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

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

Kazantsev Viktor Borisovich, Institute of Applied Physics of the Russian Academy of Sciences
Vorobev Artem Viktorovich, Lobachevsky State University of Nizhny Novgorod

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.

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