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The rate of exocytic events from both neurons and non-neuronal cells exhibits fluctuations consistent with fractal (self-similar) behavior in time, as evidenced by a number of statistical measures. We explicitly demonstrate this for neurotransmitter secretion at Xenopus neuromuscular junctions and for rat hippocampal synapses in culture; the exocytosis of exogenously supplied neurotransmitter from cultured Xenopus myocytes and from rat fibroblasts behaves similarly. The magnitude of the fluctuations of the rate of exocytic events about the mean decreases slowly as the rate is computed over longer and longer time periods, the periodogram decreases in power-law manner with frequency, and the Allan factor (relative variance of the number of exocytic events) increases as a power-law function of the counting time. These features are hallmarks of self-similar behavior. Their description requires models that exhibit long-range correlation (memory) in event occurrences. We have developed a physiologically plausible model that accords with all of the statistical measures that we have examined. The appearance of fractal behavior at synapses, as well as in systems comprising collections of synapses, indicates that such behavior is ubiquitous in neural signaling.
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