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Statistical crossover and nonextensive behavior of neuronal short-term depression

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Abstract

The theoretical basis of neuronal coding, associated with short-term degradation in synaptic transmission, is a matter of debate in the literature. In fact, electrophysiological signals are commonly characterized as inversely proportional to stimulus intensity. Among theoretical descriptions of this phenomenon, models based on 1/f-dependency are employed to investigate the biophysical properties of short-term synaptic depression. In this work, we formulate a model based on a paradigmatic q-differential equation to obtain a generalized formalism useful for investigation of nonextensivity in this specific type of synaptic plasticity. Our analysis reveals nonextensivity in data from electrophysiological recordings and also a statistical crossover in neurotransmission. In particular, statistical transitions provide additional support to the hypothesis of heterogeneous release probability of neurotransmitters. On the other hand, the simple vesicle model agrees with data only at low-frequency stimulations. Thus, the present work presents a method to demonstrate that short-term depression is not only governed by random mechanisms but also by nonextensive behavior. Our findings also conciliate morphological and electrophysiological investigations into a coherent biophysical scenario.

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  • 27 November 2017

    The authors apologize for the following errors published in the article. However, these errors do not modify the main assumptions in our work nor affects the discussion (interpretation) of the results.

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Acknowledgments

The authors thank Constantino Tsallis for his valuable suggestions and discussions.

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Authors and Affiliations

  1. Centro de Formação em Ciências e Tecnologias Agroflorestais, Universidade Federal do Sul da Bahia, Itabuna, Bahia. CEP 45613-204, Brazil

    A. J. da Silva & D. O. C. Santos

  2. Colegiado de Engenharia Civil, Universidade Federal do Vale do São Francisco, Juazeiro, Bahia. CEP 48902-300, Brazil

    S. Floquet

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  1. A. J. da Silva
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Correspondence to A. J. da Silva.

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The original version of this article was revised: The authors apologize for the following errors published in the article. However, these errors do not modify the main assumptions in their work nor affects the discussion (interpretation) of the results. Brasil was changed to Brazil in the affiliations and some text under the Discussion and Conclusions’ sections were corrected.

A correction to this article is available online at https://doi.org/10.1007/s10867-017-9477-0.

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Silva, A.J.d., Floquet, S. & Santos, D.O.C. Statistical crossover and nonextensive behavior of neuronal short-term depression. J Biol Phys 44, 37–50 (2018). https://doi.org/10.1007/s10867-017-9474-3

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