Since the pioneering work of Fatt and Katz at the neuromuscular junction (NMJ), spontaneous synaptic release (minis), that is, the quantal discharge of neurotransmitter molecules which occurs in the absence of action potentials, has been unanimously considered a memoryless random Poisson process where each quantum is discharged with a very low release probability independently from other quanta. When this model was thoroughly tested, for both population and single-synapse recordings, some clear evidence in favor of a more complex scenario emerged. This included short- and long-range correlation in mini occurrences and divergence from mono-exponential inter-mini-interval distributions, both unexpected for a homogeneous Poisson process, that is, with a rate parameter that does not change over time. Since we are interested in accurately quantifying the fractal exponent of the spontaneous neurotransmitter release process at central synaptic sites, this work was aimed at evaluating the sensitivity of the most established methods available, such as the periodogram, the Allan, factor and the detrended fluctuation analysis. For this analysis we matched spontaneous release series recorded at individual hippocampal synapses (single-synapse recordings) to generate large collections of simulated quantal events by means of a custom algorithm combining Monte Carlo sampling methods with spectral methods for the generation of series. These tests were performed by varying separately: (i) the fractal exponent of the rate driving the release process; (ii) the distribution of intervals between successive releases, mimicking those encountered in single-synapse experimental series; (iii) the number of samples. The aims were to provide a methodological framework for approaching the fractal analysis of single-unit spontaneous release series recorded at central synapses. 1. Introduction Based on classical work at the neuromuscular junction (NMJ) and at other peripheral terminals , individual synaptic release sites have been always assumed to behave independently and to discharge quanta at a very low and stable rate. Regrettably, based on the large number of contrasting evidence which has accumulated since then, this memory-less description of the spontaneous release process might not always apply to CNS synapses [2–4]. For example, it has been shown that the occurrence of minis does exhibit long-term correlations , a synaptic memory that might be expressed, for example, by a correlating phenomenon such as a local changes in intracellular calcium at the active zone, where
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