ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Sinitsina M. S., Gordleeva S. Y., Kazantsev V. B., Pankratova E. V. Calcium concentration in astrocytes: Emergence of complicated spontaneous oscillations and their cessation. Izvestiya VUZ. Applied Nonlinear Dynamics, 2021, vol. 29, iss. 3, pp. 440-448. DOI: 10.18500/0869-6632-2021-29-3-440-448

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Language: 
English
Heading: 
Nonlinear Dynamics and Neuroscience
Article type: 
Article
UDC: 
530.182
DOI: 
10.18500/0869-6632-2021-29-3-440-448

Calcium concentration in astrocytes: Emergence of complicated spontaneous oscillations and their cessation

Autors: 
Sinitsina Maria Sergeevna, Lobachevsky State University of Nizhny Novgorod
Gordleeva Susanna Yurevna, Lobachevsky State University of Nizhny Novgorod
Kazantsev Viktor Borisovich, Institute of Applied Physics of the Russian Academy of Sciences
Pankratova Evgenija Valerevna, Volga State Academy of Water Transport (VGAVT)
Abstract: 

The purpose of this work is to show the mechanisms of transitions between different dynamic modes of spontaneous astrocytic calcium activity. With this aim, dynamics of recently introduced Lavrentovich–Hemkin mathematical model was examined by both analytical and numerical techniques. Methods. In order to obtain the conditions for the oscillations cessation, the linear stability analysis for the equilibrium point was carried out. Complicated dynamics was studied numerically by calculations of time traces and bifurcation diagrams. Results. The mechanisms of oscillatory mode development with the increase of the maximal calcium flux out of the SERCA pump in the presence of low and high level of extracellular calcium concentration were demonstrated. It was shown that emergence of oscillations occurs via supercritical Andronov–Hopf bifurcation, and the properties of the oscillatory mode with further increase of the maximal calcium flux out of the SERCA pump are highly dependent on the value of extracellular calcium concentration. Notably, emergence of chaotic spontaneous calcium oscillations for specific level of calcium ions outside the cell was revealed. Conclusion. Based on the analysis of various dynamical modes of spontaneous astrocytic chemical activity, the peculiarities in astrocyte-neuron interaction in complex multicellular systems can be further investigated.

Key words: 
mathematical modeling
calcium concentration in astrocytes
oscillatory mode
stationary mode
Acknowledgments: 
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. This study was supported by the Ministry of Science and Higher Education of the Russian Federation (project No. 0729-2020-0061)
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Received: 
17.11.2020
Accepted: 
27.01.2021
Published: 
31.05.2021
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