Journal of Biological Physics

, Volume 35, Issue 4, pp 425–445 | Cite as

Dynamical patterns of calcium signaling in a functional model of neuron–astrocyte networks

  • D. E. Postnov
  • R. N. Koreshkov
  • N. A. Brazhe
  • A. R. Brazhe
  • O. V. Sosnovtseva
Original Paper


We propose a functional mathematical model for neuron-astrocyte networks. The model incorporates elements of the tripartite synapse and the spatial branching structure of coupled astrocytes. We consider glutamate-induced calcium signaling as a specific mode of excitability and transmission in astrocytic–neuronal networks. We reproduce local and global dynamical patterns observed experimentally.


Tripartite synapse Astrocyte Neuron Calcium waves Modeling 



This work was partly supported by the European Commission (NoE BioSim, Contract No. 4SHB-CT-2004-005137). N.B and A.B. acknowledge support from the Lundbeck Foundation and O.S. acknowledges the Skou grant from Forskningsraadet for Natur og Univers. D.P. and R.K. acknowledge support from the RFBR grant 090201049.


  1. 1.
    Haydon, P.G.: Glia: listening and talking to the synapse. Nat. Rev. 2, 185–193 (2001)CrossRefGoogle Scholar
  2. 2.
    Fields, R.D., Stevens-Graham, B.: New insights into neuron–glia communication. Science 298, 556–562 (2002)CrossRefADSGoogle Scholar
  3. 3.
    Bonvento, G., Giaume, C., Lorenceau, J.: Neuron–glia interactions: from physiology to behavior. J. Physiol. 96, 167–168 (2002)Google Scholar
  4. 4.
    Fiacco, T.A.: Advances in understanding new roles for astrocytes in the modulation of neuronal activity. Physiol. News 72, 18–20 (2008)Google Scholar
  5. 5.
    Nedergaard, M.: Direct signaling from astrocytes to neurons in cultures of mammalian brain cells. Science 263, 1768–1771 (1994)CrossRefADSGoogle Scholar
  6. 6.
    Carmignoto, G.: Reciprocal communication systems between astrocytes and neurons. Prog. Neurobiol. 62, 561–581 (2000)CrossRefGoogle Scholar
  7. 7.
    Finkbeiner, S.: Calcium waves in astrocytes—filling in the gaps. Neuron 8, 1101–1108 (1992)CrossRefGoogle Scholar
  8. 8.
    Dani, J.W., Chernjavsky, A., Smith, S.J.: Neuronal activity triggers calcium waves in hippocampal astrocyte network. Neuron 8, 429–440 (1992)CrossRefGoogle Scholar
  9. 9.
    Butt, A.M., Ransom, B.R.: Morphology of astrocytes and oligodendrocytes during development in the intact optic rat nerve. J. Comp. Neurol. 338, 141–158 (1993)CrossRefGoogle Scholar
  10. 10.
    Pasti, L., Pozzan, T., Carmignotto, G.: Intracellular calcium oscillations in astrocytes: a highly plastic, bidirectional form of communication between neurons and astrocytes in situ. J. Neurosci. 17, 7817–7830 (1997)Google Scholar
  11. 11.
    Lee, S.H., Kim, W.T., Cornell-Bell, A.H., Sontheimer, H.: Astrocytes exhibit regional specificity in gap-junctional coupling. Glia 11, 315–325 (1994)CrossRefGoogle Scholar
  12. 12.
    Cornell-Bell, A.H., Sontheimer, H., Cooper, S.M., Smith, S.J.: Glutamate induces calcium waves in cultured astrocytes: long-range glial signaling. Science 247, 470–473 (1990)CrossRefADSGoogle Scholar
  13. 13.
    Newman, E.A.: Glial cell inhibition of neurons by release of ATP. J. Neurosci. 23, 1659–1666 (2003)Google Scholar
  14. 14.
    Fellin, T., Pascual, O., Haydon, P.G.: Astrocytes coordinate synaptic networks: balanced excitation and inhibition. Physiology 21, 208–215 (2006)CrossRefGoogle Scholar
  15. 15.
    Bowser, D.N., Khakh, B.S.: ATP excites interneurons and astrocytes to increase synaptic inhibition in neuronal networks. J. Neurosci. 24, 8606–8620 (2004)CrossRefGoogle Scholar
  16. 16.
    Koizumi, S., Fujishita, K., Tsuda, M., Shigemoto-Mogami, Y., Inoue, K.: Dynamic inhibition of excitatory synaptic transmission by astrocyte-derived ATP in hyppocampal cultures. Proc. Natl. Acad. Sci. U. S. A. 100, 11023–11028 (2003)CrossRefADSGoogle Scholar
  17. 17.
    Serrano, A., Naddjeri, N., Lacaille, J.-C., Robitaille, R.: GABAergic network activation of glial cells underlies hippocampal heterosynaptic depression. J. Neurosci. 26, 5370–5382 (2006)CrossRefGoogle Scholar
  18. 18.
    Hansson, E.: Could chronic pain and spread of pain sensation be induced and maintained by glial activation? Acta Physiol. (Oxf.) 187, 321–327 (2006)CrossRefGoogle Scholar
  19. 19.
    Fellin, T., Gomez-Gonzalo, M., Gobbo, S., Carmignoto, G., Haydon, P.G.: Astrocytic glutamate is not necessary for the generation of epileptiform neuronal activity in hippocampal slices. J. Neurosci. 26, 9312–9322 (2006)CrossRefGoogle Scholar
  20. 20.
    Tian, G.-F., Azmi, H., Takano, T., Xu, Q., Peng, W., Lin, J., Oberheim, NA., Lou, N., Zeilke, R., Kang, R., Nedergaard, M.: An astrocyte basis of epilepsy. Nat. Med. 11, 973–981 (2005)Google Scholar
  21. 21.
    Nadkarni, S., Jung, P.: Spontaneous oscillations of dressed neurons: a new mechanism for epilepsy? Phys. Rev. Lett. 91, 268101 (2003)CrossRefADSGoogle Scholar
  22. 22.
    Nadkarni, S., Jung, P.: Dressed neurons: modeling neural–glia interactions. Phys. Biol. 1, 35–41 (2004)CrossRefADSGoogle Scholar
  23. 23.
    Nadkarni, S., Jung, P.: Modeling synaptic transmission of the tripartite synapse. Phys. Biol. 4, 1–9 (2007)CrossRefADSGoogle Scholar
  24. 24.
    Nadkarni, S., Jung, P., Levine, H.: Astrocytes optimize the synaptic transmission of information. PLoS Comput. Biol. 4(5), e1000088 (2008)CrossRefMathSciNetGoogle Scholar
  25. 25.
    Stamatakis, M., Mantzaris, N.V.: Modeling of ATP-mediated signal transduction and wave propagation in astrocytic cellular networks. J. Theor. Biol. 241, 649–668 (2006)CrossRefMathSciNetGoogle Scholar
  26. 26.
    Bennett, M.R., Farnell, L., Gibson, W.G.: A quantitative model of purinergic junctional transmission of calcium waves in astrocyte networks. Biophys. J. 89, 2235-2250 (2005)CrossRefGoogle Scholar
  27. 27.
    Gibson, W.G., Farnell, L., Bennett, M.R.: A computational model relating changes in cerebral blood volume to synaptic activity in neurons. Neurocomputing 70, 1674–1679 (2007)CrossRefGoogle Scholar
  28. 28.
    Postnov, D.E., Ryazanova, L.S., Brazhe, N.A., Brazhe, A.R., Maximov, G.V., Mosekilde, E., Sosnovtseva, O.V.: Giant glial cell: new insight throuth mechanism-based modeling. J. Biol. Phys. 34, 441–457 (2008)CrossRefGoogle Scholar
  29. 29.
    Postnov, D.E., Ryazanova, L.S., Sosnovtseva, O.V.: Functional modeling of neural–glial interaction. Biosystems 89(1–3), 84–91 (2007)CrossRefGoogle Scholar
  30. 30.
    FitzHugh, R.A.: Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1, 445–446 (1961)CrossRefADSGoogle Scholar
  31. 31.
    Kopell, N., Ermentrout, G.B., Whittington, M.A., Traub, R.D.: Gamma rhythms and beta rhythms have different synchronization properties. Proc. Natl. Acad. Sci. U. S. A. 97, 1867–1872 (2000)CrossRefADSGoogle Scholar
  32. 32.
    Keener, J., Sneyd, J.: Mathematical Physiology. Springer, New York (1998)zbMATHGoogle Scholar
  33. 33.
    Dupont, G., Goldbeter, A.: One-pool model for Ca2+ oscillations involving Ca2+ and inositol 1,4,5-triphosphate as co-agonists for Ca2+ release. Cell Calcium 14, 311–322 (1993)CrossRefGoogle Scholar
  34. 34.
    Jung, P., Cornell-Bell, A., Madden, K.S., Moss, F.: Noise-induced spiral waves in astrocyte syncytia show evidence of self-organized criticality. J. Neurophysiol. 79, 1098–1101 (1998)Google Scholar
  35. 35.
    Zhu, X., Bergles, D.E., Nishiyama, A.: NG2 cells generate both oligodendrocytes and gray matter astrocytes. Development 135, 145–157 (2008)CrossRefGoogle Scholar
  36. 36.
    Katyal, S., El-Khamisy, S.F., Russell, H.R., Li, Y., Ju, L., Caldecott, K.W., McKinnon, P.J.: TDP1 facilitates chromosomal single-strand break repair in neurons and is neuroprotective in vivo. EMBO J. 26, 4720–4731 (2007)CrossRefGoogle Scholar
  37. 37.
    Martin, A., Hofmann, H.D., Kirsch, M.: Glial reactivity in ciliary neurotrophic factor-deficient mice after optic nerve lesion. J. Neurosci. 23(13), 5416–5424 (2003)Google Scholar
  38. 38.
    Bushong, E.A., Martone, M.E., Ellisman, M.H.: Maturation of astrocyte morphology and the establishment of astrocyte domains during postnatal hippocampal development. Int. J. Dev. Neurosci. 22, 73–86 (2004)CrossRefGoogle Scholar
  39. 39.
    Bushong, E.A., Martone, M.E., Jones, Y.Z., Ellisman, M.H.: Protoplasmic astrocytes in CA1 stratum radiatum occupy separate anatomical domains. J. Neurosci. 22(1), 183–192 (2002)Google Scholar
  40. 40.
    Mi, H., Barres, B.A.: Purification and characterization of astrocyte precursor cells in the developing rat optic nerve. J. Neurosci. 19(3), 1049–1061 (1999)Google Scholar
  41. 41.
    Lee, M.Y., Deller, T., Kirsch, M., Frotscher, M., Hofmann, H.D.: Differential regulation of ciliary neurotrophic factor (CNTF) and CNTF receptor alpha expression in astrocytes and neurons of the fascia dentata after entorhinal cortex lesion. J. Neurosci. 17(3), 1137–1146 (1997)Google Scholar
  42. 42.
  43. 43.
    Fellin, T., Carmignoto, G.: Neurone-to-astrocyte signaling in the brain represents a distinct multifunctional unit. J. Physiol. 559(1), 3–15 (2004)CrossRefGoogle Scholar
  44. 44.
    Manzoni, O.J., Manabe, T., Nikoll, R.A.: Release of adenosine by activation of NMDA receptor in the hippocampus. Science 265, 2098–2101 (1994)CrossRefADSGoogle Scholar
  45. 45.
    Ryazanova, L., Trenikhina, Y., Zhirin, R., Postnov, D.: Noise-induced firing patterns in generalized neuron model with subthreshold oscillations. Proc. SPIE 6436, 64360W (2007)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • D. E. Postnov
    • 1
  • R. N. Koreshkov
    • 1
  • N. A. Brazhe
    • 2
  • A. R. Brazhe
    • 2
  • O. V. Sosnovtseva
    • 3
  1. 1.Physics DepartmentSaratov State UniversitySaratovRussia
  2. 2.Biophysics Department, Biological FacultyMoscow State UniversityMoscowRussia
  3. 3.Department of PhysicsTechnical University of DenmarkKongens LyngbyDenmark

Personalised recommendations