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Maximum-likelihood q-estimator uncovers the role of potassium at neuromuscular junctions

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Abstract

Recently, we demonstrated the existence of nonextensive behavior in neuromuscular transmission (da Silva et al. in Phys Rev E 84:041925, 2011). In this letter, we first obtain a maximum-likelihood q-estimator to calculate the scale factor (\(\alpha \)) and the q-index of q-Gaussian distributions. Next, we use the indexes to analyze spontaneous miniature end plate potentials in electrophysiological recordings from neuromuscular junctions. These calculations were performed assuming both normal and high extracellular potassium concentrations \([K^{+}]_{o}\). This protocol was used to test the validity of Tsallis statistics under electrophysiological conditions closely resembling physiological stimuli. The analysis shows that q-indexes are distinct depending on the extracellular potassium concentration. Our letter provides a general way to obtain the best estimate of parameters from a q-Gaussian distribution function. It also expands the validity of Tsallis statistics in realistic physiological stimulus conditions. In addition, we discuss the physical and physiological implications of these findings.

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Acknowledgments

This work was supported in part by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPQ). The authors would like to thank Constantino Tsallis for his valuable comments and Christopher Kushmerick for his support.

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Author notes

  1. A. J. da Silva

    Present address: Instituto de Humanidades, Artes e Ciências, Universidade Federal do Sul da Bahia, Itabuna, Bahia, CEP 45613-204, Brazil

Authors and Affiliations

  1. Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, CEP 31270-901, Brazil

    A. J. da Silva

  2. Departamento de Ciências Exatas e da Terra, Universidade do Estado da Bahia, Alagoinhas, Bahia, CEP 48040-210, Brazil

    M. A. S. Trindade

  3. Instituto de Humanidades, Artes e Ciências, Universidade Federal do Sul da Bahia, Itabuna, Bahia, CEP 31270-901, Brazil

    D. O. C. Santos

  4. Departamento de Fisiologia e Farmacologia, Faculdade de Medicina, Universidade Federal do Ceará, Fortaleza, Ceará, CEP 60430-270, Brazil

    R. F. Lima

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Correspondence to A. J. da Silva.

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da Silva, A.J., Trindade, M.A.S., Santos, D.O.C. et al. Maximum-likelihood q-estimator uncovers the role of potassium at neuromuscular junctions. Biol Cybern 110, 31–40 (2016). https://doi.org/10.1007/s00422-015-0673-3

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