OSCILLATORY INSTABILITY AND SPONTANEOUS SUBTHRESHOLD OSCILLATIONS IN A NETWORK OF DIFFUSIVELY COUPLED CALCIUM OSCILLATORS
Cite this article as:
Kazantsev V. B., Vorobiev А. V. OSCILLATORY INSTABILITY AND SPONTANEOUS SUBTHRESHOLD OSCILLATIONS IN A NETWORK OF DIFFUSIVELY COUPLED CALCIUM OSCILLATORS. Izvestiya VUZ. Applied Nonlinear Dynamics, 2009, vol. 17, iss. 2, pp. 123-137. DOI: https://doi.org/10.18500/0869-6632-2009-17-2-123-137
The paper is devoted to the investigation of the dynamics of a network of interacting astrocytes. The astrocytes represent brain glial cells capable to generate chemical activity signals (calcium pulses). Similarly to nerve cells (neurons) the astrocytes form networksof interacting units coupled by means of gap junctions. The junctions represent special protein channels providing the diffusion of chemically active species between neighboring cells. It is believed that calcium signals in astrocytes can regulate the efficiency of synaptic transmission in neighboring neuronal cells. In the present paper we investigate the processes of oscillatory activity generation in a one-dimensional network of coupled astrocytes. The dynamics of local cell is described by the third order nonlinear differential equation system that has been obtained from the detailed description of biochemical kinetics in the cell (de Young and Keizer, 1992; Li and Rinzel, 2003; Ullah, et al., 2006) The model accounting for the diffusive coupling represent a three-component reactiondiffusion network with single diffusing component. It is proven that there exists a critical value of diffusion coefficient above which the oscillatory instability at 0.1 Hz frequency develops and spontaneous low-amplitude quasisinusoidal oscillations (of 0.05 mM) appear. Corresponding eigenvalue spectrum is obtained and analyzed. It is found that further increase of the coupling coefficients leads to the appearance of multi-frequency mode with the modulation of the oscillation amplitude and spontaneous calcium pulse generation.
1. Николлс Дж., Мартин Р., Валлас Б. Фукс П. От нейрона к мозгу. М.: Изд-во УРСС. 2003. 672 C.
2. Рубин А.Б. Биофизика: В 2 т. М.: Книжный дом «Университет» , 2000. 486 c.
3. Principles of Neural Science / Eds. E.R. Kandel, J.H. Schwartz, T.M. Jessell. Third Edition. Prentice-Hall Intern. Inc. 1991. 1135 p.
4. Scott A. Neuroscience: a mathematical premier. Springer-Verlag, Berlin, 2002.
5. Izhikevich E.M. Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting, MIT Press, 2007.
6. Verkhratsky A., Butt A. Glial Neurobiology, Wiley, 2007.
7. De Young G.W., Keizer J. A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca2+ concentration //Proc. Natl. Acad. Sci. USA. 1992. Vol. 89. P. 9895.
8. Li Y., Rinzel J. Equations for InsP3 receptor-mediated [Ca2+]i oscillations derived from a detailed kinetic model: a Hodgkin–Huxley-like formalism //J. Theor. Biol. 1994. Vol. 166. P. 461.
9. Ullah G., Jung P., Cornell-Bell A.H. Anti-phase calcium oscillations in astrocytes via inositol (1, 4, 5)-trisphosphate regeneration //Cell Calcium. 2006. Vol. 39. P. 197.
10. Bennett M.V.L., Jorge E.C., Bukauskas F.F., Saez J.C. ́ New roles for astrocytes: Gap junction hemichannels have something to communicate //Trends in Neurosciences. 2003. Vol. 26, No 11. P. 610.
11. Timofeeva Y., Coombes S.. Wave bifurcation and propagation failure in a model of Ca2+ release // J. Math. Biol. 2003. Vol. 47, No 3. P. 249.
12. Nadkarni S., Jung P. Spontaneous oscillations of dressed neurons: a new mechanism for epilepsy? // Phys. Rev. Lett. 2003. Vol. 91. P. 268101.
13. Volman V., Ben-Jacob E., Levine H. The astrocyte as a gatekeeper of synaptic information transfer // Neural Comp. 2007. Vol. 19. P. 303.
14. Halassa M.M., Fellin T., Takano H., Dong J.-H., Haydon P.G. Synaptic islands defined by the territory of a single astrocyte // J. Neurosci. Vol. 27, No 24. P. 6473.
15. Nekorkin V.I., Velarde M.G. Synergetic Phenomena in Active Lattices. Berlin: Springer, 2002.
16. CRC Standard Mathematical Tables and Formulae / Ed. D. Zwillinger. Boca Raton, FL: CRC Press, 1995.
17. Makarov V.A., Nekorkin V.I., Velarde M.G. Spiking behavior in a noise-driven system combining oscillatory and excitatory properties // Phys. Rev. Lett. 2001. Vol. 86, No 15. P. 3431.
BibTeX
author = {V. B. Kazantsev and А. V. Vorobiev},
title = {OSCILLATORY INSTABILITY AND SPONTANEOUS SUBTHRESHOLD OSCILLATIONS IN A NETWORK OF DIFFUSIVELY COUPLED CALCIUM OSCILLATORS},
year = {2009},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {17},number = {2},
url = {https://old-andjournal.sgu.ru/en/articles/oscillatory-instability-and-spontaneous-subthreshold-oscillations-in-network-of-diffusively},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2009-17-2-123-137},pages = {123--137},issn = {0869-6632},
keywords = {Calcium signals,subthreshold oscillations,diffusive instability,astrocyte.},
abstract = {The paper is devoted to the investigation of the dynamics of a network of interacting astrocytes. The astrocytes represent brain glial cells capable to generate chemical activity signals (calcium pulses). Similarly to nerve cells (neurons) the astrocytes form networksof interacting units coupled by means of gap junctions. The junctions represent special protein channels providing the diffusion of chemically active species between neighboring cells. It is believed that calcium signals in astrocytes can regulate the efficiency of synaptic transmission in neighboring neuronal cells. In the present paper we investigate the processes of oscillatory activity generation in a one-dimensional network of coupled astrocytes. The dynamics of local cell is described by the third order nonlinear differential equation system that has been obtained from the detailed description of biochemical kinetics in the cell (de Young and Keizer, 1992; Li and Rinzel, 2003; Ullah, et al., 2006) The model accounting for the diffusive coupling represent a three-component reactiondiffusion network with single diffusing component. It is proven that there exists a critical value of diffusion coefficient above which the oscillatory instability at 0.1 Hz frequency develops and spontaneous low-amplitude quasisinusoidal oscillations (of 0.05 mM) appear. Corresponding eigenvalue spectrum is obtained and analyzed. It is found that further increase of the coupling coefficients leads to the appearance of multi-frequency mode with the modulation of the oscillation amplitude and spontaneous calcium pulse generation. }}