Neural spike train synchronization indices: definitions, interpretations,and applications

A comparison of previously defined spike train synchronization indices is undertaken within a stochastic point process framework. The second-order cumulant density (covariance density) is shown to be common to all the indices. Simulation studies were used to investigate the sampling variability of a single index based on the second-order cumulant. The simulations used a paired motoneurone model and a paired regular spiking cortical neurone model. The sampling variability of spike trains generated under identical conditions from the paired motoneurone model varied from 50% to 160% of the estimated value. On theoretical grounds, and on the basis of simulated data a rate dependence is present in all synchronization indices. The application of coherence and pooled coherence estimates to the issue of synchronization indices is considered. This alternative frequency domain approach allows an arbitrary number of spike train pairs to be evaluated for statistically significant differences, and combined into a single population measure. The pooled coherence framework allows pooled time domain measures to be derived, application of this to the simulated data is illustrated. Data from the cortical neurone model is generated over a wide range of firing rates (1-250 spikes/s). The pooled coherence framework correctly characterizes the sampling variability as not significant over this wide operating range. The broader applicability of this approach to multielectrode array data is briefly discussed.

[1]  S. Kidambi Srinivasan,et al.  Stochastic point processes and their applications , 1974 .

[2]  E E Fetz,et al.  Cross‐correlation assessment of synaptic strength of single Ia fibre connections with triceps surae motoneurones in cats. , 1987, The Journal of physiology.

[3]  J. Stephens,et al.  Synchronization of motor unit activity during voluntary contraction in man. , 1990, The Journal of physiology.

[4]  J. R. Rosenberg,et al.  Identification of patterns of neuronal connectivity—partial spectra, partial coherence, and neuronal interactions , 1998, Journal of Neuroscience Methods.

[5]  P. Kirkwood,et al.  Evidence from Motoneurone Synchronization for Disynaptic Pathways in the Control of Inspiratory Motoneurones in the Cat , 1997, The Journal of physiology.

[6]  M K Habib,et al.  Dynamics of neuronal firing correlation: modulation of "effective connectivity". , 1989, Journal of neurophysiology.

[7]  J. R. Rosenberg,et al.  An extended difference of coherence test for comparing and combining several independent coherence estimates: theory and application to the study of motor units and physiological tremor , 1997, Journal of Neuroscience Methods.

[8]  Peter A. Getting.  Reconstruction of small neural networks , 1989 .

[9]  J. R. Rosenberg,et al.  Time and Frequency Domain Analysis of Spike Train and Time Series Data , 1999 .

[10]  T. Sears,et al.  Short‐term synchronization of intercostal motoneurone activity. , 1976, The Journal of physiology.

[11]  J. R. Rosenberg,et al.  The Fourier approach to the identification of functional coupling between neuronal spike trains. , 1989, Progress in biophysics and molecular biology.

[12]  Kenneth D. Miller,et al.  Physiological Gain Leads to High ISI Variability in a Simple Model of a Cortical Regular Spiking Cell , 1997, Neural Computation.

[13]  A J Fuglevand,et al.  Estimating the strength of common input to human motoneurons from the cross‐correlogram. , 1992, The Journal of physiology.

[14]  J A Stephens,et al.  Variation in the degree of synchronization exhibited by motor units lying in different finger muscles in man. , 1991, The Journal of physiology.

[15]  D. R. Cox,et al.  On the Estimation of the Intensity Function of a Stationary Point Process , 1965 .

[16]  D. Brillinger.  The Identification of Point Process Systems , 1975 .

[17]  C. D. Kemp,et al.  Kendall's Advanced Theory of Statistics, Volume 1, Distribution Theory. , 1988 .

[18]  P. Matthews.  Relationship of firing intervals of human motor units to the trajectory of post‐spike after‐hyperpolarization and synaptic noise. , 1996, The Journal of physiology.

[19]  P. Ashby,et al.  Characteristics of postsynaptic potentials produced in single human motoneurons by homonymous group 1 volleys , 2004, Experimental Brain Research.

[20]  P. Ellaway,et al.  THE ORIGINS AND CHARACTERISTICS OF CROSS‐CORRELATED ACTIVITY BETWEEN γ‐MOTONEURONES IN THE CAT , 1985 .

[21]  Pa Kirkwood,et al.  SYNAPTIC CONNECTIONS TO INTERCOSTAL MOTONEURONS AS REVEALED BY AVERAGE COMMON EXCITATION POTENTIAL , 1978 .

[22]  H. Robinson,et al.  Spatio-temporal cholinergic modulation in cultured networks of rat cortical neurons: Spontaneous activity , 2005, Neuroscience.

[23]  P. Ellaway,et al.  THE SOURCE AND DISTRIBUTION OF SHORT-TERM SYNCHRONY BETWEEN γ-MOTONEURONES IN THE CAT , 1985 .

[24]  P. Ashby,et al.  Relationship between EPSP shape and cross-correlation profile explored by computer simulation for studies on human motoneurons , 2004, Experimental Brain Research.

[25]  Junichi Ushiba,et al.  Synchronization analysis using joint peri-stimulus time histograms for human motor units , 2002, Journal of Neuroscience Methods.

[26]  F Bruyninckx,et al.  Motor unit synchronization in physiologic, enhanced physiologic, and voluntary tremor in man , 1988, Annals of neurology.

[27]  Sidarta Ribeiro,et al.  Multielectrode recordings: the next steps , 2002, Current Opinion in Neurobiology.

[28]  J. R. Rosenberg,et al.  On the application, estimation and interpretation of coherence and pooled coherence , 2000, Journal of Neuroscience Methods.

[29]  A M Amjad,et al.  A framework for the analysis of mixed time series/point process data--theory and application to the study of physiological tremor, single motor unit discharges and electromyograms. , 1995, Progress in biophysics and molecular biology.

[30]  S. Baker.  ‘Pooled coherence’ can overestimate the significance of coupling in the presence of inter-experiment variability , 2000, Journal of Neuroscience Methods.

[31]  J A Stephens,et al.  Correlation between the discharges of motor units recorded from the same and from different finger muscles in man. , 1991, The Journal of physiology.

[32]  D. L. Tuck,et al.  Investigation of intercostal neuronal intracellular processes and connectivity by signal analysis and computer simulation , 1977 .

[33]  S. Farmer,et al.  Central nervous pathways underlying synchronization of human motor unit firing studied during voluntary contractions. , 1991, The Journal of physiology.

[34]  M. Laubach,et al.  Cortical ensemble activity increasingly predicts behaviour outcomes during learning of a motor task , 2022 .

[35]  B. Gustafsson,et al.  Afterhyperpolarization conductance time course in lumbar motoneurones of the cat. , 1974, Acta physiologica Scandinavica.

[36]  J. Jack,et al.  Electric current flow in excitable cells , 1975 .

[37]  B. Conway,et al.  Detection of weak synaptic interactions between single Ia afferent and motor‐unit spike trains in the decerebrate cat. , 1993, The Journal of physiology.

[38]  R. Enoka,et al.  Motor-unit coherence during isometric contractions is greater in a hand muscle of older adults. , 2003, Journal of neurophysiology.

[39]  J. R. Rosenberg,et al.  Load-independent contributions from motor-unit synchronization to human physiological tremor. , 1999, Journal of neurophysiology.

[40]  L. Adams,et al.  Synchronization of motor unit firing during different respiratory and postural tasks in human sternocleidomastoid muscle. , 1989, The Journal of physiology.

[41]  D. Halliday,et al.  The frequency content of common synaptic inputs to motoneurones studied during voluntary isometric contraction in man. , 1993, The Journal of physiology.

[42]  Hai-Qing Gong,et al.  Firing rates and dynamic correlated activities of ganglion cells both contribute to retinal information processing , 2004, Brain Research.

[43]  D. Brillinger.  Estimation of the Second-Order Intensities of a Bivariate Stationary Point Process , 1976 .

[44]  A. Stuart,et al.  Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory , 1988 .

[45]  M. Bartlett.  The Spectral Analysis of Point Processes , 1963 .