Long-term correlations in the spike trains of medullary sympathetic neurons

Fano factor analysis was used to characterize the spike trains of single medullary neurons with sympathetic nerve-related activity in cats that were decerebrate or anesthetized with Dial-urethan or urethan. For this purpose, values (Fano factor) of the variance of the number of extracellularly recorded spikes divided by the mean number of spikes were calculated for window sizes of systematically varied length. For window sizes less than or equal to 10 ms, the Fano factor was close to one, as expected for a Bernoulli process with a low probability of success. The Fano factor dipped below one as the window size approached the shortest interspike interval (ISI) and reached its nadir at window sizes near the modal ISI. The extent of the dip reflected the shape (skewness) of the ISI histogram with the dip being smallest for the most asymmetric distributions. Most importantly, for a wide range of window sizes exceeding the modal ISI, the Fano factor curve took the form of a power law function. This was the case independent of the component (cardiac related, 10 Hz, or 2-6 Hz) of inferior cardiac sympathetic nerve discharge to which unit activity was correlated or the medullary region (lateral tegmental field, raphe, caudal and rostral ventrolateral medulla) in which the neuron was located. The power law relationship in the Fano factor curves was eliminated by randomly shuffling the ISIs even though the distribution of the intervals was unchanged. Thus the power law relationship arose from long-term correlations among ISIs that were disrupted by shuffling the data. The presence of long-term correlations across different time scales reflects the property of statistical self-similarity that is characteristic of fractal processes. In most cases, we found that mean ISI and variance for individual spike trains increased as a function of the number of intervals counted. This can be attributed to the clustering of long and short ISIs, which also is an inherent property of fractal time series. We conclude that the spike trains of brain stem sympathetic neurons have fractal properties.