Neuronal Exocytosis Exhibits Fractal Behavior
The time sequence of exocytic events in both neurons and non-neuronal cells exhibits fractal (self-similar) properties, as evidenced by a number of statistical measures. Such fractal activity occurs in neurotransmitter secretion at Xenopus neuromuscular junctions and rat hippocampal synapses in culture, and in the exocytosis of exogenously supplied neurotransmitter from cultured Xenopus myocytes and rat fibroblasts. 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 fashion 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, power-law-decaying 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 fractal lognormal-noise-driven doubly stochastic Poisson process (FLNDP). In particular, we show that the experimental rate function is well modeled by fractal lognormal noise (FLN). The appearance of behavior with fractal characteristics at synapses, as well as in systems comprising collections of synapses, indicates that such behavior is an inherent property of neuronal signaling.
KeywordsFractal Behavior Membrane Voltage Allan Variance Homogeneous Poisson Process Interevent Time
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