A pattern grouping algorithm for analysis of spatiotemporal patterns in neuronal spike trains. 1. Detection of repeated patterns

The existence of precise temporal relations in sequences of spike intervals, referred to as 'spatiotemporal patterns', is suggested by brain theories that emphasize the role of temporal coding. Specific analytical methods able to assess the significance of such patterned activity are extremely important to establish its function for information processing in the brain. This study proposes a new method called 'pattern grouping algorithm' (PGA), designed to identify and evaluate the statistical significance of patterns which differ from each other by a defined and small jitter in spike timing of the order of few ms. The algorithm performs a pre-selection of template patterns with a fast computational approach, optimizes the jitter for each spike in the template and evaluates the statistical significance of the pattern group using three complementary statistical approaches. Simulated data sets characterized by various types of known non stationarities are used for validation of PGA and for comparison of its performance to other methods. Applications of PGA to experimental data sets of simultaneously recorded spike trains are described in a companion paper (Tetko IV, Villa AEP. A pattern grouping algorithm for analysis of spatiotemporal patterns in neuronal spike trains. 2. Application to simultaneous single unit recordings. J Neurosci Method 2000; accompanying article).     

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.     

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.     

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.     

PSTH-based classification of sensory stimuli using ensembles of single neurons

The problem of understanding how ensembles of neurons code for somatosensory information has been defined as a classification problem: given the response of a population of neurons to a set of stimuli, which stimulus generated the response on a single-trial basis? Multivariate statistical techniques such as linear discriminant analysis (LDA) and artificial neural networks (ANNs), and different types of preprocessing stages, such as principal and independent component analysis, have been used to solve this classification problem, with surprisingly small performance differences. Therefore, the goal of this project was to design a new method to maximize computational efficiency rather than classification performance. We developed a peri-stimulus time histogram (PSTH)-based method, which consists of creating a set of templates based on the average neural responses to stimuli and classifying each single trial by assigning it to the stimulus with the 'closest' template in the Euclidean distance sense. The PSTH-based method is computationally more efficient than methods as simple as linear discriminant analysis, performs significantly better than discriminant analyses (linear, quadratic or Mahalanobis) when small binsizes are used (1 ms) and as well as LDA with any other binsize, is optimal among other minimum-distance classifiers and can be optimally applied on raw neural data without a previous stage of dimension reduction. We conclude that the PSTH-based method is an efficient alternative to more sophisticated methods such as LDA and ANNs to study how ensemble of neurons code for discrete sensory stimuli, especially when datasets with many variables are used and when the time resolution of the neural code is one of the factors of interest.     

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.     

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.     

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 improved method for the estimation of firing rate dynamics using an optimal digital filter

In most neural systems, neurons communicate by means of sequences of action potentials or 'spikes'. Information encoded by spike trains is often quantified in terms of the firing rate which emphasizes the frequency of occurrence of action potentials rather than their exact timing. Common methods for estimating firing rates include the rate histogram, the reciprocal interspike interval, and the spike density function. In this study, we demonstrate the limitations of these aforementioned techniques and propose a simple yet more robust alternative. By convolving the spike train with an optimally designed Kaiser window, we show that more robust estimates of firing rate are obtained for both low and high-frequency inputs. We illustrate our approach by considering spike trains generated by simulated as well as experimental data obtained from single-unit recordings of first-order sensory neurons in the vestibular system. Improvements were seen in the prevention of aliasing, phase and amplitude distortion, as well as in the noise reduction for sinusoidal and more complex input profiles. We review the generality of the approach, and show that it can be adapted to describe neurons with sensory or motor responses that are characterized by marked nonlinearities. We conclude that our method permits more robust estimates of neural dynamics than conventional techniques across all stimulus conditions.     

Estimating the correlation between bursty spike trains and local field potentials

To further understand rhythmic neuronal synchronization, an increasingly useful method is to determine the relationship between the spiking activity of individual neurons and the local field potentials (LFPs) of neural ensembles. Spike field coherence (SFC) is a widely used method for measuring the synchronization between spike trains and LFPs. However, due to the strong dependency of SFC on the burst index, it is not suitable for analyzing the relationship between bursty spike trains and LFPs, particularly in high frequency bands. To address this issue, we developed a method called weighted spike field correlation (WSFC), which uses the first spike in each burst multiple times to estimate the relationship. In the calculation, the number of times that the first spike is used is equal to the spike count per burst. The performance of this method was demonstrated using simulated bursty spike trains and LFPs, which comprised sinusoids with different frequencies, amplitudes, and phases. This method was also used to estimate the correlation between pyramidal cells in the hippocampus and gamma oscillations in rats performing behaviors. Analyses using simulated and real data demonstrated that the WSFC method is a promising measure for estimating the correlation between bursty spike trains and high frequency LFPs.     

Active Licking Shapes Cortical Taste Coding

Neurons in the gustatory cortex (GC) represent taste through time-varying changes in their spiking activity. The predominant view is that the neural firing rate represents the sole unit of taste information. It is currently not known whether the phase of spikes relative to lick timing is used by GC neurons for taste encoding. To address this question, we recorded spiking activity from >500 single GC neurons in male and female mice permitted to freely lick to receive four liquid gustatory stimuli and water. We developed a set of data analysis tools to determine the ability of GC neurons to discriminate gustatory information and then to quantify the degree to which this information exists in the spike rate versus the spike timing or phase relative to licks. These tools include machine learning algorithms for classification of spike trains and methods from geometric shape and functional data analysis. Our results show that while GC neurons primarily encode taste information using a rate code, the timing of spikes is also an important factor in taste discrimination. A further finding is that taste discrimination using spike timing is improved when the timing of licks is considered in the analysis. That is, the interlick phase of spiking provides more information than the absolute spike timing itself. Overall, our analysis demonstrates that the ability of GC neurons to distinguish among tastes is best when spike rate and timing is interpreted relative to the timing of licks.SIGNIFICANCE STATEMENT Neurons represent information from the outside world via changes in their number of action potentials (spikes) over time. This study examines how neurons in the mouse gustatory cortex (GC) encode taste information when gustatory stimuli are experienced through the active process of licking. We use electrophysiological recordings and data analysis tools to evaluate the ability of GC neurons to distinguish tastants and then to quantify the degree to which this information exists in the spike rate versus the spike timing relative to licks. We show that the neuron''s ability to distinguish between tastes is higher when spike rate and timing are interpreted relative to the timing of licks, indicating that the lick cycle is a key factor for taste processing.     

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.     

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.     

Nonlinear modeling of neural population dynamics for hippocampal prostheses

Developing a neural prosthesis for the damaged hippocampus requires restoring the transformation of population neural activities performed by the hippocampal circuitry. To bypass a damaged region, output spike trains need to be predicted from the input spike trains and then reinstated through stimulation. We formulate a multiple-input, multiple-output (MIMO) nonlinear dynamic model for the input–output transformation of spike trains. In this approach, a MIMO model comprises a series of physiologically-plausible multiple-input, single-output (MISO) neuron models that consist of five components each: (1) feedforward Volterra kernels transforming the input spike trains into the synaptic potential, (2) a feedback kernel transforming the output spikes into the spike-triggered after-potential, (3) a noise term capturing the system uncertainty, (4) an adder generating the pre-threshold potential, and (5) a threshold function generating output spikes. It is shown that this model is equivalent to a generalized linear model with a probit link function. To reduce model complexity and avoid overfitting, statistical model selection and cross-validation methods are employed to choose the significant inputs and interactions between inputs. The model is applied successfully to the hippocampal CA3–CA1 population dynamics. Such a model can serve as a computational basis for the development of hippocampal prostheses.     

Interactions between behaviorally relevant rhythms and synaptic plasticity alter coding in the piriform cortex

Understanding how neural and behavioral timescales interact to influence cortical activity and stimulus coding is an important issue in sensory neuroscience. In air-breathing animals, voluntary changes in respiratory frequency alter the temporal patterning olfactory input. In the olfactory bulb, these behavioral timescales are reflected in the temporal properties of mitral/tufted (M/T) cell spike trains. As the odor information contained in these spike trains is relayed from the bulb to the cortex, interactions between presynaptic spike timing and short-term synaptic plasticity dictate how stimulus features are represented in cortical spike trains. Here, we demonstrate how the timescales associated with respiratory frequency, spike timing, and short-term synaptic plasticity interact to shape cortical responses. Specifically, we quantified the timescales of short-term synaptic facilitation and depression at excitatory synapses between bulbar M/T cells and cortical neurons in slices of mouse olfactory cortex. We then used these results to generate simulated M/T population synaptic currents that were injected into real cortical neurons. M/T population inputs were modulated at frequencies consistent with passive respiration or active sniffing. We show how the differential recruitment of short-term plasticity at breathing versus sniffing frequencies alters cortical spike responses. For inputs at sniffing frequencies, cortical neurons linearly encoded increases in presynaptic firing rates with increased phase-locked, firing rates. In contrast, at passive breathing frequencies, cortical responses saturated with changes in presynaptic rate. Our results suggest that changes in respiratory behavior can gate the transfer of stimulus information between the olfactory bulb and cortex.     

Measuring spike train synchrony

Estimating the degree of synchrony or reliability between two or more spike trains is a frequent task in both experimental and computational neuroscience. In recent years, many different methods have been proposed that typically compare the timing of spikes on a certain time scale to be optimized by the analyst. Here, we propose the ISI-distance, a simple complementary approach that extracts information from the interspike intervals by evaluating the ratio of the instantaneous firing rates. The method is parameter free, time scale independent and easy to visualize as illustrated by an application to real neuronal spike trains obtained in vitro from rat slices. In a comparison with existing approaches on spike trains extracted from a simulated Hindemarsh-Rose network, the ISI-distance performs as well as the best time-scale-optimized measure based on spike timing.     

Time-resolved and time-scale adaptive measures of spike train synchrony

A wide variety of approaches to estimate the degree of synchrony between two or more spike trains have been proposed. One of the most recent methods is the ISI-distance which extracts information from the interspike intervals (ISIs) by evaluating the ratio of the instantaneous firing rates. In contrast to most previously proposed measures it is parameter free and time-scale independent. However, it is not well suited to track changes in synchrony that are based on spike coincidences. Here we propose the SPIKE-distance, a complementary measure which is sensitive to spike coincidences but still shares the fundamental advantages of the ISI-distance. In particular, it is easy to visualize in a time-resolved manner and can be extended to a method that is also applicable to larger sets of spike trains. We show the merit of the SPIKE-distance using both simulated and real data.     

Neural assemblies: technical issues, analysis, and modeling.

Neurons often work together to compute and process information, and neural assemblies arise from synaptic interactions and neural circuits. One way to study neural assemblies is to simultaneously record from several or many neurons and study the statistical relations among their spike trains. From this analysis researchers can try to understand the nature of the assemblies, which can also lead to attempts at modeling the underlying mechanisms. In this review we discuss three important parts of this process: (1) technical issues related to simultaneously recording more than one single unit, (2) ways of analyzing the data and (3) recent models offering hypothetical mechanisms of neural assemblies, especially models which incorporate feedback.