Journal of Computational Neuroscience

, Volume 25, Issue 2, pp 349–365 | Cite as

Computer simulations of neuron-glia interactions mediated by ion flux



Extracellular potassium concentration, [K+]o, and intracellular calcium, [Ca2+]i, rise during neuron excitation, seizures and spreading depression. Astrocytes probably restrain the rise of K+ in a way that is only partly understood. To examine the effect of glial K+ uptake, we used a model neuron equipped with Na+, K+, Ca2+ and Cl conductances, ion pumps and ion exchangers, surrounded by interstitial space and glia. The glial membrane was either “passive”, incorporating only leak channels and an ion exchange pump, or it had rectifying K+ channels. We computed ion fluxes, concentration changes and osmotic volume changes. Increase of [K+]o stimulated the glial uptake by the glial 3Na/2K ion pump. The [K+]o flux through glial leak and rectifier channels was outward as long as the driving potential was outwardly directed, but it turned inward when rising [K+]o/[K+]i ratio reversed the driving potential. Adjustments of glial membrane parameters influenced the neuronal firing patterns, the length of paroxysmal afterdischarge and the ignition point of spreading depression. We conclude that voltage gated K+ currents can boost the effectiveness of the glial “potassium buffer” and that this buffer function is important even at moderate or low levels of excitation, but especially so in pathological states.


Glial ion channels Potassium regulation Potassium buffer Neuron-glia interaction Firing pattern Seizures Spreading depression 


  1. Amzica, F., Massimini, M., & Manfridi, A. (2002). Spatial buffering during slow and paroxysmal sleep oscillations in cortical networks of glial cells in vivo. Journal of Neuroscience, 22, 1042–1053.PubMedGoogle Scholar
  2. Anderson, W. W., Lewis, D. V., Swartzwelder, H. S., & Wilson, W. A. (1986). Magnesium-free medium activates seizure-like eventsin the rat hippocampal slice. Brain Research, 398, 215–219.PubMedCrossRefGoogle Scholar
  3. Ballanyi, K., Grafe, P., & Ten Bruggencate, G. (1987). Ion activities and potassium uptake mechanisms of glial cells in guinea-pig olfactory cortex slices. Journal of Physiology, 382, 159–174.PubMedGoogle Scholar
  4. Barres, B. A., Chun, L. Y., & Corey, D. P. (1990). Ion channels in vertebrate glia. Annual Review of Neuroscience, 13, 441–474.PubMedCrossRefGoogle Scholar
  5. Binder, D. K., & Steinhäuser, C. (2006). Functional changes in astroglial cells in epilepsy. Glia, 54, 358–368.PubMedCrossRefGoogle Scholar
  6. Bordey, A., & Sontheimer, H. (1997). Postnatal development of ionic currents in rat hippocampal astrocytes in situ. Journal of Neurophysiology, 78, 461–477.PubMedGoogle Scholar
  7. Boyle, P. J., & Conway, E. J. (1941). Potassium accumulation in muscle and associated changes. Journal of Physiology, 100, 1–63.PubMedGoogle Scholar
  8. Brockhaus, J., Ballanyi, K., Smith, J. C., & Richter, D. W. (1993). Microenvironment of respiratory neurons in the in vitro brainstem—spinal cord of neonatal rats. Journal of Physiology, 462, 421–445.PubMedGoogle Scholar
  9. Calvin, W. H., & Sypert, G. W. (1976). Fast and slow pyramidal tract neurons: an analysis of their contrasting repetitive firing properties in the cat. Journal of Neurophysiology, 39, 420–434.PubMedGoogle Scholar
  10. Connors, B., Dray, A., Fox, P., Hilmy, M., & Somjen, G. (1979). LSD’s effect on neuron populations in visual cortex gauged by transient responses of extracellular potassium evoked by optical stimuli. Neuroscience Letters, 13, 147–150.PubMedCrossRefGoogle Scholar
  11. Connors, B. W., & Gutnick, M. J. (1990). Intrinsic firing patterns of diverse neocortical neurons. Trends in Neurosciences, 13, 99–104.PubMedCrossRefGoogle Scholar
  12. Cordingley, G. E., & Somjen, G. G. (1978). The clearing of excess potassium from extracellular space in spinal cord and cerebral cortex. Brain Research, 151, 291–306.PubMedCrossRefGoogle Scholar
  13. D’Ambrosio, R., Wenzel, J., Schwartzkroin, P. A., McKhann, G. M., & Janigro, D. (1998). Functional specialization and topographic segregation of hippocampal astrocytes. Journal of Neuroscience, 18, 4425–4438.PubMedGoogle Scholar
  14. Dietzel, I., & Heinemann, U. (1986). Dynamic variations of the brain cell microenvironment in relation to neuronal hyperactivity. Annals of the New York Academy of Sciences, 481, 72–85.PubMedCrossRefGoogle Scholar
  15. Dietzel, I., Heinemann, U., Hofmeier, G., & Lux, H.-D. (1980). Transient changes in the size of extracellular space in the sensorimotor cortex of cats in relation to stimulus-induced changes in potassium concentration. Experimental Brain Research, 40, 432–439.CrossRefGoogle Scholar
  16. Dietzel, I., Heinemann, U., & Lux, H. D. (1989). Relations between slow extracellular potential changes, glial potassium buffering and electrolyte and cellular volume changes during neuronal hyperactivity in cat brain. Glia, 2, 25–44.PubMedCrossRefGoogle Scholar
  17. Duffy, S., Fraser, D. D., & MacVicar, B. A. (1995). Potassium channels. In H. Kettenmann, & B. R. Ransom (Eds.) Neuroglia (pp. 185–201). New York: Oxford University Press.Google Scholar
  18. Fernandez, F. R., Engbers, J. D. T., & Turner, R. W. (2007). Firing Dynamics of Cerebellar Purkinje Cells. Journal of Neurophysiology, 98, 278–294.PubMedCrossRefGoogle Scholar
  19. Fertziger, A. P., & Ranck, J. B. (1970). Potassium accumulation in interstitial space during epileptiform seizures. Experimental Neurology, 26, 571–585.PubMedCrossRefGoogle Scholar
  20. Frankenhäuser, B., & Hodgkin, A. L. (1956). The after-effect of impulses in the giant nerve fibers of Loligo. Journal of Physiology, 131, 341–376.Google Scholar
  21. Gardner-Medwin, A. R. (1983). Analysis of potassium dynamics in mammalian brain tissue. Journal of Physiology, 335, 393–426.PubMedGoogle Scholar
  22. Gnatenco, C., Han, J., Snyder, A. K., & Kim, D. (2002). Functional expression of TRRE K-2 K+ channel in cultured rat brain astrocytes. Brain Research, 931, 56–67.PubMedCrossRefGoogle Scholar
  23. Green, J. D. (1964). The hippocampus. Physiological Reviews, 44, 561–608.PubMedGoogle Scholar
  24. Green, J. D., & Petsche, H. (1961). Hippocampal electrical activity. IV. Abnormal electrical activity. Electroencephalography and Clinical Neurophysiology, 13, 868–879.CrossRefGoogle Scholar
  25. Hansen, A. J., & Olsen, C. E. (1980). Brain extracellular space during spreading depression and ischemia. Acta Physiologica Scandinavica, 108, 355–365.PubMedGoogle Scholar
  26. Heinemann, U., & Lux, H. D. (1975). Undershoots following stimulus-induced rises of extracellular potassium concentration in cerebral cortex of cat. Brain Research, 93, 63–76.PubMedCrossRefGoogle Scholar
  27. Heinemann, U., & Lux, H. D. (1977). “Ceiling” of stimulus induced rises in extracellular potassium concentration in cerebral cortex of cats. Brain Research, 120, 231–250.PubMedCrossRefGoogle Scholar
  28. Henn, F. A., Haljamäe, H., & Hamberger, A. (1972). Glial cell function: Active control of extracellular K+ concentration. Brain Research, 43, 437–443.PubMedCrossRefGoogle Scholar
  29. Herreras, O., & Somjen, G. G. (1993). Effects of prolonged elevation of potassium in hippocampus of anesthetized rats. Brain Research, 617, 194–203.PubMedCrossRefGoogle Scholar
  30. Hertz, L. (1973). Ion Effects on Metabolism in the Adult Mammalian Brain in vitro. Evidence of a Potassium-induced Stimulation of Active Uptake of KCl into Neuroglial Cells, dissertation. Københaven: FADLs Forlag.Google Scholar
  31. Hertz, L. (1978). An intense potassium uptake into astrocytes, its further enhancement by high concentrations of potassium, and its possible involvement in potassium homeostasis at the cellular level. Brain Research, 145, 202–208.PubMedCrossRefGoogle Scholar
  32. Izhikevich, E. M. (2007). Dynamical Systems in Neuroscience: The geometry of excitable bursting. Cambridge, Massachusetts: MIT.Google Scholar
  33. Jefferys, J. G. R., & Haas, H. L. (1982). Synchronized bursting of CA1 hippocampal pyramidal cells in the absence of synaptic transmission. Nature, 300, 448–450.PubMedCrossRefGoogle Scholar
  34. Jensen, M. S., Azouz, R., & Yaari, Y. (1994). Variant firing patterns in rat hippocampal pyramidal cells modulated by extracellular potassium. Journal of Neurophysiology, 71, 831–839.PubMedGoogle Scholar
  35. Jing, J., Aitken, P. G., & Somjen, G. G. (1991). Lasting neuron depression induced by high potassium and its prevention by low calcium and NMDA receptor blockade. Brain Research, 557, 177–183.PubMedCrossRefGoogle Scholar
  36. Jing, J., Aitken, P. G., & Somjen, G. G. (1994). Interstitial volume changes during spreading depression (SD) and SD-like hypoxic depolarization in hippocampal tissue slices. Journal of Neurophysiology, 71, 2548–2551.PubMedGoogle Scholar
  37. Kager, H., Wadman, W. J., & Somjen, G. G. (2000). Simulated seizures and spreading depression in a neuron model incorporating interstitial space and ion concentrations. Journal of Neurophysiology, 84, 495–512.PubMedGoogle Scholar
  38. Kager, H., Wadman, W. J., & Somjen, G. G. (2002). Conditions for the triggering of spreading depression studied with computer simulation. Journal of Neurophysiology, 88, 2700–2712.PubMedCrossRefGoogle Scholar
  39. Kager, H., Wadman, W. J., & Somjen, G. G. (2007). Seizure-like after discharges simulated in a neuron model. Journal of Computational Neuroscience, 22, 105–128.PubMedCrossRefGoogle Scholar
  40. Kandel, E. R., & Spencer, W. A. (1961). Electrophysiological properties of an archicortical neuron. Annals of the New York Academy of Sciences, 94, 570–603.PubMedCrossRefGoogle Scholar
  41. Kawasaki, K., Czéh, G., & Somjen, G. G. (1988). Prolonged exposure to high potassium concentration results in irreversible loss of synaptic transmission in hippocampal tissue slices. Brain Research, 457, 322–329.PubMedCrossRefGoogle Scholar
  42. Kimelberg, H. K. (2004). The problem of astrocyte identity. Neurochemistry International, 45, 191–202.PubMedCrossRefGoogle Scholar
  43. Kivi, A., Lehmann, T. N., Kovács, R., Eilers, A., Jauch, R., Meeneke, H.-J., et al. (2000). Effects of barium on stimulus-induced rises of [K+]o in human epileptic non-sclerotic and sclerotic hippocampal area CA1. European Journal of Neuroscience, 12, 2039–2048.PubMedCrossRefGoogle Scholar
  44. Kofuji, P., & Newman, E. A. (2004). Potassium buffering in the central nervous system. Neuroscience, 129, 1045–1056.PubMedCrossRefGoogle Scholar
  45. Konnerth, A., Heinemann, U., & Yaari, Y. (1986). Nonsynaptic epileptogenesis in the mammalian hippocampus in vitro. I. Development of seizurelike activity in low extracellular calcium. Journal of Neurophysiology, 56, 409–423.PubMedGoogle Scholar
  46. Krnjević, K., Morris, M. E., & Reiffenstein, R. J. (1982). Stimulation-evoked changes in extracellular K+ and Ca2+ in pyramidal layers of the rat hippocampus. Canadian Journal of Physiology and Pharmacology, 60, 1643–1657.PubMedGoogle Scholar
  47. Krnjević, K., & Schwartz, S. (1967). Some properties of unresponsive cells in cerebral cortex. Experimental Brain Research, 3, 306–319.CrossRefGoogle Scholar
  48. Kuffler, S. W., & Nicholls, J. G. (1966). The physiology of neuroglial cells. Ergebnisse der Physiologie, Biologischen Chemie und Experimentellen Pharmakologie, 57, 1–90.PubMedCrossRefGoogle Scholar
  49. Lothman, E., LaManna, J., Cordingley, G., Rosenthal, M., & Somjen, G. (1975). Responses of electrical potential, potassium levels and oxidative metabolism in cat cerebral cortex. Brain Research, 88, 15–36.PubMedCrossRefGoogle Scholar
  50. Lux, H. D. (1973). Kaliumaktivität im Hirngewebe. Untersuchungen zum Krampfproblem. Mitteilungen Max Planck Gesellsch, 1, 34–52.Google Scholar
  51. Matthias, K., Kirchhoff, F., Seifert, G., Hüttmann, K., Matyash, M., Kettenmann, H., et al. (2003). Segregated expression of AMPA-type glutamate receptors and glutamate transporters defines distinct astrocyte populations in the mouse hippocampus. Journal of Neuroscience, 23, 1750–1758.PubMedGoogle Scholar
  52. Moody, W. J., Futamachi, K. J., & Prince, D. A. (1974). Extracellular potassium activity during epileptogenesis. Experimental Neurology, 42, 248–263.PubMedCrossRefGoogle Scholar
  53. Neusch, C., Papadopoulos, N., Müller, M., Maletzki, I., Winter, S. M., Hirrlinger, J., et al. (2006). Lack of the Kir4.1 channel subunit abolishes K+ buffering properties of astrocytes in the vantral respiratory group: Impact on extracellular K+ regulation. Journal of Neurophysiology, 95, 1843–1852.PubMedCrossRefGoogle Scholar
  54. Newman, E. A. (1984). Regional specialization of retinal glial cell membrane. Nature, 309, 155–157.PubMedCrossRefGoogle Scholar
  55. Newman, E. A. (1995). Glial cell regulation of extracellular potassium. In H. Kettenmann, & B. R. Ransom (Eds.) Neuroglia (pp. 717–731). New York: Oxford University Press.Google Scholar
  56. Nicholson, C., & Rice, M. E. (1988). Use of ion selective microelectrodes and voltammetric microsensors to study brain cell microenvironment. In A. A. Boulton, G. B. Baker, & W. Walz (Eds.) Neuromethods, Vol. 9 (pp. 247–361). Clifton, NJ: Humana.Google Scholar
  57. Orkand, R. K., Nicholls, J. G., & Kuffler, S. W. (1966). Effect of nerve impulses on the membrane potential of glial cells in the central nervous system of amphibia. Journal of Neurophysiology, 29, 788–806.PubMedGoogle Scholar
  58. Paulson, O. B., & Newman, E. A. (1987). Does the release of potassium from astrocyte end feet regulate cerebral blood flow. Science, 237, 896–898.PubMedCrossRefGoogle Scholar
  59. Picker, S., Pieper, C. F., & Goldring, S. (1981). Glial membrane potentials and their relationship to [K+]o in man and guinea pig. Journal of Neurosurgery, 55, 347–363.PubMedCrossRefGoogle Scholar
  60. Rutecki, P. A., Lebeda, F. J., & Johnston, D. (1985). Epileptiform activity induced by changes in extracellular potassium in hippocampus. Journal of Neurophysiology, 54, 1363–1374.PubMedGoogle Scholar
  61. Rybak, I. A., Shevtsova, N. A., St-John, W. M., Paton, J. F. R., & Pierrifiche, O. (2003). Endogenous rhythm generation in the pre-Bötzinger complex and ionic currents: modeling and in vitro studies. European Journal of Neuroscience, 18, 239–257.PubMedCrossRefGoogle Scholar
  62. Siegenbeek van Heukelom, J. (1994). The role of potassium inward rectifier in defining cell membrane potentials in low potassium media, analyzed by computer simulation. Biophysical Chemistry, 50, 345–360.CrossRefGoogle Scholar
  63. Sik, A., Smith, R. L., & Freund, T. F. (2000). Distribution of chloride channel-2-immunoreactive neuronal and astrocytic processes in the hippocampus. Neuroscience, 101, 51–65.PubMedCrossRefGoogle Scholar
  64. Singer, W., & Lux, H. D. (1975). Extracellular potassium gradients and visual receptive fields in the cat striate cortex. Brain Research, 96, 378–383.PubMedCrossRefGoogle Scholar
  65. Somjen, G. G. (1975). Electrophysiology of neuroglia. Annual Review of Physiology, 37, 163–190.PubMedCrossRefGoogle Scholar
  66. Somjen, G. G. (2004). Ions in the Brain. Normal function, Seizures and Stroke. New York: Oxford University Press,.Google Scholar
  67. Somjen, G. G., Kager, H., & Wadman, W. J. (2004). Potassium regulation and simulated seizures in a neuron—glia model. Society of Neuroscience Abstracts Program no. 228.11.Google Scholar
  68. Somjen, G. G., Kager, H., & Wadman, W. J. (2008). Calcium-sensitive non-selective cation current promotes seizure-like discharge and spreading depression in a model neuron (in press).Google Scholar
  69. Sypert, G. W., & Ward, A. A. (1974). Changes in extracellular potassium activity during neocortical propagated seizures. Experimental Neurology, 45, 19–41.PubMedCrossRefGoogle Scholar
  70. Trachtenberg, M. C., & Pollen, D. A. (1970). Neuroglia: biophysical properties and physiological function. Science, 167, 1248–1252.PubMedCrossRefGoogle Scholar
  71. Traynelis, S. F., & Dingledine, R. (1988). Potassium-induced spontaneous electrographic seizures in the rat hippocampal slice. Journal of Neurophysiology, 59, 259–276.PubMedGoogle Scholar
  72. Walz, W. (2000). Role of astrocytes in the clearance of excess potassium. Neurochemistry International, 36, 291–300.PubMedCrossRefGoogle Scholar
  73. Walz, W. (2002). Chloride/anion channels in glial cell membranes. Glia, 40, 1–10.PubMedCrossRefGoogle Scholar
  74. Walz, W., & Juurlink, B. H. J. (2002). Homeostatic properties of astrocytes. In W. Walz (Ed.) The Neuronal Environment. Brain Homeostasis in Health and Disease (pp. 159–185). Totowa: Humana.Google Scholar
  75. Xiong, Z.-Q., & Stringer, J. L. (2000). Sodium pump activity, not glial spatial buffering, clears potassium after epileptiform activity induced in the dentate gyrus. Journal of Neurophysiology, 83, 1443–1451.PubMedGoogle Scholar
  76. Yan, Y., Dempsey, R. J., & Sun, D. (2001). Expression of Na+ -K+ -Cl- cotransporter in rat brain during development and its localization in mature astrocytes. Brain Research, 911, 43–55.PubMedCrossRefGoogle Scholar
  77. Zhou, M., & Kimelberg, H. K. (2000). Freshly isolated astrocytes from rat hippocampus show two distinct current patterns and different [K+]o uptake capabilities. Journal of Neurophysiology, 84, 2746–2757.PubMedGoogle Scholar
  78. Zuckermann, E. C., & Glaser, G. H. (1970). Activation of experimental epileptogenic foci. Action of increased K+ in extracellular spaces of brain. Archives of Neurology, 23, 358–364.PubMedGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Cell BiologyDuke University Medical CenterDurhamUSA
  2. 2.SILS-Center for NeuroScienceUniversity of AmsterdamAmsterdamThe Netherlands

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