What is the meaningful measure of neuronal spike train activity?

Abstract

Neuronal spike train activity is conventionally viewed in terms of certain measures of central tendency (mean or median of intervals between discrete events or mean rate of such events) and their associated measures of variability (S.D., skew, etc.). Less commonly, investigators will compute the probabilities of occurrence in an Information Theory context. Another rarely considered measure of spike trains is serial ordering. Seldom is more than one of these approaches applied to the same spike train, and we are unaware of any case where all 3 have been applied to the same train. In order to test the inter-relationships among these approaches, we examined the same spike trains with all 3 analytic methods. Measures of central tendency were taken from the original absolute interval values, whereas entropy and serial order (Markov order) were computed from the sequences of patterns of adjacent intervals, expressed in the same non-parametric format. We found that entropy (measure of uncertainty) did not correlate well with the degree of serial ordering (Markov order). Entropy also did not correlate well with measures of central tendency (median or mean interval, or impulses/s) nor with the variability of such measures. An inverse correlation was seen between Markov order and several measures of central tendency (mean interval and rate) as well as with several measures of variability. The implications of these analyses extend beyond the analysis of spike trains to most all biological and physical time series. For neurophysiologists, these analyses may challenge our common assumptions about the most appropriate way to describe and interpret neuronal spike train activity. Our results showed that no one analytical approach may be satisfactory, or in any case, one cannot assume a priori and without empirical testing which approach will provide the best description of the data from a given experiment.