Intercellular synchronization of diffusively coupled Ca 2+ oscillators
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ORIGINAL ARTICLE
Intercellular synchronization of diffusively coupled Ca2+ oscillators Md. Jahoor Alam · Latika Bhayana · Gurumayum Reenaroy Devi · Heisnam Dinachandra Singh · R. K. Brojen Singh · B. Indrajit Sharma
Received: 9 December 2010 / Accepted: 25 August 2011 / Published online: 9 September 2011 © Springer-Verlag 2011
Abstract We examine the synchrony in the dynamics of localized [Ca2+ ]i oscillations among a group of cells exhibiting such complex Ca2+ oscillations, connected in the form of long chain, via diffusing coupling where cytosolic Ca2+ and inositol 1,4,5-triphosphate are coupling molecules. Based on our numerical results, we could able to identify three regimes, namely desynchronized, transition and synchronized regimes in the (T − ke ) (time period-coupling constant) and (A − ke ) (amplitude-coupling constant) spaces which are supported by phase plots (φ verses time) and recurrence plots, respectively. We further show the increase of synchronization among the cells as the number of coupling molecules increases in the (T − ke ) and (A − ke ) spaces. Keywords Cell signaling · Synchronization · Diffusive coupling · Network topology · Chemical coupling
Introduction The astrocytes in the central nervous system have various important roles, namely taking active part in
Md. J. Alam · L. Bhayana · G. R. Devi · H. D. Singh · R. K. B. Singh (B) Centre for Interdisciplinary Research in Basic Sciences, Jamia Millia Islamia, New Delhi 110025, India e-mail: [email protected] B. I. Sharma Department of Physics, Assam University, Silchar 788 011, Assam, India
signal processing [1–3], interact with the neighbouring neurons [4–6] etc. which leads to important responsibility of the cells in predicting disease states [7]. Since these cells interact with the environment, Ca2+ waves propagated through the cells display oscillation in the nonpropagating internal stored [Ca2+ ]i inside the cells [8]. These oscillations are sustained due to interaction of inositol 1,4,5-triphosphate (IP3) with extracellular, cytosolic and endoplasmic Ca2+ through inositol cross coupling and calcium-induced calcium release mechanisms [9–11]. The coupling among a group of these cells in a certain network topology is done through the process of cell signaling. This cell signaling is being considered as a means of complex communication and information processing among individual cells, for example, astrocytes with neurons, governing basic cellular activities and to coordinate various actions involving various complex coupling mechanisms [12]. It has been predicted that Ca2+ variation in IP3 concentration is necessary for the intercellular Ca2+ wave propagation and this variation is initiated by IP3 diffusion through gap junctions to communicate neighbouring cells [13]. Therefore, synchrony in the dynamics of the local [Ca2+ ]i oscillations is believed to be due to chemical coupling, i.e. due to exchange of cytosol Ca2+ waves and IP3 [14–17], and can exhibit synchronization of the cells over long distances [18]. However, this idea of s
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