Astrocyte Networks and Intercellular Calcium Propagation

  • Jules Lallouette
  • Maurizio De PittàEmail author
  • Hugues Berry
Part of the Springer Series in Computational Neuroscience book series (NEUROSCI)


Astrocytes organize in complex networks through connections by gap junction channels that are regulated by extra- and intracellular signals. Calcium signals generated in individual cells can propagate across these networks in the form of intercellular calcium waves, mediated by diffusion of second messengers molecules such as inositol 1,4,5-trisphosphate. The mechanisms underpinning the large variety of spatiotemporal patterns of propagation of astrocytic calcium waves, however, remains a matter of investigation. In the last decade, awareness has grown on the morphological diversity of astrocytes as well as their connections in networks, which seem dependent on the brain area, developmental stage, and the ultrastructure of the associated neuropile. It is speculated that this diversity underpins an equal functional variety, but the current experimental techniques are limited in supporting this hypothesis because they do not allow to resolve the exact connectivity of astrocyte networks in the brain. With this aim, we present a general framework to model intercellular calcium wave propagation in astrocyte networks and use it to specifically investigate how different network topologies could influence shape, frequency, and propagation of these waves.


Three-dimensional astrocyte networks Intercellular calcium waves Spatiotemporal IP\(_3\) dynamics Shell analysis 



MDP acknowledges the support of Pôle emploi Rhône-Alpes, the “Alain Bensoussan” Postdoctoral Fellowship Program by the European Research Council in Informatics and Mathematics (ERCIM), and the Junior Leader Postdoctoral Fellowship Program by “la Caixa” Banking Foundation (LCF/BQ/LI18/11630006). MDP’s research at BCAM is also made possible thanks to the support of the Basque Government by the BERC 2018–2021 program, as well as by the Spanish Ministry of Science, Innovation and Universities through the BCAM Severo Ochoa accreditation SEV-2017-0718.


  1. Aberg ND, Rönnbäck L, Eriksson PS (1999) Connexin43 mRNA and protein expression during postnatal development of defined brain regions. Dev Brain Res 115(1):97–101CrossRefGoogle Scholar
  2. Allbritton NL, Meyer T, Stryer L (1992) Range of messenger action of calcium ion and inositol 1,4,5-trisphosphate. Science 260:107–260Google Scholar
  3. Bao X, Altenberg GA, Reuss L (2004) Mechanism of regulation of the gap junction protein connexin 43 by protein kinase C-mediated phosphorylation. Am J Physiol Cell Physiol 286(3):C647–C654PubMedCrossRefPubMedCentralGoogle Scholar
  4. Barthélemy M (2010) Spatial networks. Phys Rep 499:1–101CrossRefGoogle Scholar
  5. Bazargani N, Attwell D (2016) Astrocyte calcium signaling: the third wave. Nat Neurosci 19(2):182–189PubMedPubMedCentralCrossRefGoogle Scholar
  6. Bennett M, Farnell L, Gibson W (2005) A quantitative model of purinergic junctional transmission of calcium waves in astrocyte networks. Biophys. J 89(4):2235–2250PubMedPubMedCentralCrossRefGoogle Scholar
  7. Blomstrand F, Aberg ND, Eriksson PS, Hansson E, Rönnbäck L (1999) Extent of intercellular calcium wave propagation is related to gap junction permeability and level of connexin-43 expression in astrocytes in primary cultures from four brain regions. Neuroscience 92(1):255–265PubMedCrossRefPubMedCentralGoogle Scholar
  8. Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang D-U (2006) Complex networks: structure and dynamics. Phys Rep 424(4–5):175–308CrossRefGoogle Scholar
  9. Bushong EA, Martone ME, Jones YZ, Ellisman MH (2002) Protoplasmic astrocytes in CA1 stratum radiatum occupy separate anatomical domains. J Neurosci 22(1):183–192PubMedCrossRefPubMedCentralGoogle Scholar
  10. Charles A (1998) Intercellular calcium waves in glia. Glia 24(1):39–49PubMedCrossRefPubMedCentralGoogle Scholar
  11. Chay T, Fan YS, Lee SY (1995) Bursting, spiking, chaos, fractals and universality in biological rhythms. Int J Bifurcat Chaos 5:595–635CrossRefGoogle Scholar
  12. Clements JD, Lester RAJ, Tong G, Jahr CE, Westbrook GL (1992) The time course of glutamate in the synaptic cleft. Science 258:1498–1501PubMedCrossRefPubMedCentralGoogle Scholar
  13. Codazzi F, Teruel MN, Meyer T (2001) Control of astrocyte Ca\(^{2+}\) oscillations and waves by oscillating translocation and activation of protein kinase C. Curr Biol 11(14):1089–1097PubMedCrossRefPubMedCentralGoogle Scholar
  14. Cornell-Bell AH, Finkbeiner SM, Cooper MS, Smith SJ (1990) Glutamate induces calcium waves in cultured astrocytes: long-range glial signaling. Science 247(4941):470–473CrossRefPubMedPubMedCentralGoogle Scholar
  15. Crank J (1980) The mathematics of diffusion, 2nd edn. Oxford University Press, USAGoogle Scholar
  16. D’Ambrosio R, Wenzel J, Schwartzkroin PA, McKhann GM, Janigro D (1998) Functional specialization and topographic segregation of hippocampal astrocytes. J Neurosci 18(12):4425–4438PubMedPubMedCentralCrossRefGoogle Scholar
  17. Dani JW, Chernjavsky A, Smith SJ (1992) Neuronal activity triggers calcium waves in hippocampal astrocyte networks. Neuron 8(3):429–440PubMedCrossRefPubMedCentralGoogle Scholar
  18. De Pittà M, Goldberg M, Volman V, Berry H, Ben-Jacob E (2009) Glutamate regulation of calcium and \(IP_3\) oscillating and pulsating dynamics in astrocytes. J Biol Phys 35(4):383–411PubMedPubMedCentralCrossRefGoogle Scholar
  19. De Pittà M, Volman V, Berry H, Parpura V, Liaudet N, Volterra A, Ben-Jacob E (2012) Computational quest for understanding the role of astrocyte signaling in synaptic transmission and plasticity. Front Comp Neurosci 6:98Google Scholar
  20. De Young GW, Keizer J (1992) A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca\(^{2+}\) concentration. Proc Natl Acad Sci 89(20):9895–9899PubMedCrossRefPubMedCentralGoogle Scholar
  21. Ding F, O’Donnell J, Thrane AS, Zeppenfeld D, Kang H, Xie L, Wang F, Nedergaard M (2013) \(\alpha \) 1-Adrenergic receptors mediate coordinated Ca\(^{2+}\) signaling of cortical astrocytes in awake, behaving mice. Cell Calcium 54(6):387–394PubMedCrossRefPubMedCentralGoogle Scholar
  22. Dokukina I, Gracheva M, Grachev E, Gunton J (2008) Role of network connectivity in intercellular calcium signaling. Physica D 237(6):745–754CrossRefGoogle Scholar
  23. Dupont G, Erneux C (1997) Simulations of the effects of inositol 1,4,5-trisphosphate 3-kinase and 5-phosphatase activities on Ca\(^{2+}\) oscillations. Cell Calcium 22(5):321–331PubMedPubMedCentralCrossRefGoogle Scholar
  24. Dupont G, Goldbeter A (1993) One-pool model for Ca\(^{2+}\) oscillations involving Ca\(^{2+}\) and inositol 1,4,5-trisphosphate as co-agonists for Ca\(^{2+}\) release. Cell Calcium 14:311–322CrossRefGoogle Scholar
  25. Dyhrfjeld-Johnsen J, Santhakumar V, Morgan RJ, Huerta R, Tsimring L, Soltesz I (2007) Topological determinants of epileptogenesis in large-scale structural and functional models of the dentate gyrus derived from experimental data. J Neurophysiol 97(2):1566–1587PubMedCrossRefPubMedCentralGoogle Scholar
  26. Edwards JR, Gibson WG (2010) A model for Ca\(^{2+}\) waves in networks of glial cells incorporating both intercellular and extracellular communication pathways. J Theor Biol 263(1):45–58PubMedPubMedCentralCrossRefGoogle Scholar
  27. Falcke M (2004) Reading the patterns in living cells: the physics of Ca\(^{2+}\) signaling. Adv Phys 53(3):255–440CrossRefGoogle Scholar
  28. Fiacco TA, McCarthy KD (2004) Intracellular astrocyte calcium waves in situ increase the frequency of spontaneous AMPA receptor currents in CA1 pyramidal neurons. J Neurosci 24(3):722–732PubMedCrossRefPubMedCentralGoogle Scholar
  29. Fiacco TA, McCarthy KD (2006) Astrocyte calcium elevations: properties, propagation, and effects on brain signaling. Glia 54(7):676–690PubMedCrossRefPubMedCentralGoogle Scholar
  30. Galea E, Morrison W, Hudry E, Arbel-Ornath M, Bacskai BJ, Gómez-Isla T, Stanley HE, Hyman BT (2015) Topological analyses in APP/PS1 mice reveal that astrocytes do not migrate to amyloid-\(\beta \) plaques. Proc Natl Acad Sci 112(51):15556–15561PubMedPubMedCentralGoogle Scholar
  31. Giaume C (2010) Astroglial wiring is adding complexity to neuroglial networking. Front Neuroenergetics 2:129PubMedPubMedCentralCrossRefGoogle Scholar
  32. Giaume C, Fromaget C, el Aoumari A, Cordier J, Glowinski J, Gros D (1991) Gap junctions in cultured astrocytes: single-channel currents and characterization of channel-forming protein. Neuron 6(1):133–143PubMedCrossRefPubMedCentralGoogle Scholar
  33. Giaume C, Koulakoff A, Roux L, Holcman D, Rouach N (2010) Astroglial networks: a step further in neuroglial and gliovascular interactions. Nat Rev Neurosci 11(2):87–99PubMedCrossRefPubMedCentralGoogle Scholar
  34. Giaume C, McCarthy KD (1996) Control of gap-junctional communication in astrocytic networks. Trends Neurosci 19(8):319–325PubMedCrossRefPubMedCentralGoogle Scholar
  35. Goldberg M, De Pittà M, Volman V, Berry H, Ben-Jacob E (2010) Nonlinear gap junctions enable long-distance propagation of pulsating calcium waves in astrocyte networks. PLoS Comput Biol 6(8):e1000909PubMedPubMedCentralCrossRefGoogle Scholar
  36. Golomb D, Hansel D (2000) The number of synaptic inputs and the synchrony of large, sparse neuronal networks. Neural Comput 12(5):1095–1139PubMedCrossRefPubMedCentralGoogle Scholar
  37. Harris AL (2001) Emerging issues in connexin channels: biophysics fills the gap. Q Rev Biophys 34:325–472PubMedCrossRefPubMedCentralGoogle Scholar
  38. Höfer T, Politi A, Heinrich R (2001) Intercellular Ca\(^{2+}\) wave propagation through gap-junctional Ca\(^{2+}\) diffusion: a theoretical study. Biophys J 80(1):75–87PubMedPubMedCentralCrossRefGoogle Scholar
  39. Höfer T, Venance L, Giaume C (2002) Control and plasticity of intercellular calcium waves in astrocytes: a modeling approach. J Neurosci 22(12):4850–4859CrossRefGoogle Scholar
  40. Houades V, Koulakoff A, Ezan P, Seif I, Giaume C (2008) Gap junction-mediated astrocytic networks in the mouse barrel cortex. J Neurosci 28(20):5207–5217PubMedCrossRefPubMedCentralGoogle Scholar
  41. Huang Y-F, Liao C-K, Lin J-C, Jow G-M, Wang H-S, Wu J-C (2013) Antofine-induced connexin43 gap junction disassembly in rat astrocytes involves protein kinase C\(\beta \). Neurotoxicology 35:169–179PubMedCrossRefPubMedCentralGoogle Scholar
  42. Iacobas DA, Suadicani SO, Spray DC, Scemes E (2006) A stochastic two-dimensional model of intercellular Ca\(^{2+}\) wave spread in glia. Biophys J 90(1):24–41PubMedPubMedCentralCrossRefGoogle Scholar
  43. Irvine RF, Schell MJ (2001) Back in the water: the return of the inositol phosphates. Nat Rev Mol Cell Biol 2(5):327–338PubMedCrossRefPubMedCentralGoogle Scholar
  44. Iwabuchi S, Kawahara K, Makisaka K, Sato H (2002) Photolytic flash-induced intercellular calcium waves using caged calcium ionophore in cultured astrocytes from newborn rats. Exp Brain Res 146(1):103–116PubMedCrossRefPubMedCentralGoogle Scholar
  45. Kang M, Othmer HG (2009) Spatiotemporal characteristics of calcium dynamics in astrocytes. Chaos 19(3):037116PubMedPubMedCentralCrossRefGoogle Scholar
  46. Kasthuri N, Hayworth K, Berger DR, Schalek RL, Conchello JA, Knowles-Barley S, Lee D, Vázquez-Reina A, Kaynig V, Jones TR, Roberts M, Lyskowski JM, Tapia JC, Seung HS, Roncal WG, Vogelstein JT, Burns R, Sussman DL, Priebe CE, Pfister H, Lichtman JW (2015) Saturated reconstruction of a volume of neocortex. Cell 162(3):648–661PubMedCrossRefPubMedCentralGoogle Scholar
  47. Koulakoff A, Ezan P, Giaume C (2008) Neurons control the expression of connexin 30 and connexin 43 in mouse cortical astrocytes. Glia 56(12):1299–1311PubMedCrossRefPubMedCentralGoogle Scholar
  48. Kuchibhotla KV, Lattarulo CR, Hyman BT, Bacskai BJ (2009) Synchronous hyperactivity and intercellular calcium waves in astrocytes in Alzheimer mice. Science 323(5918):1211–1215PubMedPubMedCentralCrossRefGoogle Scholar
  49. Kuga N, Sasaki T, Takahara Y, Matsuki N, Ikegaya Y (2011) Large-scale calcium waves traveling through astrocytic networks in vivo. J Neurosci 31(7):2607–2614PubMedPubMedCentralCrossRefGoogle Scholar
  50. Kummer U, Olsen LF, Green AK, Bomberg-Bauer E, Baier G (2000) Switching from simple to complex oscillations in calcium signaling. Biophys J 79:1188–1199PubMedPubMedCentralCrossRefGoogle Scholar
  51. Kunze A, Congreso MR, Hartmann C, Wallraff-Beck A, Hüttmann K, Bedner P, Requardt R, Seifert G, Redecker C, Willecke K, Hofmann A, Pfeifer A, Theis M, Steinhäuser C (2009) Connexin expression by radial glia-like cells is required for neurogenesis in the adult dentate gyrus. Proc Natl Acad Sci USA 106(27):11336–11341PubMedCrossRefPubMedCentralGoogle Scholar
  52. Kupferman R, Mitra PP, Hohenberg PC, Wang SS (1997) Analytical calculation of intracellular calcium wave characteristics. Biophys J 72(6):2430–2444PubMedPubMedCentralCrossRefGoogle Scholar
  53. Kurth-Nelson ZL, Mishra A, Newman EA (2009) Spontaneous glial calcium waves in the retina develop over early adulthood. J Neurosci 29(36):11339–11346PubMedPubMedCentralCrossRefGoogle Scholar
  54. Lallouette J (2014) Modeling calcium responses in astrocyte networks: relationships between topology and dynamics. Ph.D. thesis, INSA de LyonGoogle Scholar
  55. Lallouette J, De Pittà M, Ben-Jacob E, Berry H (2014) Sparse short-distance connections enhance calcium wave propagation in a 3D model of astrocyte networks. Front Comput Neurosci 8:45Google Scholar
  56. Li Y, Rinzel J (1994) Equations for InsP\(_3\) receptor-mediated \([\text{Ca}^{2+}]_\text{ i }\) oscillations derived from a detailed kinetic model: a Hodgkin–Huxley like formalism. J Theor Biol 166(4):461–473Google Scholar
  57. Luccioli S, Olmi S, Politi A, Torcini A (2012) Collective dynamics in sparse networks. Phys Rev Lett 109(13):138103PubMedCrossRefPubMedCentralGoogle Scholar
  58. MacDonald CL, Yu D, Buibas M, Silva GA (2008) Diffusion modeling of atp signaling suggests a partially regenerative mechanism underlies astrocyte intercellular calcium waves. Front. Neuroeng 1:1PubMedPubMedCentralCrossRefGoogle Scholar
  59. Matrosov VV, Kazantsev VB (2011) Bifurcation mechanisms of regular and chaotic network signaling in brain astrocytes. Chaos 21(2):023103PubMedPubMedCentralCrossRefGoogle Scholar
  60. Montoro RJ, Yuste R (2004) Gap junctions in developing neocortex: a review. Brain Res. Rev. 47(1–3):216–226PubMedCrossRefPubMedCentralGoogle Scholar
  61. Müller-Linow M, Hilgetag CC, Hütt M-T (2008) Organization of excitable dynamics in hierarchical biological networks. PLoS Comput Biol 4(9):e1000190PubMedPubMedCentralCrossRefGoogle Scholar
  62. Nagy JI, Rash JE (2000) Connexins and gap junctions of astrocytes and oligodendrocytes in the CNS. Brain Res Rev 32(1):29–44PubMedCrossRefPubMedCentralGoogle Scholar
  63. Nedergaard M, Ransom B, Goldman SA (2003) New roles for astrocytes: Redefining the functional architecture of the brain. Trends Neurosci 26(10):523–530PubMedCrossRefPubMedCentralGoogle Scholar
  64. Newman MEJ (2003) The structure and function of complex networks. SIAM Rev. 45(2):167–256CrossRefGoogle Scholar
  65. Nimmerjahn A, Kirchhoff F, Kerr JND, Helmchen F (2004) Sulforhodamine 101 as a specific marker of astroglia in the neocortex in vivo. Nat Methods 1(1):31–37PubMedCrossRefPubMedCentralGoogle Scholar
  66. Olmi S, Livi R, Politi A, Torcini A (2010) Collective oscillations in disordered neural networks. Phys Rev E 81(4):046119CrossRefGoogle Scholar
  67. Pannasch U, Rouach N (2013) Emerging role for astroglial networks in information processing: from synapse to behavior. Trends Neurosci 36(7):405–417PubMedCrossRefPubMedCentralGoogle Scholar
  68. Parri HR, Gould TM, Crunelli V (2001) Spontaneous astrocytic Ca\(^{2+}\) oscillations in situ drive NMDAR-mediated neuronal excitation. Nat Neurosci 4(8):803–812PubMedCrossRefPubMedCentralGoogle Scholar
  69. Pina-Benabou MHD, Srinivas M, Spray DC, Scemes E (2001) Calmodulin kinase pathway mediates the K\(^+\)-induced increase in gap junctional communication between mouse spinal cord astrocytes. J Neurosci 21(17):6635–6643PubMedPubMedCentralCrossRefGoogle Scholar
  70. Pivneva T, Haas B, Reyes-Haro D, Laube G, Veh R, Nolte C, Skibo G, Kettenmann H (2008) Store-operated Ca\(^{2+}\) entry in astrocytes: different spatial arrangement of endoplasmic reticulum explains functional diversity in vitro and in situ. Cell Calcium 43(6):591–601PubMedPubMedCentralCrossRefGoogle Scholar
  71. Rouach N, Avignone E, Même W, Koulakoff A, Venance L, Blomstrand F, Giaume C (2002) Gap junctions and connexin expression in the normal and pathological central nervous system. Biol Cell 94(7–8):457–475PubMedCrossRefPubMedCentralGoogle Scholar
  72. Rouach N, Glowinski J, Giaume C (2000) Activity-dependent neuronal control of gap-junctional communication in astrocytes. J Cell Biol 149(7):1513–1526PubMedPubMedCentralCrossRefGoogle Scholar
  73. Rouach N, Koulakoff A, Abudara V, Willecke K, Giaume C (2008) Astroglial metabolic networks sustain hippocampal synaptic transmission. Science 322(5907):1551–1555PubMedCrossRefPubMedCentralGoogle Scholar
  74. Roux L, Benchenane K, Rothstein JD, Bonvento G, Giaume C (2011) Plasticity of astroglial networks in olfactory glomeruli. Proc Natl Acad Sci U S AGoogle Scholar
  75. Roxin A, Riecke H, Solla SA (2004) Self-sustained activity in a small-world network of excitable neurons. Phys Rev Lett 92(19):198101PubMedCrossRefPubMedCentralGoogle Scholar
  76. Sánchez-Gutiérrez D, Tozluoglu M, Barry JD, Pascual A, Mao Y, Escudero LM (2016) Fundamental physical cellular constraints drive self-organization of tissues. EMBO J 35(1):77–88PubMedCrossRefPubMedCentralGoogle Scholar
  77. Sasaki T, Kuga N, Namiki S, Matsuki N, Ikegaya Y (2011) Locally synchronized astrocytes. Cereb Cortex 21:1889–1900PubMedCrossRefPubMedCentralGoogle Scholar
  78. Scemes E, Giaume C (2006) Astrocyte calcium waves: What they are and what they do. Glia 54(7):716–725PubMedPubMedCentralCrossRefGoogle Scholar
  79. Scemes E, Spray DC (2012) Extracellular K\(^+\) and astrocyte signaling via connexin and pannexin channels. Neurochem Res 37(11):2310–2316PubMedPubMedCentralCrossRefGoogle Scholar
  80. Scemes E, Suadicani SO, Spray DC (2000) Intercellular communication in spinal cord astrocytes: fine tuning between gap junctions and P2 nucleotide receptors in calcium wave propagation. J Neurosci 20(4):1435–1445PubMedPubMedCentralCrossRefGoogle Scholar
  81. Schipke CG, Boucsein C, Ohlemeyer C, Kirchhoff F, Kettenmann H (2002) Astrocyte Ca\(^{2+}\) waves trigger responses in microglial cells in brain slices. FASEB J 16(2):255–257PubMedCrossRefPubMedCentralGoogle Scholar
  82. Sherman A, Smith GD, Dai L, Miura RM (2001) Asymptotic analysis of buffered calcium diffusion near a point source. SIAM J Appl Math 61(5):1816–1838CrossRefGoogle Scholar
  83. Shuai JW, Jung P (2003) Selection of intracellular calcium patterns in a model with clustered Ca\(^{2+}\) release channels. Phys Rev E 67(3):031905CrossRefGoogle Scholar
  84. Sirnes S, Kjenseth A, Leithe E, Rivedal E (2009) Interplay between PKC and the MAP kinase pathway in connexin43 phosphorylation and inhibition of gap junction intercellular communication. Biochem Biophys Res Commun 382(1):41–45PubMedCrossRefPubMedCentralGoogle Scholar
  85. Skupin A, Kettenmann H, Winkler U, Wartenberg M, Sauer H, Tovey SC, Taylor CW, Falcke M (2008) How does intracellular Ca\(^{2+}\) oscillate: by chance or by clock? Biophys J 94:2404–2411PubMedPubMedCentralCrossRefGoogle Scholar
  86. Sneyd J, Charles AC, Sanderson MJ (1994) A model for the propagation of intracellular calcium waves. Am J Physiol 266(35):C293–C302PubMedCrossRefPubMedCentralGoogle Scholar
  87. Sneyd J, Keizer J, Sanderson MJ (1995a) Mechanisms of calcium oscillations and waves: a quantitative analysis. FASEB J 9(14):1463–1472PubMedPubMedCentralCrossRefGoogle Scholar
  88. Sneyd J, Sherratt J (1997) On the propagation of calcium waves in an inhomogeneous medium. SIAM J Appl Math 57(1):73–94CrossRefGoogle Scholar
  89. Sneyd J, Wetton BTR, Charles AC, Sanderson MJ (1995b) Intercellular calcium waves mediated by diffusion of inositol trisphosphate: a two-dimensional model. Am J Physiol 268(37):C1537–C1545PubMedCrossRefPubMedCentralGoogle Scholar
  90. Sneyd J, Wilkins M, Strahonja A, Sanderson MJ (1998) Calcium waves and oscillations driven by an intercellular gradient of inositol (1,4,5)-trisphosphate. Biophys Chem 72(1):101–109PubMedCrossRefPubMedCentralGoogle Scholar
  91. Stamatakis M, Mantzaris NV (2006) Modeling of ATP-mediated signal transduction and wave propagation in astrocytic cellular networks. J Theor Biol 241:649–668PubMedCrossRefPubMedCentralGoogle Scholar
  92. Suadicani SO, Flores CE, Urban-Maldonado M, Beelitz M, Scemes E (2004) Gap junction channels coordinate the propagation of intercellular Ca\(^{2+}\) signals generated by P2Y receptor activation. Glia 48(3):217–229PubMedPubMedCentralCrossRefGoogle Scholar
  93. Sul J-Y, Orosz G, Givens RS, Haydon PG (2004) Astrocytic connectivity in the hippocampus. Neuron Glia Biol 1(1):3–11PubMedPubMedCentralCrossRefGoogle Scholar
  94. Sun W, McConnell E, Pare J-F, Xu Q, Chen M, Peng W, Lovatt D, Han X, Smith Y, Nedergaard M (2013) Glutamate-dependent neuroglial calcium signaling differs between young and adult brain. Science 339(6116):197–200PubMedPubMedCentralCrossRefGoogle Scholar
  95. Tang Y, Othmer H (1994) A model of calcium dynamics in cardiac myocytes based on the kinetics of ryanodine-sensitive calcium channels. Biophys J 67:2223–2235PubMedPubMedCentralCrossRefGoogle Scholar
  96. Tattini L, Olmi S, Torcini A (2012) Coherent periodic activity in excitatory Erdös–Renyi neural networks: The role of network connectivity. Chaos 22(2):023133CrossRefGoogle Scholar
  97. Theodosis DT, Poulain DA, Oliet SHR (2008) Activity-dependent structural and functional plasticity of astrocyte-neuron interactions. Physiol Rev 88(3):983–1008PubMedCrossRefPubMedCentralGoogle Scholar
  98. Tian GF, Takano T, Lin JH-C, Wang X, Bekar L, Nedergaard M (2006) Imaging of cortical astrocytes using 2-photon laser scanning microscopy in the intact mouse brain. Adv Drug Deliv Rev 58(7):773–787PubMedCrossRefPubMedCentralGoogle Scholar
  99. Ullah G, Jung P, Cornell-Bell AH (2006a) Anti-phase calcium oscillations in astrocytes via inositol (1,4,5)-trisphosphate regeneration. Cell Calcium 39(3):197–208CrossRefGoogle Scholar
  100. Ullah G, Jung P, Cornell-Bell AH (2006b) Anti-phase calcium oscillations in astrocytes via inositol(1,4,5)-trisphosphate regeneration. Cell Calcium 39(3):197–208CrossRefGoogle Scholar
  101. Wallach G, Lallouette J, Herzog N, De Pittà M, Ben Jacob E, Berry H, Hanein Y (2014) Glutamate mediated astrocytic filtering of neuronal activity. PLoS Comput Biol 10(12):e1003964PubMedPubMedCentralCrossRefGoogle Scholar
  102. Wang X, Golomb D, Rinzel J (1995) Emergent spindle oscillations and intermittent burst firing in a thalamic model: specific neuronal mechanisms. Proc Natl Acad Sci U S A 92(12):5577–5581PubMedPubMedCentralCrossRefGoogle Scholar
  103. Watts DJ (1999) Small worlds: the dynamics of networks between order and randomness, chapter 2. Princeton University Press, Princeton, pp 33–36Google Scholar
  104. Weissman TA, Riquelme PA, Ivic L, Flint AC, Kriegstein AR (2004) Calcium waves propagate through radial glial cells and modulate proliferation in the developing neocortex. Neuron 43(5):647–661PubMedCrossRefPubMedCentralGoogle Scholar
  105. Witcher M, Kirov S, Harris K (2007) Plasticity of perisynaptic astroglia during synaptogenesis in the mature rat hippocampus. Glia 55(1):13–23PubMedCrossRefGoogle Scholar
  106. Zanette DH (2002) Dynamics of rumor propagation on small-world networks. Phys Rev E 65(4):041908CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Jules Lallouette
    • 1
  • Maurizio De Pittà
    • 1
    • 2
    Email author
  • Hugues Berry
    • 1
  1. 1.EPI BEAGLEINRIA Rhône-AlpesVilleurbanneFrance
  2. 2.Basque Center for Applied MathematicsBilbaoSpain

Personalised recommendations