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

For citation:

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

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 816)
Article type: 

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

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)

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.

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)
  1. Lee SG, Neiman A, Kim S. Coherence resonance in a Hodgkin–Huxley neuron. Phys. Rev. E. 1998;57(3):3292–3297. DOI: 10.1103/PhysRevE.57.3292.
  2. Belykh VN, Pankratova EV. Chaotic synchronization in ensembles of coupled neurons modeled by the FitzHugh–Rinzel system. Radiophysics and Quantum Electronics. 2006;49(11):910–921. DOI: 10.1007/s11141-006-0124-z.
  3. Pankratova EV, Belykh VN, Mosekilde E. Dynamics and synchronization of noise perturbed ensembles of periodically activated neuron cells. International Journal of Bifurcation and Chaos. 2008;18(9):2807–2815. DOI: 10.1142/S0218127408022044.
  4. Yu H, Wang J, Deng B, Wei X, Wong YK, Chan WL, Tsang KM, Yu Z. Chaotic phase synchronization in small-world networks of bursting neurons. Chaos. 2011;21(1):013127. DOI: 10.1063/1.3565027.
  5. Kazantsev VB, Asatryan SY. Bistability induces episodic spike communication by inhibitory neurons in neuronal networks. Phys. Rev. E. 2011;4(3):031913. DOI: 10.1103/PhysRevE.84.031913.
  6. Uzuntarla M. Inverse stochastic resonance induced by synaptic background activity with unreliable synapses. Phys. Lett. A. 2013;377(38):2585–2589. DOI: 10.1016/j.physleta.2013.08.009.
  7. Uzuntarla M, Ozer M, Ileri U, Calim A, Torres JJ. Effects of dynamic synapses on noise-delayed response latency of a single neuron. Phys. Rev. E. 2015;92(6):062710. DOI: 10.1103/PhysRevE.92.062710.
  8. Esir PM, Gordleeva SY, Simonov AY, Pisarchik AN, Kazantsev VB. Conduction delays can enhance formation of up and down states in spiking neuronal networks. Phys. Rev. E. 2018;98(5): 052401. DOI: 10.1103/PhysRevE.98.052401.
  9. Dityatev A, Frischknecht R, Seidenbecher CI. Extracellular matrix and synaptic functions. Results Probl. Cell Differ. 2006;43:69–97. DOI: 10.1007/400_025.
  10. Wang X, Lou N, Xu Q, Tian GF, Peng WG, Han X, Kang J, Takano T, Nedergaard M. Astrocytic Ca2+ signaling evoked by sensory stimulation in vivo. Nature Neuroscience. 2006;9(6):816–823. DOI: 10.1038/nn1703.
  11. Kazantsev V, Gordleeva S, Stasenko S, Dityatev A. A homeostatic model of neuronal firing governed by feedback signals from the extracellular matrix. PLoS One. 2012;7(7):e41646. DOI: 10.1371/journal.pone.0041646.
  12. Pankratova EV, Kalyakulina AI. Environmentally induced amplitude death and firing provocation in large-scale networks of neuronal systems. Regular and Chaotic Dynamics. 2016;21(7–8):840– 848. DOI: 10.1134/S1560354716070078.
  13. Lazarevich I, Stasenko S, Rozhnova M, Pankratova E, Dityatev A, Kazantsev V. Activity dependent switches between dynamic regimes of extracellular matrix expression. PloS One. 2020;15(1):e0227917. DOI: 10.1371/journal.pone.0227917.
  14. Rozhnova MA, Pankratova EV, Kazantsev VB. Brain extracellular matrix impact on neuronal firing reliability and spike-timing jitter. Advances in Neural Computation, Machine Learning, and Cognitive Research III. Studies in Computational Intelligence, vol. 856. International Conference on Neuroinformatics, 2019, October 7–11, Dolgoprudny, Russia. Springer, Cham; 2020. P. 190–196. DOI: 10.1007/978-3-030-30425-6_22.
  15. Gordleeva SY, Stasenko SV, Semyanov AV, Dityatev AE, Kazantsev VB. Bi-directional astrocytic regulation of neuronal activity within a network. Frontiers in Computational Neuroscience. 2012;6:92. DOI: 10.3389/fncom.2012.00092.
  16. Pankratova EV, Kalyakulina AI, Stasenko SV, Gordleeva SY, Lazarevich IA, Kazantsev VB. Neuronal synchronization enhanced by neuron–astrocyte interaction. Nonlinear Dynamics. 2019; 97(1):647–662. DOI: 10.1007/s11071-019-05004-7.
  17. Makovkin SY, Shkerin IV, Gordleeva SY, Ivanchenko MV. Astrocyte-induced intermittent synchronization of neurons in a minimal network. Chaos, Solitons & Fractals. 2020;138:109951. DOI: 10.1016/j.chaos.2020.109951.
  18. Kanakov O, Gordleeva S, Ermolaeva A, Jalan S, Zaikin A. Astrocyte-induced positive integrated information in neuron-astrocyte ensembles. Phys. Rev. E. 2019;99(1):012418. DOI: 10.1103/PhysRevE.99.012418.
  19. Matrosov V, Gordleeva S, Boldyreva N, Ben-Jacob E, Kazantsev V, De Pitta M. Emergence of regular and complex calcium oscillations by tnositol 1,4,5-Trisphosphate signaling in astrocytes. In: De Pitta M, Berry H. (eds) Computational Glioscience. Springer Series in Computational Neuroscience. Springer, Cham; 2019. DOI: 10.1007/978-3-030-00817-8_6.
  20. Wu YW, Gordleeva S, Tang X, Shih PY, Dembitskaya Y, Semyanov A. Morphological profile determines the frequency of spontaneous calcium events in astrocytic processes. Glia. 2019;67(2): 246–262. DOI: 10.1002/glia.23537.
  21. Parri HR, Crunelli V. The role of Ca2+ in the generation of spontaneous astrocytic Ca2+ oscillations. Neuroscience. 2003;120(4):979–992. DOI: 10.1016/s0306-4522(03)00379-8.
  22. Perea G, Araque A. Properties of synaptically evoked astrocyte calcium signal reveal synaptic information processing by astrocytes. The Journal of Neuroscience: The Official Journal of the Society for Neuroscience. 2005;25(9):2192–2203. DOI: 10.1523/JNEUROSCI.3965-04.2005.
  23. Gordleeva SY, Ermolaeva AV, Kastalskiy IA, Kazantsev VB. Astrocyte as spatiotemporal integrating detector of neuronal activity. Frontiers in Physiology. 2019;10:294. DOI: 10.3389/fphys.2019.00294.
  24. Gordleeva SY, Lebedev SA, Rumyantseva MA, Kazantsev VB. Astrocyte as a detector of synchronous events of a neural network. JETP Letters. 2018;107(7):440–445. DOI: 10.1134/S0021364018070032.
  25. Swillens S, Dupont G, Combettes L, Champeil P. From calcium blips to calcium puffs: Theoretical analysis of the requirements for interchannel communication. Proceedings of the National Academy of Sciences of the United States of America. 1999;96(24):13750–13755. DOI: 10.1073/pnas.96.24.13750.
  26. Lavrentovich M, Hemkin S. A mathematical model of spontaneous calcium (II) oscillations in astrocytes. J. Theor. Biol. 2008;251(4):553–560. DOI: 10.1016/j.jtbi.2007.12.011.
  27. Stammers AN, Susser SE, Hamm NC, Hlynsky MW, Kimber DE, Kehler DS, Duhamel TA. The regulation of sarco(endo)plasmic reticulum calcium-ATPases (SERCA). Canadian Journal of Physiology and Pharmacology. 2015;93(10):843–854. DOI: 10.1139/cjpp-2014-0463.
  28. Periasamy M, Kalyanasundaram A. SERCA pump isoforms: Their role in calcium transport and disease. Muscle Nerve. 2007;35(4):430–442. DOI: 10.1002/mus.20745.
  29. Sinitsina MS, Gordleeva SY, Kazantsev VB, Pankratova EV. Emergence of complicated regular and irregular spontaneous Ca2+ oscillations in astrocytes. 2020 4th Scientific School on Dynamics of Complex Networks and their Application in Intellectual Robotics (DCNAIR). 2020, September 7–9, Innopolis, Russia. IEEE; 2020. P. 217–220. DOI: 10.1109/DCNAIR50402.2020.9216897.
  30. Semyanov A, Henneberger C, Agarwal A. Making sense of astrocytic calcium signals – from acquisition to interpretation. Nature Reviews Neuroscience. 2020;21(10):551–564. DOI: 10.1038/s41583-020-0361-8.
  31. Gordleeva SY, Tsybina YA, Krivonosov MI, Ivanchenko MV, Zaikin AA, Kazantsev VB and Gorban AN. Modeling working memory in a spiking neuron network accompanied by astrocytes. Front. Cell. Neurosci. 2021;15:631485. DOI: 10.3389/fncel.2021.631485.
  32. Santello M, Toni N, Volterra A. Astrocyte function from information processing to cognition and cognitive impairment. Nature Neuroscience. 2019;22(2):154–166. DOI: 10.1038/s41593-018-0325-8.
  33. Gordleeva S, Kanakov O, Ivanchenko M, Zaikin A, Franceschi C. Brain aging and garbage cleaning. Seminars in Immunopathology. 2020;42(5):647–665. DOI: 10.1007/s00281-020-00816-x.
  34. Whitwell HJ, Bacalini MG, Blyuss O, Chen S, Garagnani P, Gordleeva SY, Jalan S, Ivanchenko M, Kanakov O, Kustikova V, Marino IP, Meyerov I, Ullner E, Franceschi C, Zaikin A. The human body as a super network: Digital methods to analyze the propagation of aging. Frontiers in Aging Neuroscience. 2020;12:136. DOI: 10.3389/fnagi.2020.00136.