Serial ordering in spike trains: what's it "trying to tell us"?

Abstract

Summarized herein is the evidence that supports the hypothesis that neuronal action potentials (spike trains) are coded not only in terms of simple discharge rate but also can be serially coded by certain patterns of spike intervals. Based on the relative interval description method of Sherry and Marczynski (1972), our analyses of single-unit activity from cerebellar cortex neurons of rats seem to support three principal categories of conclusions; (1) Serial dependence of intervals does exist. This has been demonstrated with a variety of conventional statistical tests. These serial dependencies have also been shown to be independent of the (nonsequential) interval distribution variability. (2) Information theory is appropriate for evaluating spike trains. We have developed and tested methods for computing a fractional entropy for a given number of adjacent intervals, for assessing the relative fractional entropy of any one interval in a set of intervals, for computing for a group of neurons the mean and standard deviation of fractional entropy for specified clusters or intervals, and for transforming these values so that interval clusters of differing number can all be compared on the same numerical entropy scale (percentage maximum fractional entropy). In addition to the descriptive and quantitative value of such measures, we have also demonstrated their utility in testing hypotheses and in making empirical correlations. (3) The nervous system seems to process spike train intervals in "bytes", not "hits", of adjacent, serially ordered intervals. Among the several lines of evidence for this conclusion is the demonstration that drug-induced (ethanol) changes in fractional entropy of specific interval clusters seem to involve a "linked" combination of certain interval clusters, some which increase and others which decrease in incidence. Also, by using n-dimensional Chi-Square methodology, we have demonstrated that the relationships of adjacent intervals represent a Markovian process in which the duration of a given interval is partially determined by the duration of as many as four immediately preceding intervals. Finally, we showed that the relative fractional entropy (% maximum) of interval clusters of different numbers does not have a Gaussian distribution but rather is distributed in surprising ways by the specific number and relative durations of adjacent intervals. So just what is the serial ordering and information content of spike train intervals trying to tell us?. Perhaps it is trying to say that the nervous system processes information on a moment-by-moment basis in terms of "bytes" of short sequences of spikes with specific patterns of relative interspike durations. If so, we should be able to identify and characterize those "bytes". Much further testing must be done before we can claim that "neural codes" operate on the principles described herein. Nonetheless, we have made the issues explicit, and in our opinion have provided enough evidence to warrant further investigation.