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Quiescence-to-Oscillations Transition Features in Dynamics of Spontaneous Astrocytic Calcium Concentration

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Book cover Mathematical Modeling and Supercomputer Technologies (MMST 2020)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1413))

Abstract

Recent experimental data show that neural network dynamics significantly depends on the properties of an active nonlinear environment in the brain. Chemical activity of astrocytes is one of the main factor modifying the excitability of the neuronal membrane and regulating the efficiency of signal transmission between neurons. It is known that astrocytes can demonstrate both spontaneous changes in calcium concentration and calcium signals caused by neuronal activity. We focus on spontaneous calcium concentration dynamics in astrocytes. Nonlinear differential equations describing molecular t between neuronsransport in the astrocytes are investigated. Particularly, within the frame of Lavrentovich-Hemkin mathematical model for calcium dynamics, the bifurcation mechanisms of spontaneous calcium concentration change are determined. We show that both soft (emergence of small-amplitude oscillations via supercritical Andronov-Hopf bifurcation) and hard (instantaneous emergence of large-amplitude oscillations via fold limit cycle bifurcation) ways for oscillations emergence can be realized in the astrocyte dynamics.

This work was supported by grant of the President of the Russian Federation for state support of leading scientific schools No. NSh-2653.2020.2. SG work was supported by the RFBR grants No. 20-32-70081, 18-29-10068 and the grant of the Ministry of Science and Higher Education of the Russian Federation project No. 0729-2020-0061.

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Authors and Affiliations

  1. Department of Applied Mathematics, Institute of Information Technologies, Mathematics and Mechanics, Lobachevsky State University of Nizhni Novgorod, 23, Gagarin Avenue, Nizhny Novgorod, 603950, Russia

    Maria S. Sinitsina & Evgeniya V. Pankratova

  2. Neurotechnology Department, Lobachevsky State University of Nizhni Novgorod, 23, Gagarin Avenue, Nizhny Novgorod, 603950, Russia

    Victor B. Kazantsev

  3. Neuroscience and Cognitive Technology Laboratory, Center for Technologies in Robotics and Mechatronics Components, Innopolis University, 1, Universitetskaya Street, Innopolis, 420500, Russia

    Susanna Yu. Gordleeva & Victor B. Kazantsev

  4. Neuroscience Research Institute, Samara State Medical University, 89, Chapaevskaya Street, Samara, 443099, Russia

    Victor B. Kazantsev

Authors
  1. Maria S. Sinitsina
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  2. Susanna Yu. Gordleeva
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  3. Victor B. Kazantsev
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  4. Evgeniya V. Pankratova
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Corresponding author

Correspondence to Maria S. Sinitsina .

Editor information

Editors and Affiliations

  1. Lobachevsky State University of Nizhni Novgorod, Nizhny Novgorod, Russia

    Dmitry Balandin

  2. Lobachevsky State University of Nizhni Novgorod, Nizhny Novgorod, Russia

    Konstantin Barkalov

  3. Lobachevsky State University of Nizhni Novgorod, Nizhniy Novgorod, Russia

    Victor Gergel

  4. Lobachevsky State University of Nizhni Novgorod, Nizhny Novgorod, Russia

    Iosif Meyerov

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Sinitsina, M.S., Gordleeva, S.Y., Kazantsev, V.B., Pankratova, E.V. (2021). Quiescence-to-Oscillations Transition Features in Dynamics of Spontaneous Astrocytic Calcium Concentration. In: Balandin, D., Barkalov, K., Gergel, V., Meyerov, I. (eds) Mathematical Modeling and Supercomputer Technologies. MMST 2020. Communications in Computer and Information Science, vol 1413. Springer, Cham. https://doi.org/10.1007/978-3-030-78759-2_10

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  • DOI: https://doi.org/10.1007/978-3-030-78759-2_10

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