Detection of synchrony in the discharge of a population of neurons. I. Development of a synchronization index

A test for synchronization among the spike trains of muscle afferents or motor units is described which utilizes averages of neurograms and rectified neurograms. Synchronization is quantified by the increase of a synchronization index Is above a theoretical value for asynchrony. The dependence of the Is on signal amplitude and certain experimental conditions and a method of estimating confidence limits for the test are presented.     

Neural networks a century after Cajal

At the time of Golgi and Cajal's reception of the Nobel Prize in 1906 most scientists had accepted the notion that neurons are independent units. Although neuroscientists today still believe that neurons are independent anatomical units, functionally, it is thought that some sort of population coding occurs. Throughout this essay, we provide evidence that suggests that populations of neurons can code information through the synchronization of their responses. This synchronization occurs at several levels in the brain. Whereas spike synchrony refers to the correlation between spikes of different neurons' spike trains, oscillatory synchrony refers to the synchronization of oscillatory responses, generally among large groups of neurons. In the first section of this essay we describe the dependence of the brain's developmental processes on synchronous firing and how these processes form a brain that supports and is sensitive to synchronous spikes. Data are then presented that suggest that spike and oscillatory synchrony may serve as useful neural codes. Examples from sensory (auditory, olfactory and somatosensory), motor and higher cognitive (attention, memory) systems are then presented to illustrate potential roles for these synchronous codes in normal brain function. Results from these studies collectively suggest that spike synchrony in sensory and motor systems may provide detail information not available from changes in firing rate. Oscillatory synchrony, on the other hand, may be globally involved in the coordination of long-distance neuronal communication during higher cognitive processes. These concepts represent a dramatic shift in direction since the times of Golgi and Cajal.     

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.     

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.     

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.     

Excitatory afferent modulation of complex spike synchrony

Inferior olivary neurons receive extensive glutamatergic and GABAergic innervation. Yet, because of the membrane properties of olivary neurons these neurotransmitters can produce only small changes in the firing rates of these cells. Moreover, olivary neurons can generate spontaneous spike activity in the absence of excitatory glutamatergic input. These facts suggest that glutamate and GABA have additional roles within the olivocerebellar system beyond simply modulating single cell firing probability. Indeed, one of the characteristics of the olivocerebellar system is its ability to generate synchronous complex spike activity across populations of Purkinje cells. The pattern of synchronous activity changes rapidly, and is thought to reflect the momentary distribution of effective electrotonic coupling between olivary neurons as shaped by afferent input to the inferior olive. However, it also possible that synchronous olivocerebellar activity is the result of synchrony inherent in the afferent activity itself. The issue of the origin of complex spike synchrony, and the role of glutamatergic olivary afferents in modulating its distribution were recently studied using multiple electrode recordings from Purkinje cells. The results of these studies, reviewed here, demonstrate that synchronous complex spike activity occurs in the absence of glutamatergic (and GABAergic) input to the inferior olive, and therefore indicate that synchronization of complex spike activity primarily results from the electrotonic coupling of olivary neurons, rather than from synchronization present within their afferents. Instead of triggering synchronous discharges directly, the results suggest that the function of tonic excitatory activity is to modulate the effective coupling of spike activity between olivary neurons. Blocking glutamate within the inferior olive causes an enhancement of the normal banding pattern of complex spike synchrony, with higher synchrony among parasagittally aligned Purkinje cells and less synchrony between non-aligned cells. This is in contrast to the more uniform synchrony distribution that follows block of GABAergic olivary afferents. Thus, GABA and glutamate play critical, and complementary, roles in determining the patterns of synchronous complex spike activity that are likely central to the functioning of the olivocerebellar system.     

Synchronization of single motor units during voluntary contractions in the upper and lower extremities.

OBJECTIVE: To investigate motor unit synchronization in the time and frequency domains and compare the amount and nature of this synchronization between upper and lower extremity muscles in human subjects. METHODS: A total of 120 motor unit pairs from biceps brachii (BB), first dorsal interosseous (1DI), vastus medialis (VM), and tibialis anterior (TA) on the dominant side were analyzed and compared. Pairs of motor unit spike trains were recorded from two concentric needle electrodes inserted within these muscles in healthy volunteers. Subjects were instructed to maintain a weak isometric contraction of these muscles so that an individual motor unit recorded from each concentric needle discharged at a steady rate of approximately 10 impulses/s. Pairs of motor unit spike trains were cross-correlated in the time domain, and coherence analysis in the frequency domain was performed on the same spike train data. RESULTS: Synchronization was seen in all the muscles studied. Strength of motor unit synchronization, expressed as synchronization index (SI), was greater in 1DI muscles compared to other muscles (P<0.01). Coherence analysis revealed significant association between motor unit firings in the 1--5 and 25--30 Hz frequency ranges in all the muscles studied. The incidence of 25--30 Hz coherence peaks were found to be greater for 1DI muscles compared to other muscles. CONCLUSION: The above results suggest a possible role for corticospinal projections in producing pre-synaptic inputs responsible for synchronization of motor unit firings and 25--30 Hz coherence peaks.     

Ontogenetic development of somatosensory thalum. II. Electrogenesis.

Electrodes were implanted into the brains of newborn kittens to study chronically the ontogenesis of unit spike and slow-wave phenomena in the somatosensory thalamus and adjacent structures. In general, the upper brain stem and midline (nonspecific) thalamus showed evidences of functional maturation appreciably sooner than the more laterally lying sensory nuclei. State-dependent changes in single-unit behavior began to develop relatively early (fourth postnatal day) and occasional, scattered spike bursts could be seen by the tenth to 14th day, especially during slow wave sleep. However, this scattered, low-density burst pattern, with total absence of synchrony across leads from the same electrode cluster, at a time when runs of thalamic slow waves or spindles are already very obvious, casts considerable doubt on any obligatory relationship between these two phenomena. Alternative functional models for the production of thalamic wave trains are considered.     

Interaction of synchronized dynamics in cortex and basal ganglia in Parkinson's disease

Parkinson's disease pathophysiology is marked by increased oscillatory and synchronous activity in the beta frequency band in cortical and basal ganglia circuits. This study explores the functional connections between synchronized dynamics of cortical areas and synchronized dynamics of subcortical areas in Parkinson's disease. We simultaneously recorded neuronal units (spikes) and local field potentials (LFP) from subthalamic nucleus (STN) and electroencephalograms (EEGs) from the scalp in parkinsonian patients, and analysed the correlation between the time courses of the spike–LFP synchronization and inter‐electrode EEG synchronization. We found the (non‐invasively obtained) time course of the synchrony strength between EEG electrodes and the (invasively obtained) time course of the synchrony between spiking units and LFP in STN to be weakly, but significantly, correlated with each other. This correlation is largest for the bilateral motor EEG synchronization, followed by bilateral frontal EEG synchronization. Our observations suggest that there may be multiple functional modes by which the cortical and basal ganglia circuits interact with each other in Parkinson's disease: not only may synchronization be observed between some areas in cortex and the basal ganglia, but also synchronization within cortex and within basal ganglia may be related, suggesting potentially a more global functional interaction. More coherent dynamics in one brain region may modulate or activate the dynamics of another brain region in a more powerful way, causing correlations between changes in synchrony strength in the two regions.     

Artifactual synchrony via capacitance coupling in multi-electrode recording from cat striate cortex

Elucidation of neural connectivity patterns in the brain are thought to give us a mechanistic understanding of how the brain works. Functional connectivity is best studied by simultaneous recording of single-unit activity from many neurons. Accordingly, various types of multiple-microelectrode systems have been developed. We have studied long-range lateral interactions in cat striate cortex. To physiologically characterize interacting cells recorded simultaneously, we used two microelectrodes whose movements were controlled by two independently-movable microdrives. The tips of the two microelectrodes were separated by approximately 2 mm or more. During preliminary plotting of two receptive fields of cell pairs, we often noted the emergence of perfectly synchronous firing between two spike trains (amplitude ratio, about 20:1) registered with two microelectrodes. Synchronously firing, smaller spikes disappeared when larger spikes of the pair were lost to either substantial advancement of or placing an electrolytic lesion at the electrode registering the latter. The synchrony also disappeared when two microdrive systems were shielded individually. We concluded that the synchrony was attained through capacitance coupling between two microdrive systems. We proposed a few practical recommendations to avoid the contamination of cross correlograms with the false-positive, narrow peak at time zero due to the presence of reflected spike trains.     

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.     

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.     

Neural interactions in the frontal cortex of a behaving monkey: signs of dependence on stimulus context and behavioral state.

In order to gain an understanding of the processes taking place within and between neuronal assemblies, we made simultaneous recordings of spike trains from groups of up to 11 neurons in the frontal cortex of a rhesus monkey, that was trained to perform a sensorimotor behavioral task. We report here on preliminary results from correlation analysis of these neuronal activities, with special emphasis on signs of behaviorally induced modifications of neural interaction, possibly due to rapid modulations of discharge synchronization among the neurons. Our findings suggest that different functional groups of neurons may co-exist within each small volume of cortex, and that neurons may be dynamically recruited into such a group to fulfil a specific function.     

Synchronization analysis using joint peri-stimulus time histograms for human motor units

The concurrence of action potentials from two motor units (MUs) happens more frequently in human than what one would expect by chance. It can be visualized as the central peak of the Cross-Correlogram of spike trains from two MUs. It is widely believed that a common pre-synaptic input to motoneurons from the cortical tract generates the concurrence. A number of synchronization indices have been proposed in order to evaluate the quantity of the common input, however, these indices are dependent on the firing rates of the MUs. To resolve this issue, we introduce a new synchronization index β using a joint peri-stimulus time histograms (JPSTH). In this paper, we discuss the dependence of synchronization indices on firing rates using a spike model, and the application of JPSTH and the index β to experimental data for the quantitative analysis of MU synchronization. We confirm that the novel index β represents the synchronization state independently from firing rates, and that it also accurately traces event-related temporal modulation of synchronization. In conclusion, we consider the index β to be a valuable index for the analysis of MU synchronization.     

Sensorimotor network hypersynchrony as an endophenotype in families with genetic generalized epilepsy: A resting‐state functional magnetic resonance imaging study

Recent evidence suggests that three specific brain networks show state‐dependent levels of synchronization before, during, and after episodes of generalized spike‐wave discharges (GSW) in patients with genetic generalized epilepsy (GGE). Here, we investigate whether synchronization in these networks differs between patients with GGE (n = 13), their unaffected first‐degree relatives (n = 17), and healthy controls (n = 18). All subjects underwent two 10‐minute simultaneous electroencephalographic–functional magnetic resonance imaging (fMRI) recordings without GSW. Whole‐brain data were divided into 90 regions, and blood oxygen level–dependent (BOLD) phase synchrony in a 0.04–0.07‐Hz band was estimated between all pairs of regions. Three networks were defined: (1) the network with highest synchrony during GSW events, (2) a sensorimotor network, and (3) an occipital network. Average synchrony (mean node degree) was inferred across each network over time. Notably, synchrony was significantly higher in the sensorimotor network in patients and in unaffected relatives, compared to controls. There was a trend toward higher synchrony in the GSW network in patients and in unaffected relatives. There was no difference between groups for the occipital network. Our findings provide evidence that elevated fMRI BOLD synchrony in a sensorimotor network is a state‐independent endophenotype of GGE, present in patients in the absence of GSW, and present in unaffected relatives.     

Automatic wave form classification of extracellular multineuron recordings.

A PC-based method for the reconstruction of individual spike trains from extracellular multineuron recordings is described. Starting with virtually no knowledge about the wave forms in a record, a fully automatic template-finding algorithm extracts templates using the entire data set. In a second step, individual spike trains are reconstructed.     

Odour encoding in olfactory neuronal networks beyond synchronization

It has been suggested that odour encoding in olfactory systems occurs by synchronized firing in neuronal populations. Neurons correlated in terms of the Lempel-Ziv distance of spike trains and the sequential superparamagnetic clustering algorithm belong to the same cluster if they show similar, but not necessarily synchronous, firing patterns. Using multielectrode array recordings from the rat olfactory bulb, we have determined cluster incidence and stability in the neuronal network using both the Lempel-Ziv distance and a measure of synchronization. In the Lempel-Ziv paradigm, we found pronounced stabilization and destabilization effects in the neuronal network in response to odour presentation when compared with the synchronization paradigm. This suggests that synchronization alone may be insufficient for understanding olfactory coding.     

Measurement of variability dynamics in cortical spike trains

We propose a method for the time-resolved joint analysis of two related aspects of single neuron variability, the spiking irregularity measured by the squared coefficient of variation (CV(2)) of the ISIs and the trial-by-trial variability of the spike count measured by the Fano factor (FF). We provide a calibration of both estimators using the theory of renewal processes, and verify it for spike trains recorded in vitro. Both estimators exhibit a considerable bias for short observations that count less than about 5-10 spikes on average. The practical difficulty of measuring the CV(2) in rate modulated data can be overcome by a simple procedure of spike train demodulation which was tested in numerical simulations and in real spike trains. We propose to test neuronal spike trains for deviations from the null-hypothesis FF=CV(2). We show that cortical pyramidal neurons, recorded under controlled stationary input conditions in vitro, comply with this assumption. Performing a time-resolved joint analysis of CV(2) and FF of a single unit recording from the motor cortex of a behaving monkey we demonstrate how the dynamic change of their quantitative relation can be interpreted with respect to neuron intrinsic and extrinsic factors that influence cortical variability in vivo. Finally, we discuss the effect of several additional factors such as serial interval correlation and refractory period on the empiric relation of FF and CV(2).     

Superiority of nonlinear mapping in decoding multiple single-unit neuronal spike trains: a simulation study

One of the most important building blocks of the brain–machine interface (BMI) based on neuronal spike trains is the decoding algorithm, a computational method for the reconstruction of desired information from spike trains. Previous studies have reported that a simple linear filter is effective for this purpose and that no noteworthy gain is achieved from the use of nonlinear algorithms. In order to test this premise, we designed several decoding algorithms based on the linear filter, and two nonlinear mapping algorithms using multilayer perceptron (MLP) and support vector machine regression (SVR). Their performances were assessed using multiple neuronal spike trains generated by a biophysical neuron model and by a directional tuning model of the primary motor cortex. The performances of the nonlinear algorithms, in general, were superior. The advantages of using nonlinear algorithms were more profound for cases where false-positive/negative errors occurred in spike trains. When the MLPs were trained using trial-and-error, they often showed disappointing performance comparable to that of the linear filter. The nonlinear SVR showed the highest performance, and this may be due to the superiority of SVR in training and generalization.