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


For citation:

Kazantsev V. B., Vorobev A. 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: 10.18500/0869-6632-2009-17-2-123-137

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Language: 
Russian
Article type: 
Article
UDC: 
577.381, 530.182

Oscillatory instability and spontaneous subthreshold oscillations in a network of diffusively coupled calcium oscillators

Autors: 
Kazantsev Viktor Borisovich, Institute of Applied Physics of the Russian Academy of Sciences
Vorobev Artem Viktorovich, Lobachevsky State University of Nizhny Novgorod
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 networks of 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 µM) 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.

Reference: 
  1. Nicholls J, Martin R, Wallas B, Fuchs P. From neuron to brain. Moscow: URSS; 2003. 672 p. (In Russian).
  2. Rubin AB. Biophysics. Moscow: Bookhouse "Universitet"; 2000. 486 p. (In Russian).
  3. Principles of Neural Science. Eds. Kandel ER, Schwartz JH, Jessell TM. Third Edition. Prentice-Hall Intern. Inc. 1991. 1135 p.
  4. Scott A. Neuroscience: a mathematical premier. Berlin: Springer-Verlag; 2002. 357 p.
  5. Izhikevich EM. Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. London: MIT Press Cambridge; 2007. 497 p.
  6. Verkhratsky A, Butt A. Glial Neurobiology. Chichester, UK: Wiley, 2007. 215 p.
  7. De Young GW, Keizer J. A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca2+ concentration. Proc Natl Acad Sci U S A. 1992;89(20):9895-9899. DOI: 10.1073/pnas.89.20.9895.
  8. Li YX, 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;166(4):461-473. DOI: 10.1006/jtbi.1994.1041.
  9. Ullah G, Jung P, Cornell-Bell AH. Anti-phase calcium oscillations in astrocytes via inositol (1, 4, 5)-trisphosphate regeneration. Cell Calcium. 2006;39(3):197-208. DOI: 10.1016/j.ceca.2005.10.009.
  10. Bennett MV, Contreras JE, Bukauskas FF, Sáez JC. New roles for astrocytes: gap junction hemichannels have something to communicate. Trends Neurosci. 2003;26(11):610-617. DOI: 10.1016/j.tins.2003.09.008.
  11. Timofeeva Y, Coombes S. Wave bifurcation and propagation failure in a model of Ca2+ release. J. Math. Biol. 2003;47(3):249–269. DOI: 10.1007/s00285-003-0205-y.
  12. Nadkarni S, Jung P. Spontaneous oscillations of dressed neurons: a new mechanism for epilepsy? Phys Rev Lett. 2003;91(26):268101. DOI: 10.1103/PhysRevLett.91.268101.
  13. Volman V, Ben-Jacob E, Levine H. The astrocyte as a gatekeeper of synaptic information transfer. Neural Comput. 2007;19(2):303-326. DOI: 10.1162/neco.2007.19.2.303.
  14. Halassa MM, Fellin T, Takano H, Dong J-H, Haydon PG. Synaptic islands defined by the territory of a single astrocyte. J. Neurosci. 2007;27(24):6473–6477. DOI: 10.1523/JNEUROSCI.1419-07.2007.
  15. Nekorkin VI, Velarde MG. Synergetic Phenomena in Active Lattices. Berlin: Springer; 2002. 357 p.
  16. CRC Standard Mathematical Tables and Formulae. Ed. Zwillinger D, Boca Raton FL: CRC Press; 1995. 872 p.
  17. Makarov VA, Nekorkin VI, Velarde MG. Spiking behavior in a noise-driven system combining oscillatory and excitatory properties. Phys. Rev. Lett. 2001;86(15):3431–3434. DOI: 10.1103/PHYSREVLETT.86.3431.
Received: 
22.10.2008
Accepted: 
01.02.2009
Published: 
30.06.2009
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