A pattern grouping algorithm for analysis of spatiotemporal patterns in neuronal spike trains. 2. Application to simultaneous single unit recordings

This study demonstrates the practical application of the pattern grouping algorithm (PGA), presented in the companion paper (Tetko IV, Villa AEP. A pattern grouping algorithm for analysis of spatiotemporal patterns in neuronal spike trains. 1. Detection of repeated patterns. J. Neurosci. Methods 2000; accompanying article), to data sets including up to 30 simultaneously recorded spike trains. The analysis of a large network of simulated neurons shows that the incidence of patterns cannot be simply related to an increase in firing rates obtained after Hebbian learning. Patterns that disappeared and reappeared in the thalamus of anesthetized rats when the cerebral cortex was reversibly inactivated suggest that widespread cell assemblies contribute to the generation and propagation of precisely timed activity. In an another experiment multiple spike trains were recorded from the temporal cortex of freely moving rats performing a complex two-choice discrimination task. The presence or absence of particular patterns in the period preceding the cue was associated with changes in reaction time. In conclusion, neuronal network interactions may generate spatiotemporal firing patterns detectable by PGA. We provide evidence of such patterned activity associated with specific animal's behavior, thus suggesting the existence of complex temporal coding schemes in the higher nervous centers of the brain.     

Analysis of phase-locked oscillations in multi-channel single-unit spike activity with wavelet cross-spectrum

Electrophysiological measures of neural activity frequently display oscillatory patterns at various frequencies. Furthermore, these oscillatory patterns can become dynamically synchronized across a wide region of the brain in a task-dependent manner. In this study, phase-locked oscillations in simultaneously recorded spike trains were analyzed using the wavelet cross-spectrum. Adaptation of the existent methods of calculating wavelet cross-spectrum to spike train data was straightforward. In contrast, new methods were needed for evaluating the statistical significance of the cross-spectrum. Although a permutation test based on a large number of re-sampled cross-spectra can provide a reliable estimate of statistical significance, this was quite time-consuming. As an alternative, statistical significance was determined with a normal probability density function estimated from a small number of re-sampled cross-spectra. When applied to neuron pairs recorded in the primate supplementary motor area, the re-sampling procedure produced a reliable outcome even when it was based on as few as ten re-sampled cross-spectra. These results suggest that the wavelet analysis in combination with a re-sampling procedure provides a useful tool to examine the dynamic patterns of temporal correlation in cortical 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].     

Favored patterns in spontaneous spike trains.

By using the modified detection method, favored patterns can be detected in a total of 44 spontaneous spike trains. Among these the 'periodical burst' discharge of one sympathetic preganglionic neuron and the 'fast-slow' alternative discharge of some hypothalamic neurons have visible characteristics, hence we use them to test the reliability of our method by comparing the detected patterns with the non-sequential interval histograms and oscillograms of the spike trains. The comparisons show that our method is reliable. The spike trains of nucleus raphe magnus (NRM) and the locus coeruleus (LC) have no visible characteristics; from these the following results have been observed: (1) all spike trains have one or more favored patterns; (2) some spike trains from neurons in the same nucleus have common fragments of favored patterns; (3) the favored patterns in spike trains recorded from different nuclei are different from each other; (4) some favored patterns in spike trains of the NRM neurons remain unchanged from beginning to end in 35-min records and their repetitions are relatively stable; and (5) microinjection of normal saline or normal serum into the LC has no significant influence on the occurrence of favored patterns in 35-min records of spike trains of the LC neurons. The above results indicate that the favored patterns in spike trains are objective and regular phenomena with relative stability. It seems likely that favored pattern may be used (as an index of the neuronal activity) in combination with the microinjection technique, etc., for various studies including studies on neural coding.     

Statistical significance of sequential firing patterns in multi-neuronal spike trains

Sequential firings with fixed time delays are frequently observed in simultaneous recordings from multiple neurons. Such temporal patterns are potentially indicative of underlying microcircuits and it is important to know when a repeatedly occurring pattern is statistically significant. These sequences are typically identified through correlation counts. In this paper we present a method for assessing the significance of such correlations. We specify the null hypothesis in terms of a bound on the conditional probabilities that characterize the influence of one neuron on another. This method of testing significance is more general than the currently available methods since under our null hypothesis we do not assume that the spiking processes of different neurons are independent. The structure of our null hypothesis also allows us to rank order the detected patterns. We demonstrate our method on simulated spike trains.     

Properties of favored patterns in spontaneous spike trains and responses of favored patterns to electroacupuncture in evoked trains.

By using 'the modified detection method', our previous study has shown that all spontaneous spike trains recorded from several areas of brain and spinal cord have favored patterns (FPs). The present study further shows that: (1) all newly detected spike trains from substantia nigra zona compacta, nucleus periventricularis hypothalami and nucleus hypothalamicus posterior also have FPs, and some spike trains from neurons in the same nucleus have a common favored pattern (CF, i.e. they share the same FP), indicating that FP and CF in spike trains are common phenomena; (2) all serial correlation coefficients of FP repetitions (in serial order) in different spike trains detected are less than 0.3 (close to 0), revealing that the repetition of FPs is a renewal process; (3) in different periods of the spike trains evoked by electroacupuncture (EA), the number of different FPs and the number of repetitions of the same representative FP either increase or decrease along with the change of firing rate. The tendencies of these changes are very similar, but after EA the repetitions of different FPs in the same spike trains change differently, showing that different (hidden) responses exist at the same time. The above results suggest that the FPs in spike trains may represent various neural codes, and 'the modified detection method of FP' can pick up more information from spike trains than the firing rate analysis, hence it is a very useful tool for the study of neural coding.     

Neural timing nets.

Formulations of artificial neural networks are directly related to assumptions about neural coding in the brain. Traditional connectionist networks assume channel-based rate coding, while time-delay networks convert temporally-coded inputs into rate-coded outputs. Neural timing nets that operate on time structured input spike trains to produce meaningful time-structured outputs are proposed. Basic computational properties of simple feedforward and recurrent timing nets are outlined and applied to auditory computations. Feed-forward timing nets consist of arrays of coincidence detectors connected via tapped delay lines. These temporal sieves extract common spike patterns in their inputs that can subserve extraction of common fundamental frequencies (periodicity pitch) and common spectrum (timbre). Feedforward timing nets can also be used to separate time-shifted patterns, fusing patterns with similar internal temporal structure and spatially segregating different ones. Simple recurrent timing nets consisting of arrays of delay loops amplify and separate recurring time patterns. Single- and multichannel recurrent timing nets are presented that demonstrate the separation of concurrent, double vowels. Timing nets constitute a new and general neural network strategy for performing temporal computations on neural spike trains: extraction of common periodicities, detection of recurring temporal patterns, and formation and separation of invariant spike patterns that subserve auditory objects.     

Symmetric temporal patterns in cortical spike trains during performance of a short-term memory task

Abstract

The trion model is a highly structured representation of cortical organization_l which predicts families of symmetric spatial-temporal firing patterns inherent in cortical activity. The symmetries of these inherent firing patterns are used by the brain in short-term memory to perform higher level computations. In the present study, symmetric temporal patterns were searched for in spike trains recorded from cells in parietal cortex of a monkey performing a short-term memory task. A new method of analysis was used to map neuronal firing into sequences of integers representing relative levels of firing rate about the mean (i.e. -1, 0 and 1). The results of this analysis show families of patterns related by symmetry operations. These operations are: i. the interchanging of all the + l’s and -l’s in a given pattern sequence (CT symmetry), ii. the inverting of the temporal sequence of the mapping (T symmetry)1 and iii. the combination of the two previous operations (CT symmetry). Patterns of a given family are found across cells especially in the memory periods of the task; in most cases they reoccur within a given spike train. The pattern families predicted by the model and reported here should be further investigated in multiple microelectrode and EEG recordings. [Neural Res 1997; 19: 509-514]     

Spike train signatures of retinal ganglion cell types

The mammalian retina deconstructs the visual world using parallel neural channels, embodied in the morphological and physiological types of ganglion cells. We sought distinguishing features of each cell type in the temporal pattern of their spikes. As a first step, conventional physiological properties were used to cluster cells in eight types by a statistical analysis. We then adapted a method of P. Reinagel et al. (1999: J. Neurophysiol., 81, 2558-2569) to define epochs within the spike train of each cell. The spike trains of many cells were found to contain robust patterns that are defined by the (averaged) timing of successive interspike intervals in brief activity epochs. The patterns were robust across four different types of visual stimulus. Although the patterns are conserved in different visual environments, they do not prevent the cell from signaling the strength of its response to a particular stimulus, which is expressed in the number of spikes contained in each coding epoch. Clustering based on the spike train patterns alone showed that the spike train patterns correspond, in most but not all cases, to cell types pre-defined by traditional criteria. That the congruence is less than perfect suggests that the typing of rabbit ganglion cells may need further refinement. Analysis of the spike train patterns may be useful in this regard and for distinguishing the many unidentified ganglion cell types that exist in other mammalian retinas.     

Neuronal firing patterns in the feline hippocampus during sleep and wakefulness

The study addressed the problem of information transmission in mammalian brain as reflected in the emergence or disappearence of temporal patterns in extra-cellularly monitored single action potentials from the dorsal hippocampus of unrestrained cats during slow wave sleep (SWS), rapid eye movement sleep (REM), and motionless quiet wakefulness (QW). The spike trains were analyzed with a non-paarametric technique. Chi-square statistics were used to measure deviations of firing patterns from the theoretical model which is based on the assumption that the intervals are random and/or independent from each other. The plots of the chi-square values for a given set of patterns represented the neuronal ‘signatures’ characteristic a behavioral state.During SWS most neurons followed the theoretical model, i.e. their ‘signatures’ were flat and statistically non-significant. However, during REM sleep and QW their firing modes showed specific deviations from the theoretical model: some patters occured more often while others less often than expected, thus generating large and statistically significant ‘signatures’.During REM sleep some neurons shared similar tendencies in their departures from the theoretical model. However, during QW the same neurons developed their individual ‘signatures’ which were significantly different from each other. Hence, the QW episodes were characterized by a greater differentiation of neuronal firing patterns. The mean firing rate and the shape of the time interval histogramwere not necessarily correlated with the emergence of specific temporal patterns in spike trains.The results suggest that information transmission from one neuron to anothe depends on the emergence of repetitive and specific temporal patterns. The strong tendency of most neurons to lapse during SWS into a firing mode that closely follows the theoretical model constitutes the basis for a working hypothesis which states that the essence of SWS recovery processes in cognitive systems is the disappearance of temporal patterns, and that the ‘noisy’ interactions between neurons plays an important role in the recuperative processes.     

A model for the interaction of oscillations and pattern generation with real-time computing in generic neural microcircuit models.

It is shown that real-time computations on spike patterns and temporal integration of information in neural microcircuit models are compatible with potentially descruptive additional inputs such as oscillations. A minor change in the connection statistics of such circuits (making synaptic connections to more distal target neurons more likely for excitatory than for inhibitory neurons) endows such generic neural microcircuit model with the ability to generate periodic patterns autonomously. We show that such pattern generation can also be multiplexed with pattern classification and temporal integration of information in the same neural circuit. These results can be interpreted as showing that periodic activity provides a second channel for communication in neural systems which can be used to synchronize or coordinate spatially separated processes, without encumbering local real-time computations on spike trains in diverse neural circuits.     

Self‐organization of repetitive spike patterns in developing neuronal networks in vitro

The appearance of spontaneous correlated activity is a fundamental feature of developing neuronal networks in vivo and in vitro. To elucidate whether the ontogeny of correlated activity is paralleled by the appearance of specific spike patterns we used a template‐matching algorithm to detect repetitive spike patterns in multi‐electrode array recordings from cultures of dissociated mouse neocortical neurons between 6 and 15 days in vitro (div). These experiments demonstrated that the number of spiking neurons increased significantly between 6 and 15 div, while a significantly synchronized network activity appeared at 9 div and became the main discharge pattern in the subsequent div. Repetitive spike patterns with a low complexity were first observed at 8 div. The number of repetitive spike patterns in each dataset as well as their complexity and recurrence increased during development in vitro. The number of links between neurons implicated in repetitive spike patterns, as well as their strength, showed a gradual increase during development. About 8% of the spike sequences contributed to more than one repetitive spike patterns and were classified as core patterns. These results demonstrate for the first time that defined neuronal assemblies, as represented by repetitive spike patterns, appear quite early during development in vitro, around the time synchronized network burst become the dominant network pattern. In summary, these findings suggest that dissociated neurons can self‐organize into complex neuronal networks that allow reliable flow and processing of neuronal information already during early phases of development.     

Deterministic neural dynamics transmitted through neural networks

Precise spatiotemporal sequences of neuronal discharges (i.e., intervals between epochs repeating more often than expected by chance), have been observed in a large set of experimental electrophysiological recordings. Sensitivity to temporal information, by itself, does not demonstrate that dynamics embedded in spike trains can be transmitted through a neural network. This study analyzes how synaptic transmission through three archetypical types of neurons (regular-spiking, thalamo-cortical and resonator), simulated by a simple spiking model, can affect the transmission of precise timings generated by a nonlinear deterministic system (i.e., the Zaslavskii mapping in the present study). The results show that cells with subthreshold oscillations (resonators) are very sensitive to stochastic inputs, and are not a good candidate for transmitting temporally coded information. Thalamo-cortical neurons may transmit very well temporal patterns in the absence of background activity, but jitter accumulates along the synaptic chain. Conversely, we observed that cortical regular-spiking neurons can propagate filtered temporal information in a reliable way through the network, and with high temporal accuracy. We discuss the results in the general framework of neural dynamics and brain theories.     

An associative memory readout for ESNs with applications to dynamical pattern recognition.

The use of echo state networks (ESN) to find patterns in time (dynamical pattern recognition) has been limited. This paper argues that ESNs are particularly well suited for dynamical pattern recognition and proposes a linear associative memory (LAM) as a novel readout for ESNs. From the class of LAMs, the minimum average correlation energy (MACE) filter is adopted because of its high rejection characteristics that allow its use as a detector in the automatic pattern recognition literature. In the ESN application, the MACE interprets the states of the ESN as a two-dimensional "image", one dimension being time and the other the processing element index (space). An optimal template image for each class, which associates ESN states with the class label, can be analytically computed using training data. During testing, ESN states are correlated with each template image and the class label of the template with the highest correlation is assigned to the input pattern. The ESN-MACE combination leads to a nonlinear template matcher with robust noise performance as needed in non-Gaussian, nonlinear digital communication channels. A real-world data experiment for chemical sensing with an electronic nose is included to demonstrate the validity of this approach. Moreover, the proposed readout can also be used with liquid state machines eliminating the need to convert spike trains into continuous signals by binning or low-pass filtering.     

Towards statistical summaries of spike train data

Statistical inference has an important role in analysis of neural spike trains. While current approaches are mostly model-based, and designed for capturing the temporal evolution of the underlying stochastic processes, we focus on a data-driven approach where statistics are defined and computed in function spaces where individual spike trains are viewed as points. The first contribution of this paper is to endow spike train space with a parameterized family of metrics that takes into account different time warpings and generalizes several currently used metrics. These metrics are essentially penalized L(p) norms, involving appropriate functions of spike trains, with penalties associated with time-warpings. The second contribution of this paper is to derive a notion of a mean spike train in the case when p=2. We present an efficient recursive algorithm, termed Matching-Minimization algorithm, to compute the sample mean of a set of spike trains. The proposed metrics as well as the mean computations are demonstrated using an experimental recording from the motor cortex.     

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.     

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.     

Conditioned spikes: a simple and fast method to represent rates and temporal patterns in multielectrode recordings

Increasing evidence suggests that the brain utilizes distributed codes that can only be analyzed by simultaneously recording the activity of multiple neurons. This paper introduces a new methodology for studying neural ensemble recordings. The method uses a novel representation to provide complementary information about the stimuli which are contained in the temporal pattern of the spike sequence. By using this procedure, a high correlation of synchronized events with stimuli times is apparent. To quantify the results and to compare the performance of this method against the most traditional raster plot, we have used Fano factor and cross-correlation analysis. Our results suggest that several consecutive spikes from different neurons within an extended time window may encode behaviorally relevant information. We propose that this new representation, in addition to the other approaches currently used (standard raster plots, multivariate statistical methods, neuronal networks, information theory, etc.), can be a useful procedure to describe population spike dynamics.