The development of spontaneous bioelectric activity (SBA) was studied in dissociated occipital cortex cultures prepared from 19 day old rat fetuses. All cultures, recorded one per diem from 5 to 33 days in vitro (div), showed SBA. Computer analysis of 76 extracellularly recorded single unit spike trains was carried out after selection on the basis of stationarity criteria. Statistically significant developmental trends were found in (i) interspike interval dependencies and (ii) fluctuations in mean firing rate, on the order of a minute or longer. The highly dependent firing patterns, including stereotyped bursting, were present mostly in the 9–12 div group, whereas minute-to-minute fluctuations in the intensity of firing were considerably more pronounced in the oldest group (22–33 div) than in the younger cultures. In addition, firing categories defined on the basis of factor-analysis revealed that such fluctuations were almost exclusively to be found in neurons which fired in a pronounced ‘burst’, rather than a relatively continuous fashion. Only a few mature appearing synaptic structures were observed electron microscopically prior to 12 div, but increased steadily in number thereafter. No cultures prior to 14 div, but all cultures older than this, stained positively for the presence of glutamic acid decarboxylase. An extensive immunoreactive, putative GABAergic, network was present by three weeks in vitro.

Spontaneous neuronal firing patterns in fetal rat cortical networks during development in vitro: a quantitative analysis.

Serial interval statistics of spontaneous activity in cortical neurons in vivo and in vitro

Markov-dependency and spectral analyses on spike-counts in mesencephalic reticular neurons during sleep and attentive states

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

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

Testing the order of discrete Markov chains using surrogate data

To evaluate the order and the values of Markov properties of the time series of events, we have proposed a statistical measure "dependency":D m = (H 0 ?H m )/H 0 , whereH 0 andH m are Shannon's entropy and them-th order conditional entropy, respectively. It is indicated that $$\tilde D_m = \sum\limits_{v = 1}^m {(\hat D_v - \bar D_v^{sh} } )$$ is a better point estimator ofD m, giving a total value of them-th order Markov process. Here $$\hat D_m $$ and $$\bar D_m^{sh} $$ are the estimate ofD m and the arithmetic mean of $$\hat D_m^{sh} $$ when them-th order shuffling is made many times for a given observed series, respectively. The value $$\hat D_m - \bar D_m^{sh} = d_m $$ represents Markov value of the orderm. Under the assumption that the series has continuous variables and the normal distribution, simplified dependency is defined by[Figure not available: see fulltext.], where |S m | is the determinant of serial correlation coefficients. It is shown that[Figure not available: see fulltext.] is practically useful for the estimation of the order and the values of Markov processes with small sample size. It is also indicated that[Figure not available: see fulltext.] analysis is basically equivalent to the least mean-square analysis of autoregressive models.

H. Fujii

Papers

Dependency as a measure to estimate the order and the values of Markov processes