Detection of synchrony in the discharge of a population of neurons. II. Implementation and sensitivity of a synchronization index

Third-order motifs are sufficient to fully and uniquely characterize spatiotemporal neural network activity

Neuroscientific analyses balance between capturing the brain's complexity and expressing that complexity in meaningful and understandable ways. Here we present a novel approach that fully characterizes neural network activity and does so by uniquely transforming raw signals into easily interpretable and biologically relevant metrics of network behavior. We first prove that third-order (triple) correlation describes network activity in its entirety using the triple correlation uniqueness theorem. Triple correlation quantifies the relationships among three events separated by spatial and temporal lags, which are triplet motifs. Classifying these motifs by their event sequencing leads to fourteen qualitatively distinct motif classes that embody well-studied network behaviors including synchrony, feedback, feedforward, convergence, and divergence. Within these motif classes, the summed triple correlations provide novel metrics of network behavior, as well as being inclusive of commonly used analyses. We demonstrate the power of this approach on a range of networks with increasingly obscured signals, from ideal noiseless simulations to noisy experimental data. This approach can be easily applied to any recording modality, so existing neural datasets are ripe for reanalysis. Triple correlation is an accessible signal processing tool with a solid theoretical foundation capable of revealing previously elusive information within recordings of neural networks.

A comparison of cross-correlation and surface EMG techniques used to quantify motor unit synchronization in humans

Two methods used to estimate the strength of motor unit (MU) synchronization in a muscle are the direct cross-correlation of MU discharge times, and averaging of the surface electromyogram (SEMG) with respect to discharge of a reference MU. Although indirect, the latter approach has the advantage that a global estimate of MU synchrony can be obtained quickly and easily. The two methods are generally regarded as providing equivalent information on the extent of MU synchronization in a muscle, but this proposition has not previously been tested quantitatively. In the present study, we used both the SEMG technique (189 MUs) and cross-correlation of MU discharge (498 MU pairs) to estimate MU synchrony in 28 first dorsal interosseus (FDI) muscles from 16 subjects. Despite considerable overlap in the identity of MUs used to quantify synchrony with each method, linear regression revealed no significant correlation between the estimates of MU synchronization in FDI muscles obtained with the two techniques (r2= 0.04, n = 28). This discrepancy was not due to insufficient sampling of the MU population with the cross-correlation method, although we found evidence for a non-uniform tendency for synchronous discharge in two of 13 motor units providing sufficient data for the analysis. The most likely explanation for the discrepancy between the estimates of MU synchrony is that methodological problems with the SEMG technique limit its accuracy. These problems are difficult to avoid under normal experimental conditions, and we conclude that the SEMG method is not reliable for quantitative comparisons of MU synchrony between muscles and subjects.

Limitations of the surface electromyography technique for estimating motor unit synchronization

Motor unit synchronization was estimated from the surface electromyograms (EMG) of the first dorsal interosseus muscle of human volunteers by a simplified surface-EMG technique (Milner-Brown et al. 1973, 1975). Single motor units were identified from intramuscular recordings and were used to obtain a spike-triggered average of the surface-EMG. The discharge rate of a reference motor unit was controlled at two levels (high and low), and the effect of motor unit activity on the surface-EMG estimate of synchronization was studied in 56 motor units. The surface-EMG estimate of motor unit synchronization was significantly higher when the reference motor unit discharged at the high rate than when it discharged at the low rate. A regression analysis indicated that the synchronization ratio calculated from the surface EMG was significantly correlated with the level of EMG activity in the muscle. Motor unit synchronization was also estimated from surface-EMG measurements that were derived by computer simulation. The simulation permitted manipulation of motor unit activity (discharge rate and recruitment) with a complete absence of synchrony among the units in the pool. The stimulated surface-EMG index was influenced by an artifact associated with signal rectification, and this effect changed non-monotonically with motor unit activity. Furthermore, the increase in the motor unit activity reduced the signal-to-noise ratio of the spike-triggered surface EMG average, and consequently decreased the sensitivity of the surface-EMG index as an estimate of motor unit synchronization. We conclude that the simplified surface-EMG method (Milner-Brown et al. 1973, 1975) does not provide a useful index of motor unit synchronization due to its inability to accurately distinguish the synchronization from methodological effects related to a rectification artifact and variation in the signal-to-noise ratio.

Artifactual averaged 'twitch tension' waveforms resulting from synchronized activity: recording from feline diaphragmatic motor units

Averaging techniques have been used to measure contractile properties of spontaneously active motor units (MUs). This study examined the potential for artifactual results due to synchronization between the triggering, single-MU action potentials, and activity of other MUs within the muscle. A muscle strip was formed in situ from feline diaphragm. Single MUs were recorded from the strip and from the contralateral diaphragm. The diaphragm including the muscle strip continue to contract rhythmically in this preparation and a high-gain, AC-coupled recording of force was averaged using MUs recorded in either hemidiaphragm to trigger the averager. Twitch-tension waveforms occurred in 42 of 49 cases triggering from spikes of MUs contained within the strip and in 13 of 19 averages triggered from contralateral MUs. The waveforms generated using contralateral MUs as triggers could only arise from synchronization with MUs contained within the diaphragmatic strip. Although twitch waveforms that were generated from external and internal triggers could appear similar qualitatively, contraction times were significantly (P less than 0.05) longer for averages using contralateral MUs. This study demonstrates that synchronization of triggering events is a major source for error in determining mechanical properties of MUs.

What do GABA neurons really do? They make possible variability generation in relation to demand

It is proposed that GABA neurons play key roles in maintaining meaningful communications within and among neural units by making possible variability generation in relation to demand. Activities of GABAergic inhibitory projection neurons from command centers and local circuit GABAergic inhibitory interneurons allow adaptive nervous system function to take place in a manner characterized by freedom without license. Through their multiple activities and connections these neurons make possible smooth transitions between modes of nervous system function over a range of increasing demands (neural pressures), enabling organisms to explore full ranges of their options.

Synchronous afferent discharge from a passive muscle of the cat: significance for interpreting spike-triggered averages

Evidence is presented for the existence of synchrony between the spike trains of muscle afferents of the passive cat medial gastrocnemius muscle held at fixed length. Synchrony between the spike trains of a population of muscle afferents was quantified by means of a synchronization index (Is), derived from spike-triggered averages of the muscle-nerve neurogram and the rectified neurogram. A previously used test based solely upon the neurogram average (Watt, Stauffer, Taylor, Reinking & Stuart, 1976) is shown to be invalid. The differences between experimentally derived Is values and theoretical Is values derived for the condition of asynchrony were compared to estimated confidence limits for those differences. This comparison revealed that twenty-two of fifty-three muscle-afferent spike trains whose rectified averages satisfied certain conditions for interpreting the Is were synchronized with the discharge of other afferents. The form of the rectified averages of another eight afferents suggested that these afferents might also have been synchronized. Synchrony in the discharge of muscle afferents was found in three experiments in which the neurogram was recorded from a single nerve branch to medial gastrocnemius, as well as in the data of experiments in which the whole muscle nerve was used. The degree of synchrony was similar for Ia, spindle group II and Ib afferents. The magnitude of the synchrony found in these experiments was judged by comparison to the results of analog simulations and the increase in Is values resulting from the application of small, quick stretches to the medial gastrocnemius muscle. The degree of synchrony found on average was approximately equivalent to that of a single spike occurring once for every four discharges of the reference spike train. Simulations were performed to determine the distortion of monosynaptic excitatory post-synaptic potentials (e.p.s.p.s) obtained by spike-triggered averaging which would be produced by synchrony between the spike trains of Ia and spindle group II afferents of the magnitude found in this study. These simulations indicate that the apparent amplitude would be increased by approximately 4 microV on average. Both the 10-90% rise time and the half-width would increase, the effects being greater for smaller e.p.s.p.s. Consequently, the synchrony found in this study is of most concern in the study of small post-synaptic potentials, such as those due to spindle group II afferents.

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.