Simultaneously recorded trains of action potentials: analysis and functional interpretation.

A new kind of statistical display, the joint peri-stimulus-time scatter diagram, facilitates the analysis and interpretation of two or more simultaneously recorded trains of action potentials. The display is a generalization of the cross correlation and the peri-stimulus-time histogram, and it reflects specific underlying neuronal interactions. The technique yields quantitative measures of interaction in terms of effectiveness of synaptic connections.

Plasticity of synchronous activity in a small neural net.

Electrical activity from three neurons at a time was recorded in a pleural ganglion of Aplysia. Synchonous activity could be temporally patterned by electrical stimulation over a single nerve. After a period of pairing with electrical stimuli over another nerve the degree and time course of the synchrony were altered. Such alterations reverted after 5 to 30 minutes.

Cross-correlation measures of unresolved multi-neuron recordings.

An increasing number of laboratories are studying population properties of the nervous system using data where the spike activity of more than one neuron is recorded on each electrode and where, accidentally or deliberately, these activities are not resolved into single unit spike trains. We have previously examined the consequences for measurement of cross-correlation between two such electrodes in the limited case where all individual distant (between electrode) correlations are the same and all individual close (on a single electrode) correlations are the same [Bedenbaugh, P.H., and Gerstein, G.L. (1997). Multiunit normalized cross correlation differs from the average single-unit normalized correlation. Neural Computation 9, 1265-1275]. Here, we lift these unrealistic restrictions to allow all values of individual correlation, and examine explicitly the cases of two or three unresolved neurons on each electrode. In these situations, the cross-correlation coefficient measured between the electrodes is a linear sum of the distant correlations, divided by a non-linear function of the close correlations. We then examine in detail the case of a single direct distant correlation and take account of all relevant indirect correlations. The measured interelectrode correlation shows a reduction of this actual distant correlation by a non-linear function of the close correlations on each electrode over most of their possible values. Finally, we examine the consequences of poor waveform sorting for correlation measures; here a supposedly isolated spike train is contaminated by some fraction of the activity of another train, a situation that unfortunately is all too common in experiments. All these distortions become far more serious in the more realistic situation of dynamic firing rates and correlations. This paper is intended as a cautionary note for those who want to draw inferences about neuronal organization and/or coding or representation by using cross-correlation analysis of unresolved recordings.

A rapid method for production of sharp tips on preinsulated microwires.

A rapid method is described which makes it possible to obtain sharp, pencil-like tips on factory-insulated tungsten wires. These features cannot be achieved on preinsulated wire using electrolytic etching techniques. In essence, the cut end of an insulated 25 micron wire is ground on a flat metal surface containing a thin layer of powdered diamond. When both the wire and the diamond-covered disc are rotated simultaneously, a sharp pointed tip is produced within 2-5 min with a smoothly tapering sleeve of insulation. The resulting tips yielded high-quality single-unit spike trains when tested in rat cochlear nucleus. This method lends itself well to those single unit or multineuronal studies requiring rapid, low-cost electrode production, and minimum tissue damage.

Unsupervised waveform classification for multi-neuron recordings: a real-time, software-based system. I. Algorithms and implementation.

We describe a new, mostly software-based device for the sorting of waveforms in an extracellular multi-neuron recording situation. The sorting algorithm is largely unattended, and, after an initial 'learning' process, works in real time. Shape comparisons are based on up to 8 time points in the waveform; these points (the reduced feature set) are chosen automatically by analyzing the current incoming data stream. A feasibility version has been implemented on a LSI-11/2 system, using FORTRAN for set-up calculations and assembler for the real-time operations. Detailed comparisons with performance of other sorting devices are presented in the companion paper.

A low-cost single-board solution for real-time, unsupervised waveform classification of multineuron recordings.

We describe a low-cost single-board system for unsupervised, real-time spike sorting of recordings from a number of neurons on a single microelectrode. The maximum number of spike classes depends on the quality of the recording; it will typically be between 2 and 5. The spike sorter communicates with a conventional microcomputer through a standard serial port (RS232). For typical firing rates as measured in the mammalian central nervous system, this set-up will accommodate up to some 10 parallel spike sorters for as many separate microelectrodes.

Unsupervised waveform classification for multi-neuron recordings: a real-time, software-based system. II. Performance comparison to other sorters.

The companion paper has described a new, fully automatic device for the sorting of action potential waveforms in real time. We present here a brief comparison of performance between this new device and several of the older, more traditional devices used for this purpose. We include in the comparison the performance of 3 human observers.

Signal-to-noise ratio improvement in multiple electrode recording.

Recordings of spike trains made with microwires or silicon electrodes include more noise from various sources that contaminate the observed spike shapes compared with recordings using sharp microelectrodes. This is a particularly serious problem if spike shape sorting is required to separate the several trains that might be observed on a particular electrode. However, if recordings are made with an array of such electrodes, there are several mathematical methods to improve the effective signal (spikes) to noise ratio, thus considerably reducing inaccuracy in spike detection and shape sorting. We compare the theoretical basis of three such methods and evaluate their performance with simulated and real data.

Evaluation of neuronal connectivity: sensitivity of cross-correlation.

Cross-correlation analysis of separable multi-unit activity is one of the most commonly used methods to investigate connectivity in neural networks. In the course of development of new analysis techniques which go beyond the study of pairs or triplets of neurons, the need arose for a simple yet versatile simulator to generate spike trains from networks of specified structure. The present paper describes such a simulator and presents some examples of its performance as analyzed by cross-correlation. We noted a distinct asymmetry in the sensitivity of cross-correlation for the presence of excitatory vs inhibitory connections. A theoretical analysis is given from which quantitative criteria for detectability were derived. It appears that indeed the sensitivity of cross-correlation for excitation is larger to an order of magnitude than it is for inhibition. Possible consequences of this finding are indicated, and the relation to commonly used methods to measure strength of interaction are discussed.

Cortical auditory neuron interactions during presentation of 3-tone sequences: effective connectivity.

The role of cat's primary auditory cortex (AI) in both pattern discrimination and sound localization has been demonstrated by observing that ablations of it disrupt these functions. This research studied effective connectivity variations as a function of modifications in the temporal pattern of acoustic stimulation. Recordings of 10-15 neurons (simultaneously and separably) were made in AI of sedated cats. A bundle of 7 microelectrodes was stereotaxically placed along a tangential path. Stimuli were permutations of 3-tone bursts sequences. Each recorded neuron pair was analyzed off-line by cross-correlation. Cross-correlation of spike trains from neuron pairs showed signatures of direct and/or shared input. These appeared individually or in combination and for most pairs were present in spontaneous conditions. However, in stimulated conditions these spontaneous interactions were strongly modulated. The analysis detected differences in neuronal interaction during presentation of different tones. Similar differences occurred during presentation of any single particular stimulus if there was a history of different immediately previous tones. When individual neuron pair cross-correlations were put together to form an effective connectivity diagram among all recorded neurons, they turned out as different diagrams for different stimulus conditions.

Gravitational representation of simultaneously recorded brainstem respiratory neuron spike trains.

Experiments designed to study concurrent processes in neural networks have been hampered by limitations of available analytical methods. A recently described gravitational representation of spike train data was used to evaluate groups of simultaneously monitored medullary respiratory related neurons in anesthetized, vagotomized cats. The results establish that the method can detect and define functional associations among elements of such groups after as few as 20 respiratory cycles.

Dynamic temporal properties of effective connections in rat dorsal cochlear nucleus.

In a prior report we presented evidence that functionally connected dorsal cochlear nucleus (DCN) neurons in close proximity can show differing peristimulus time histograms (PSTHs) in response to the same stimulus. We wished to further investigate how interconnections between such neurons might participate in the PSTH patterns. Methodology has recently been developed which permits measurement of rapid changes in effective connectivity between neuron pairs: the normalized joint PSTH. Using this technique we have observed that rapid changes in effective connectivity do occur in the DCN. These observations demonstrate that the effects of one DCN neuron on another cannot necessarily be understood by sequential recordings from single units, even if anatomical connectivity can be established.

Coordinated activity of neuron pairs in anesthetized rat dorsal cochlear nucleus.

We have recorded from small groups of neurons in the dorsal cochlear nucleus of anesthetized rats in an effort to study neuronal interactions. Multi-unit recordings on each single electrode were sorted by waveform into spike trains from individual neurons using a principal components spike sorter. Pairs of such sorted spike trains were studied with cross-correlation analysis to detect excitatory and/or inhibitory interactions. In a few cases recordings were obtained from two electrodes simultaneously, thus allowing cross-correlation studies without the consequences of spike train waveform sorting. All neurons were characterized by their strongest response frequency (at a fixed sound pressure level) and peristimulus histogram responses to 55 ms tone bursts. Fifty-eight percent of the neuron pairs studied showed peaks in their cross-correlograms indicative of coordinated neural activity. Of these pairs, 86% showed peak configurations (i.e. correlograms with asymmetrically located peaks) consistent with the interpretation that one cell induced the other to discharge. The remaining correlograms contained symmetric peaks which were centrally located, possibly due to shared input to these neuron pairs. Latencies of asymmetric peaks in cross-correlograms were typically 2 ms; consequently, an intervening excitatory synapse may be involved. Similar results were obtained from at least one pair of neurons where each neuron was recorded by a separate electrode. Strongest response frequencies of each neuron pair, for which they could be determined, were within 0.17 log units. Peristimulus histograms from each neuron in these pairs revealed that it was common for adjacent cells to respond with differing time patterns under the same stimulus conditions. The variations in histogram patterns of interconnected neurons suggests some relatively complex integrative function for these circuits.

Identification of functionally related neural assemblies.

Present-day techniques of multiple-electrode together with computer-aided separation of impulses arising from different neurons permit the simultaneous recording of nerve-impulse timings in sets of neurons exceeding 20 in number. This in turn makes it feasible to search for functional groups of neurons, defined as subsets that tend to fire in near simultaneity significantly more often than would independent neurons at corresponding mean rates. A statistical technique is described that permits the detection and identification of such functional groups. The method is accretional, based on identification of associated neurons through interative application of a significance test on multiple coincidences of neuronal firings within an observational window. Examples of the operation of the method and indications as to its sensitivity are furnished through computer simulations of neural networks. The entire algorithm may be used as a screening technique to select smaller groups of neurons for cross-correlational and related finer-grained temporal analyses, or it may be used in its own right to detect and characterize functional groups that are not distinguishable by other statistical procedures.

Elaboration of a conditioned reflex in a single experiment with simultaneous recording of neural activity.

In 18 of 20 experiments with click CS, and in 5 of 10 experiments with flash CS, we have elaborated a conditioned EMG response in a single session (less than 60 pairings). The US was direct electrical stimulation of the rabbit's motor cortex that evoked a movement of the forelimb. Electrical stimulation of the lateral hypothalamus was used as reinforcement. Parameters for this reinforcement were chosen to evoke a feeding reaction or self-stimulation in the freely behaving animal. The elaborated EMG response satisfied most of the required characteristics of a conditioned reflex. These included spontaneous recovery after extinction, savings of long duration, specificity to stimulus pairing, and weak efferent and afferent generalization. In most experiments with click CS, the elaborated phasic response had an amplitude of 0.1-6 mV with a latency of 12-16 msec. In form and latency the conditioned response was similar to the unconditioned startle reaction of the same animal under chloralose anesthesia, or to its unanesthetized response to a loud sound. However, the conditioned response differed from the startle reaction in that it was localized. Extracellular recordings of 2-5 neurons were simultaneously made from sensory motor cortex near the point at which the US was applied. In 7 experiments 17 neurons were followed through the entire cycle of elaboration and extinction of the conditioned response. Seven neurons showed a statistically significant (P less than 0.05) increase of the response to CS during conditioning. Latencies were 20-140 msec. Interactions between neurons were studied by computing cross-correlograms and joint PST scatter diagrams. These measures were less informative than we had hoped because of the low level of spontaneous and evoked activity, and because of the small numbers of stimulus presentations that were needed for elaboration and extinction of the conditioned reflex. In isolated presentations of the CS after elaboration of the CR, we sometimes observed neural responses to click with a latency less than 6 msec. We propose that at least one of the pathways involved in the localized conditioned startle reflex reported here goes through the sensory motor cortex.

Nerve-impulse patterns: a quantitative display technique for three neurons.

A scatter diagram is described that displays the relative timings of nerve impulses in 3 simultaneously monitored neurons. The technique is a generalization of the cross-correlation histogram for two impulse trains. The time intervals between impulses in different neurons are plotted on triangular coordinates to yield a Joint Impulse Configuration Scatter Diagram. The resulting 'snowflake' plot shows a pattern of spots and lines, which is interpretable in terms of the functional circuitry among teh neurons. Illustrations are given of the snowflakes produced by a variety of three-neuron circuits, which may serve as a preliminary catalog of snowflake types for interpretation of experimental data.

Simulation of dynamic receptive fields in primary visual cortex.

A model network of spiking neurons with lateral connections was used to simulate short-term receptive field (RF) changes by removal of afferent input in the primary visual system. Several possible mechanisms for the dynamic RFs were explored and the simulation results were compared with experimental results obtained by Pettet and Gilbert [(1992) Proceedings of the National Academy of Science, U.S.A., 89, 8366-8370]. We found that appropriate input stimuli could induce a shift in the balance between modeled cortical lateral excitation and inhibition and in doing so cause RF expansion. Synaptic plasticity was neither necessary nor appropriate for short-term RF changes. An inhibition dominant network with neural adaptation successfully simulated Pettet and Gilbert's experiment of RF expansion and its reversibility induced by an "artificial scotoma". RF expansions induced by lesions were also explored with the model.

A model of cortically induced synchronization in the lateral geniculate nucleus of the cat: a role for low-threshold calcium channels.

Recently Sillito et al. (Nature 1994;369:479-82) discovered correlations in the spike trains of a relatively distant pair of cat lateral geniculate nucleus cells when simultaneously stimulated by a drifting grating; no such correlation occurs when the visual cortex is removed. In a further analysis of the data, we have found that short, high-frequency bursts contribute substantially to the synchronization and we hypothesize that the origin of the bursts is the low-threshold calcium spike. Guided by this hypothesis, our model of the corticogeniculate pathway and early visual system reproduces the experimental data in nearly every detail, as well as making predictions about cortical activity during the synchronizing process. We also discuss the possible behavioral relevance of correlations in the geniculo-cortical loop as well as other neural systems.

Auditory frequency discrimination in the white rat.

Frequency discrimination was investigated in the albino rat using a modified go/no-go positive reinforcement procedure in which subjects reported frequency increments in an ongoing series of pure tone bursts. Weber ratios (frequency difference limen/frequency) were measured from 5 to 32 kHz at 50 dB sound pressure level. A signal detection analysis of the procedure enabled a direct comparison to be made with the rat's performance in a discrete trial go/no-go task. A mean Weber ratio of 3.06+/-0.44% was measured in the frequency range 5-32 kHz. This indicates that the rat has better frequency discrimination acuity than has previously been thought. The result is discussed in the context of factors affecting performance. Among the factors that were explored we found that long training times and the specific training paradigm played important roles. In comparison to discrete trial go/no-go paradigms, rats performed much better when detecting signals from a repeating background. Frequency discrimination performance decreased linearly for tones less than 50 ms in duration. For longer tone duration performance was unaffected. The means and variability of reaction times for threshold changes of frequency were greater in comparison with supra-threshold frequency changes.

Spectral time-course analysis of firing patterns in the dorsal cochlear nucleus.

Many previous studies of central auditory neurons have involved independent analyses of spectral and temporal response properties. The spectral response analysis is useful for defining the frequency and intensity regions over which a neuron is excited or inhibited. However, the conventional spectral response analysis only defines this distribution for the synaptic polarity (excitation or inhibition) which dominates the duration of the response. PST histograms of dorsal cochlear nucleus neurons however, often exhibit both excitatory and inhibitory (i.e. pause) components. The distribution of these transient pause intervals may in turn be highly dependent on stimulus parameters suggesting that the spectral area of excitation and inhibition, when considered in terms of short time frames, may be time-dependent. We performed a temporal analysis of the spectral response areas of neurons in the rat dorsal cochlear nucleus and present here an example based on a neuron showing distinct pauser and buildup responses in its PST histograms. The resulting analysis yielded a time course of the spectral response area which indicates that the transient periods of inhibition may have the effect of narrowing the bandwidth of excitation during the early portion of stimulation. Possible implications of this time course are discussed in relation to the narrower tuning that cochlear nucleus neurons often display in response to frequency sweeps than to pure tones.