the protein is represented as a graph. The patterns from proteins are compared pair-wise to detect patterns common to a protein pair based on content and geometry criteria. The recurring pattern is then detected using an automated search algorithm from the all-against-all pair-wise comparison data of proteins. Intra-protein pattern comparison data are used to enable detection of patterns recurring within a protein. A method has been proposed for empirical calculation of statistical significance of recurring pattern. The method was tested on 17 protein sets of varying size, composed of non-redundant representatives from SCOP superfamilies. Recurring patterns in serine proteases, cysteine proteases, lipases, cupredoxin, ferredoxin, ferritin, cytochrome c, aspartoyl proteases, peroxidases, phospholipase A2, endonuclease, SH3 domain, EF-hand and lectins show additional residues conserved in the vicinity of the known functional sites. On the basis of the recurring patterns in ferritin, EF-hand and lectins, we could separate proteins or domains that are structurally similar yet different in metal ion-binding characteristics. In addition, novel recurring patterns were observed in glutathione-S-transferase, phospholipase A2 and ferredoxin with potential structural/functional roles. The results are discussed in relation to the known functional sites in each family. Between 2000 and 50,000 patterns were enumerated from each protein with between ten and 500 patterns detected as common to an evolutionarily related protein pair. Our results show that unbiased extraction of functional site pattern is not feasible from an evolutionarily related protein pair but is feasible from protein sets comprising five or more proteins. The DRESPAT method does not require a user-defined pattern, size or location of the pattern and therefore, has the potential to uncover new functional sites in protein families.     

Inspiratory neuron activity in the ventrolateral medulla of the dog

The purpose of this study was to describe the distribution and activity pattern of respiratory neurons located in the ventrolateral medulla (VLM) of the dog. Spike activity of 129 respiratory neurons was recorded in 23 ketamine-anesthetized spontaneously breathing dogs. Pontamine blue dye was used to mark the location of each neuron. Most VLM neurons displaying respiratory related spike patterns were located in a column related closely to ambigual and retroambigual nuclei. Both inspiratory and expiratory neurons were present with inspiratory units being grouped more rostrally. The predominant inspiratory neuron firing pattern was "late" inspiratory, although eight "early" types were located. All expiratory firing patterns were the late expiratory variety. Each neuron burst pattern was characterized by determining burst duration (BD), spikes per burst (S/B), peak frequency (PF), time to peak frequency (TPF), rate of rise to peak frequency (PF/TPF), and mean frequency. CO2-induced minute ventilation increases were associated with decreases in BD and TPF and increases in PF, S/B, and PF/TPF. In 11 experiments the relative influences of vagotomy and tracheal occlusion on late inspiratory units were compared. Tracheal occlusion increased late inspiratory BD and S/B but did not alter PF/TPF. Vagotomy increased BD and S/B beyond those obtained by tracheal occlusion and, in some neurons, decreased the PF/TPF. We conclude that the location of respiratory units in the VLM of the dog is similar to that in other species, the discharge pattern of VLM respiratory units is similar to those in cat VLM, and vagotomy and tracheal occlusion affect discharge patterns differently.     

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

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

Quantifying Spike Train Oscillations: Biases,Distortions and Solutions

Estimation of the power spectrum is a common method for identifying oscillatory changes in neuronal activity. However, the stochastic nature of neuronal activity leads to severe biases in the estimation of these oscillations in single unit spike trains. Different biological and experimental factors cause the spike train to differentially reflect its underlying oscillatory rate function. We analyzed the effect of factors, such as the mean firing rate and the recording duration, on the detectability of oscillations and their significance, and tested these theoretical results on experimental data recorded in Parkinsonian non-human primates. The effect of these factors is dramatic, such that in some conditions, the detection of existing oscillations is impossible. Moreover, these biases impede the comparison of oscillations across brain regions, neuronal types, behavioral states and separate recordings with different underlying parameters, and lead inevitably to a gross misinterpretation of experimental results. We introduce a novel objective measure, the "modulation index", which overcomes these biases, and enables reliable detection of oscillations from spike trains and a direct estimation of the oscillation magnitude. The modulation index detects a high percentage of oscillations over a wide range of parameters, compared to classical spectral analysis methods, and enables an unbiased comparison between spike trains recorded from different neurons and using different experimental protocols.     

Analyzing multiple spike trains with nonparametric granger causality

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

Evaluation of neuronal coupling dynamics

Temporary correlated activity of neuron assemblies is believed to play a substantial role for the brain's pattern recognition ability. To study the underlying principles of such mechanisms, a method is proposed for the characterization of the interneuronal and stimulus-response coupling changes of two periodically driven and simultaneously recorded units. The coupling measure is derived from the cross correlation function by calculating the actual correlation contributions without performing the subsequent time-average (which would give the cross correlation function). Examples are given for simultaneously recorded spike trains from visual cortical units, but the method can be applied equally well to evoked potentials or intracellular recordings.     

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.     

The Relationship between Respiration-Related Membrane Potential Slow Oscillations and Discharge Patterns in Mitral/Tufted Cells: What Are the Rules?

Background

A slow respiration-related rhythm strongly shapes the activity of the olfactory bulb. This rhythm appears as a slow oscillation that is detectable in the membrane potential, the respiration-related spike discharge of the mitral/tufted cells and the bulbar local field potential. Here, we investigated the rules that govern the manifestation of membrane potential slow oscillations (MPSOs) and respiration-related discharge activities under various afferent input conditions and cellular excitability states.

Methodology and Principal Findings

We recorded the intracellular membrane potential signals in the mitral/tufted cells of freely breathing anesthetized rats. We first demonstrated the existence of multiple types of MPSOs, which were influenced by odor stimulation and discharge activity patterns. Complementary studies using changes in the intracellular excitability state and a computational model of the mitral cell demonstrated that slow oscillations in the mitral/tufted cell membrane potential were also modulated by the intracellular excitability state, whereas the respiration-related spike activity primarily reflected the afferent input. Based on our data regarding MPSOs and spike patterns, we found that cells exhibiting an unsynchronized discharge pattern never exhibited an MPSO. In contrast, cells with a respiration-synchronized discharge pattern always exhibited an MPSO. In addition, we demonstrated that the association between spike patterns and MPSO types appeared complex.

Conclusion

We propose that both the intracellular excitability state and input strength underlie specific MPSOs, which, in turn, constrain the types of spike patterns exhibited.