Izvestiya VUZ. Applied Nonlinear Dynamics
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Izvestiya VUZ. Applied Nonlinear Dynamics, 2021, Volume 29, Issue 3, Pages 440–448
DOI: https://doi.org/10.18500/0869-6632-2021-29-3-440-448
(Mi ivp427)
 

This article is cited in 4 scientific papers (total in 4 papers)

NONLINEAR DYNAMICS AND NEUROSCIENCE

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

M. S. Sinitsinaa, S. Yu. Gordleevaab, V. B. Kazantsevabc, E. V. Pankratovaa

a Lobachevsky State University of Nizhni Novgorod, Russia
b Innopolis University, Russia
c Samara State Medical University, Russia
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.
Keywords: mathematical modeling, calcium concentration in astrocytes, oscillatory mode, stationary mode.
Funding agency Grant number
Grant of the President of the Russian Federation НШ-2653.2020.2
Russian Foundation for Basic Research 20-32-70081
18-29-10068
Ministry of Science and Higher Education of the Russian Federation 0729-2020-0061
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).
Received: 17.11.2020
Bibliographic databases:
Document Type: Article
UDC: 530.182
Language: English
Citation: M. S. Sinitsina, S. Yu. Gordleeva, V. B. Kazantsev, E. V. Pankratova, “Calcium concentration in astrocytes: emergence of complicated spontaneous oscillations and their cessation”, Izvestiya VUZ. Applied Nonlinear Dynamics, 29:3 (2021), 440–448
Citation in format AMSBIB
\Bibitem{SinGorKaz21}
\by M.~S.~Sinitsina, S.~Yu.~Gordleeva, V.~B.~Kazantsev, E.~V.~Pankratova
\paper Calcium concentration in astrocytes: emergence of complicated spontaneous oscillations and their cessation
\jour Izvestiya VUZ. Applied Nonlinear Dynamics
\yr 2021
\vol 29
\issue 3
\pages 440--448
\mathnet{http://mi.mathnet.ru/ivp427}
\crossref{https://doi.org/10.18500/0869-6632-2021-29-3-440-448}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000657799500011}
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Izvestiya VUZ. Applied Nonlinear Dynamics
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