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.     

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.     

Methods for estimating neural firing rates,and their application to brain–machine interfaces

Neural spike trains present analytical challenges due to their noisy, spiking nature. Many studies of neuroscientific and neural prosthetic importance rely on a smoothed, denoised estimate of a spike train’s underlying firing rate. Numerous methods for estimating neural firing rates have been developed in recent years, but to date no systematic comparison has been made between them. In this study, we review both classic and current firing rate estimation techniques. We compare the advantages and drawbacks of these methods. Then, in an effort to understand their relevance to the field of neural prostheses, we also apply these estimators to experimentally gathered neural data from a prosthetic arm-reaching paradigm. Using these estimates of firing rate, we apply standard prosthetic decoding algorithms to compare the performance of the different firing rate estimators, and, perhaps surprisingly, we find minimal differences. This study serves as a review of available spike train smoothers and a first quantitative comparison of their performance for brain–machine interfaces.     

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.     

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.     

Dynamics of information and emergent computation in generic neural microcircuit models

Numerous methods have already been developed to estimate the information contained in single spike trains. In this article we explore efficient methods for estimating the information contained in the simultaneous firing activity of hundreds of neurons. Obviously such methods are needed to analyze data from multi-unit recordings. We test these methods on generic neural microcircuit models consisting of 800 neurons, and analyze the temporal dynamics of information about preceding spike inputs in such circuits. It turns out that information spreads with high speed in such generic neural microcircuit models, thereby supporting—without the postulation of any additional neural or synaptic mechanisms—the possibility of ultra-rapid computations on the first input spikes.     

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.     

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.     

Trial-by-trial estimation of amplitude and latency variability in neuronal spike trains

The rate function underlying single-trial spike trains can vary from trial to trial. We propose to estimate the amplitude and latency variability in single-trial neuronal spike trains on a trial-by-trial basis. The firing rate over a trial is modeled by a family of rate profiles with trial-invariant waveform and trial-dependent amplitude scaling factors and latency shifts. Using a Bayesian inference framework we derive an iterative fixed-point algorithm from which the single-trial amplitude scaling factors and latency shifts are estimated. We test the performance of the algorithm on simulated data and then apply it to actual neuronal recordings from the sensorimotor cortex of the monkey.     

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.     

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.     

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].     

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.     

Editing trains of action potentials from multi-electrode arrays

When recording from multi-electrode arrays, only a short period around the time of a threshold crossing is generally saved for later analysis. Then, waveforms are often sorted automatically to identify templates of spikes from individual neurons near an electrode. As spikes sum from different neurons and noise is present, some spikes may be missed and others erroneously accepted. This paper describes methods for identifying and correcting errors in recorded spike trains to recover the pattern of spikes from each neuron as faithfully as possible. These methods are complementary to, but distinct from methods to reconstruct waveforms that arise from summation of individual templates that overlap one another. Our methods are based on the local statistics of the firing rates or inter-spike intervals and the methods work best for neurons that fire regularly (small standard deviation relative to the mean interval). First, we test whether accepting more spikes, whose waveforms are close to the templates that have been identified, will increase the regularity or smoothness of the firing rates. Then, after accepting spikes that increase regularity, we test whether individual intervals are sufficiently longer (or shorter) than their neighbors to identify spikes that have been omitted (or accepted) erroneously. The methods are tested on simulated spike trains, where spikes have been inserted or deleted at random, and on spike trains recorded from multi-electrode arrays in dorsal root ganglia of cats walking on a treadmill.