Detection of Fractal Behavior in Temporal Series of Synaptic Quantal Release Events: A Feasibility Study

Since the pioneering work of Fatt & Katz at the neuromuscular junction (NMJ), spontaneous synaptic release, i.e. the quantal discharge of neurotransmitter molecules which occurs in the absence of action potentials (minis), has been unanimously considered a memoryless random Poisson process where each quantum is discharged with a very low release probability independently from neighboring 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, i.e. with a rate parameter that does not change over time. Since we are interested in accurately quantifying the fractal exponent α of the spontaneous neurotransmitter release process at central synaptic sites, this work is 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 used spontaneous release series recorded at individual hippocampal synapses (single-synapse recordings). Based on these data, we generated large collections of simulated quantal events by means of a custom algorithm combining Monte Carlo sampling methods with spectral methods for the generation of 1/f series. These tests were performed by separately varying the fractal exponent α 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. Our results aim at providing a methodological framework for approaching the fractal analysis of single-unit spontaneous release series recorded at central synapses.