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Journal of Computational Neuroscience

, Volume 40, Issue 2, pp 177–192 | Cite as

Large extracellular space leads to neuronal susceptibility to ischemic injury in a Na+/K + pumps–dependent manner

  • Niklas HübelEmail author
  • R. David Andrew
  • Ghanim Ullah
Article

Abstract

The extent of anoxic depolarization (AD), the initial electrophysiological event during ischemia, determines the degree of brain region–specific neuronal damage. Neurons in higher brain regions exhibiting nonreversible, strong AD are more susceptible to ischemic injury as compared to cells in lower brain regions that exhibit reversible, weak AD. While the contrasting ADs in different brain regions in response to oxygen–glucose deprivation (OGD) is well established, the mechanism leading to such differences is not clear. Here we use computational modeling to elucidate the mechanism behind the brain region–specific recovery from AD. Our extended Hodgkin–Huxley (HH) framework consisting of neural spiking dynamics, processes of ion accumulation, and ion homeostatic mechanisms unveils that glial–vascular K+ clearance and Na+/K+–exchange pumps are key to the cell’s recovery from AD. Our phase space analysis reveals that the large extracellular space in the upper brain regions leads to impaired Na+/K+–exchange pumps so that they function at lower than normal capacity and are unable to bring the cell out of AD after oxygen and glucose is restored.

Keywords

Anoxic depolarization Extracellular volume Hodgkin–Huxley Ion dynamics Neural mircoenvironment Brain injury 

Notes

Acknowledgments

This study was supported by a startup grant from College of Arts and Sciences awarded to Ghanim Ullah.

Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflict of interest.

References

  1. Attwell, D., & Laughlin, S.B. (2001). An energy budget for signaling in the grey matter of the brain. Journal of Cerebral Blood Flow & Metabolism, 21(10), 1133–1145.CrossRefGoogle Scholar
  2. Barreto, E., & Cressman, J.R. (2010). Ion concentration dynamics as a mechanism for neural bursting. Journal of Biological Physics, 37(3), 361–373. doi: 10.1007/s10867-010-9212-6.CrossRefGoogle Scholar
  3. Bazhenov, M., Timofeev, I., Steriade, M., & Sejnowski, T.J. (2004). Potassium model for slow (2–3 Hz) in vivo neocortical paroxysmal oscillations. Journal of Neurophysiology, 92, 1116–1132.CrossRefPubMedPubMedCentralGoogle Scholar
  4. Berthon, B., Burgess, G.M., Capiod, T., Claret, M., & Poggioli, J. (1983). Mechanism of action of noradrenaline on the sodium–potassium pump in isolated rat liver cells. Journal of Physiology, 341, 25–40.CrossRefPubMedPubMedCentralGoogle Scholar
  5. Blanco, G. (2005). Na,k–ATPase subunit heterogeneity as a mechanism for tissue-specific ion regulation. In Seminars in nephrology, vol. 25, pp. 292–303: Elsevier.Google Scholar
  6. Brisson, C.D., & Andrew, R.D. (2012). A neuronal population in hypothalamus that dramatically resists acute ischemic injury compared to neocortex. Journal of Neurophysiology, 108(2), 419–430.CrossRefPubMedGoogle Scholar
  7. Brisson, C.D., Hsieh, Y.T., Kim, D., Jin, A.Y., & Andrew, R.D. (2014). Brainstem neurons survive the identical ischemic stress that kills higher neurons: insight to the persistent vegetative state. PloS one, 9(5).Google Scholar
  8. Brisson, C.D., Lukewich, M.K., & Andrew, R.D. (2013). A distinct boundary between the higher brains susceptibility to ischemia and the lower brains resistance. PLoS ONE, 8(11), e79,589. doi: 10.1371/journal.pone.0079589.CrossRefGoogle Scholar
  9. Centonze, D., Marfia, G., Pisani, A., Picconi, B., Giacomini, P., Bernardi, G., & Calabresi, P. (2001). Ionic mechanisms underlying differential vulnerability to ischemia in striatal neurons. Progress in neurobiology, 63 (6), 687–696.CrossRefPubMedGoogle Scholar
  10. Collins, C.E., Airey, D.C., Young, N.A., Leitch, D.B., & Kaas, J.H. (2010). Neuron densities vary across and within cortical areas in primates. Proceedings of the National Academy of Sciences, 107(36), 15,927–15,932.CrossRefGoogle Scholar
  11. Cressman Jr., J.R., Ullah, G., Ziburkus, J., Schiff, S.J., & Barreto, E. (2009). The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. single neuron dynamics. Journal of Computational Neuroscience, 26, 159–170.CrossRefPubMedPubMedCentralGoogle Scholar
  12. Cressman Jr., J.R., Ullah, G., Ziburkus, J., Schiff, S.J., & Barreto, E. (2011). Erratum to: The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. single neuron dynamics. Journal of Computational Neuroscience, 30, 781.CrossRefGoogle Scholar
  13. Dahlem, M.A., Schumacher, J., & Hübel, N. (2014). Linking a genetic defect in migraine to spreading depression in a computational model. PeerJ, 2, e379. doi: 10.7717/peerj.379.CrossRefPubMedPubMedCentralGoogle Scholar
  14. Dijkhuizen, R.M., Beekwilder, J.P., van der Worp, H.B., van der Sprenkel, J.W.B., Tulleken, K.A., & Nicolay, K. (1999). Correlation between tissue depolarizations and damage in focal ischemic rat brain. Brain research, 840(1), 194–205.CrossRefPubMedGoogle Scholar
  15. Dobretsov, M., & Stimers, J.R. (2005). Neuronal function and alpha3 isoform of the na/k–ATPase. Frontiers in Bioscience, 10, 2373–2396.CrossRefPubMedGoogle Scholar
  16. Doedel, E.J., & Oldeman, B.E. (2009). Auto-07p: Continuation and bifurcation software for ordinary differential equations. Montreal: Concordia University.Google Scholar
  17. Falini, A., Barkovich, A., Calabrese, G., Origgi, D., Triulzi, F., & Scotti, G. (1998). Progressive brain failure after diffuse hypoxic ischemic brain injury: a serial MR and proton MR spectroscopic study. American Journal of Neuroradiology, 19(4), 648–652.PubMedGoogle Scholar
  18. Fröhlich, F., & Bazhenov, M. (2006). Coexistence of tonic firing and bursting in cortical neurons. Physical Review E, 74(031922).Google Scholar
  19. Hansen, A.J., & Zeuthen, T. (1981). Extracellular ion concentrations during spreading depression and ischemia in the rat brain cortex. Acta physiologica Scandinavica, 113(4), 437–445.CrossRefPubMedGoogle Scholar
  20. Herculano-Houzel, S., & Lent, R. (2005). Isotropic fractionator: a simple, rapid method for the quantification of total cell and neuron numbers in the brain. The Journal of neuroscience, 25(10), 2518–2521.CrossRefPubMedGoogle Scholar
  21. Hines, M.L., Morse, T., Migliore, M., Carnevale, N.T., & Shepherd, G.M. (2004). ModelDB: a database to support computational neuroscience. Journal of computational neuroscience, 17(1), 7–11.CrossRefPubMedPubMedCentralGoogle Scholar
  22. Hodgkin, A.L. (1948). The local electric changes associated with repetitive action in a medullated axon. Journal of Physiology, 107, 165.CrossRefPubMedPubMedCentralGoogle Scholar
  23. Hodgkin, A.L., & Huxley, A.F. (1952a). The components of membrane conductance in the giant axon of Loligo. Journal of Physiology, 116, 473–496.CrossRefPubMedPubMedCentralGoogle Scholar
  24. Hodgkin, A.L., & Huxley, A.F. (1952b). Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo. Journal of Physiology, 116, 449–472.CrossRefPubMedPubMedCentralGoogle Scholar
  25. Hodgkin, A.L., & Huxley, A.F. (1952c). A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology, 117, 500–544.CrossRefPubMedPubMedCentralGoogle Scholar
  26. Hodgkin, A.L., Huxley, A.F., & Katz, B. (1952). Measurement of current–voltage relations in the membrane of the giant axon of Loligo. Journal of Physiology, 116, 424–448.CrossRefPubMedPubMedCentralGoogle Scholar
  27. Hoffmann, U., Sukhotinsky, I., Atalay, Y.B., Eikermann-Haerter, K., & Ayata, C. (2012). Increased glucose availability does not restore prolonged spreading depression durations in hypotensive rats without brain injury. Experimental Neurology, 238(2), 130–132.CrossRefPubMedPubMedCentralGoogle Scholar
  28. Hübel, N., & Dahlem, M.A. (2014). Dynamics from seconds to hours in Hodgkin–Huxley model with time–dependent ion concentrations and buffer reservoirs. PLoS Comparative Biology, 10, e1003,941. doi: 10.1371/journal.pcbi.1003941.CrossRefGoogle Scholar
  29. Hübel, N., Schöll, E., & Dahlem, M.A. (2014). Bistable dynamics underlying excitability of ion homeostasis in neuron models. PLoS Comparative Biology, 10, e1003,551. doi: 10.1371/journal.pcbi.1003551  10.1371/journal.pcbi.1003551.CrossRefGoogle Scholar
  30. Ingram, J., Zhang, C., Cressman, J.R., Hazra, A., Wei, Y., Koo, Y.E., žiburkus, J., Kopelman, R., Xu, J., & Schiff, S.J. (2014). Oxygen and seizure dynamics: i. experiments. Journal of neurophysiology, 112 (2), 205–212.CrossRefPubMedPubMedCentralGoogle Scholar
  31. 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
  32. Kager, H., Wadman, W.J., & Somjen, G.G. (2002). Conditions for the triggering of spreading depression studied with computer simulations. Journal of Neurophysiology, 88(5), 2700.CrossRefPubMedGoogle Scholar
  33. Kager, H., Wadman, W.J., & Somjen, G.G. (2007). Seizure–like afterdischarges simulated in a model neuron. Journal of Computational Neuroscience, 22, 105–128.CrossRefPubMedGoogle Scholar
  34. Krishnan, G.P., & Bazhenov, M. (2011). Ionic dynamics mediate spontaneous termination of seizures and postictal depression state. The Journal of Neuroscience, 31(24), 8870–8882.CrossRefPubMedPubMedCentralGoogle Scholar
  35. Krizaj, D., Rice, M.E., Wardle, R.A., & Nicholson, C. (1996). Water compartmentalization and extracellular tortuosity after osmotic changes in cerebellum of Trachemys scripta. Journal of Physiology, 42(3), 887–896.CrossRefGoogle Scholar
  36. Lauderdale, K., Murphy, T., Tung, T., Davila, D., Binder, D.K., & Fiacco, T.A. (2015). Osmotic edema rapidly increases neuronal excitability through activation of NMDA receptor–dependent slow inward currents in juvenile and adult hippocampus. ASN Neuro, 7(5), 1759091415605,115. doi: 10.1177/1759091415605115.CrossRefGoogle Scholar
  37. Luigetti, M., Goldsberry, G.T., & Cianfoni, A. (2012). Brain mri in global hypoxia–ischemia: a map of selective vulnerability. Acta Neurologica Belgica, 112(1), 105–107.CrossRefPubMedGoogle Scholar
  38. Mazel, T., Simonov, Z., & Sykov, E. (1998). Diffusion heterogeneity and anisotropy in rat hippocampus. Neuroreport, 9(7), 1299–1304.CrossRefPubMedGoogle Scholar
  39. McBain, C.J., Traynelis, S.F., & Dingledine, R. (1990). Regional variation of extracellular space in the hippocampus. Science, 249(4969), 674–677.CrossRefPubMedGoogle Scholar
  40. Mulet, J., & Mirasso, C.R. (1999). Numerical statistics of power dropouts based on the Lang-Kobayashi model. Physical Review E, 59(5), 5400–5405. doi: 10.1103/physreve.59.5400.CrossRefGoogle Scholar
  41. Murphy, T.H., Li, P., Betts, K., & Liu, R. (2008). Two-photon imaging of stroke onset in vivo reveals that nmda-receptor independent ischemic depolarization is the major cause of rapid reversible damage to dendrites and spines. The Journal of Neuroscience, 28(7), 1756–1772.CrossRefPubMedGoogle Scholar
  42. Rosenberg, G.A. (1999). Ischemic brain edema. Progress in Cardiovascular Diseases, 42(3), 209–216.CrossRefPubMedGoogle Scholar
  43. Sawas, A.H., & Gilbert, J.C. (1981). Effects of adrenergic agonists and antagonists and of the catechol nucleus on the Na+, K+–ATPase and Mg2+–ATPase activities of synaptosomes. Biochemical Pharmacology, 30(13), 1799–803.CrossRefPubMedGoogle Scholar
  44. Schüz, A., & Palm, G. (1989). Density of neurons and synapses in the cerebral cortex of the mouse. Journal of Comparative Neurology, 286(4), 442–455.CrossRefPubMedGoogle Scholar
  45. Shandilya, S.G., & Timme, M. (2011). Inferring network topology from complex dynamics. New Journal of Physical, 13(1), 013,004.CrossRefGoogle Scholar
  46. Somjen, G.G. (2004). Ions in the brain: normal function, seizures, and stroke. USA: Oxford University Press.Google Scholar
  47. Sukhotinsky, I., Yaseen, M.A., Sakadžić, S., Ruvinskaya, S., Sims, J.R., Boas, D.A., Moskowitz, M.A., & Ayata, C. (2010). Perfusion pressure–dependent recovery of cortical spreading depression is independent of tissue oxygenation over a wide physiologic range. Journal of Cerebral Blood Flow and Metabolism, 30(6), 1168–1177. doi: 10.1038/jcbfm.2009.285.CrossRefPubMedPubMedCentralGoogle Scholar
  48. Ullah, G., & Schiff, S.J. (2009). Tracking and control of neuronal hodgkin-huxley dynamics. Physical Review E, 79(4), 040,901. doi: 10.1103/physreve.79.040901.CrossRefGoogle Scholar
  49. Ullah, G., & Schiff, S.J. (2010). Assimilating seizure dynamics. PLoS Comput Biol, 6(5), e1000,776.CrossRefGoogle Scholar
  50. Ullah, G., Wei, Y., Dahlem, M.A., Wechselberger, M., & Schiff, S.J. (2015). The role of cell volume in the dynamics of seizure, spreading depression, and anoxic depolarization. PLoS Comparative Biology, 11(8), e1004,414. doi: 10.1371/journal.pcbi.1004414.CrossRefGoogle Scholar
  51. Wei, Y., Ullah, G., Ingram, J., & Schiff, S.J. (2014a). Oxygen and seizure dynamics: II. computational modeling. Journal of Neurophysiology, 112(2), 213–223.CrossRefPubMedPubMedCentralGoogle Scholar
  52. Wei, Y., Ullah, G., & Schiff, S.J. (2014b). Unification of neuronal spikes, seizures, and spreading depression. Journal of Neuroscience, 34, 11,733–11,743.CrossRefGoogle Scholar
  53. Xie, L., Kang, H., Xu, Q., Chen, M.J., Liao, Y., Thiyagarajan, M., O’Donnell, J., Christensen, D.J., Nicholson, C., Iliff, J.J., Takano, K., Deane, R., & Nedergaard, M. (2013). Sleep drives metabolite clearance from the adult brain. Science, 342(6156), 373–377. doi: 10.1126/science.1241224.CrossRefPubMedGoogle Scholar
  54. Yao, W., Huang, H., & Miura, R.M. (2011). A continuum neural model for the instigation and propagation of cortical spreading depression. Bulletin of Mathematical Biology, 73(11), 2773–2790. doi: 10.1007/s11538-011-9647-3.CrossRefPubMedGoogle Scholar
  55. Zamecnik, J., Homola, A., Cicanic, M., Kuncova, K., Marusic, P., Krsek, P., Syková, E., & Vargova, L. (2012). The extracellular matrix and diffusion barriers in focal cortical dysplasias. European Journal of Neuroscience, 36, 2017–2024. doi: 10.1111/j.1460-9568.2012.08107.x.CrossRefPubMedGoogle Scholar
  56. Zandt, B.J., ten Haken, B., van Dijk, J.G., & van Putten, M.J. (2011). Neural dynamics during anoxia and the “wave of death”. PLoS ONE, 6, e22,127. doi: 10.1371/journal.pone.0022127.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of South FloridaTampaUSA
  2. 2.Department of Biomedical and Molecular SciencesQueen’s UniversityKingstonCanada

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