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Computational Intelligence and Neuroscience
Volume 2012, Article ID 704673, 9 pages
Research Article

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

1Department of Bioengineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
2Neurobiology of Learning Unit, Scientific Institute San Raffaele and Università Vita e Salute San Raffaele, Via Olgettina 58, 20132 Milano, Italy

Received 18 January 2012; Revised 1 June 2012; Accepted 6 June 2012

Academic Editor: Marc Van Hulle

Copyright © 2012 Jacopo Lamanna et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 α 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 1/f series. These tests were performed by varying separately: (i) 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. The aims were to provide a methodological framework for approaching the fractal analysis of single-unit spontaneous release series recorded at central synapses.