Skip to main content
Log in

The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: II. Network and glial dynamics

  • Published:
Journal of Computational Neuroscience Aims and scope Submit manuscript

Abstract

In these companion papers, we study how the interrelated dynamics of sodium and potassium affect the excitability of neurons, the occurrence of seizures, and the stability of persistent states of activity. We seek to study these dynamics with respect to the following compartments: neurons, glia, and extracellular space. We are particularly interested in the slower time-scale dynamics that determine overall excitability, and set the stage for transient episodes of persistent oscillations, working memory, or seizures. In this second of two companion papers, we present an ionic current network model composed of populations of Hodgkin–Huxley type excitatory and inhibitory neurons embedded within extracellular space and glia, in order to investigate the role of micro-environmental ionic dynamics on the stability of persistent activity. We show that these networks reproduce seizure-like activity if glial cells fail to maintain the proper micro-environmental conditions surrounding neurons, and produce several experimentally testable predictions. Our work suggests that the stability of persistent states to perturbation is set by glial activity, and that how the response to such perturbations decays or grows may be a critical factor in a variety of disparate transient phenomena such as working memory, burst firing in neonatal brain or spinal cord, up states, seizures, and cortical oscillations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Notes

  1. http://senselab.med.yale.edu/modeldb/

References

  • 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(3), 1042–1053.

    PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Bikson, M., Hahn, P. J., Fox, J. E., & Jefferys, J. G. R. (2003). Depolarization block of neurons during maintenance of electrographic seizures. Journal of Neurophysiology, 90(4), 2402–2408.

    Article  PubMed  Google Scholar 

  • Chub, N., Mentis, Z. G., & O’Donovan, J. M. (2006). Chloride-sensitive MEQ fluorescence in chick embryo motoneurons following manipulations of chloride and during spontaneous network activity. Journal of Neurophysiology, 95, 323–330.

    Article  PubMed  CAS  Google Scholar 

  • Compte, A., Brunel, N., Goldman-Rakic, P. S., & Wang, X. J. (2000). Synaptic mechanisms and network dynamics underlying spatial working memory in a cortical network model. Cerebral Cortex, 10(9), 910–923.

    Article  PubMed  CAS  Google Scholar 

  • Cressman, 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. doi:10.1007/s10827-008-0132-4.

  • Durstewitz, D., Seamans, J. K., & Sejnowski, T. J. (2000). Neurocomputational models of working memory. Nature Neuroscience, 3, 1184–1191.

    Article  PubMed  CAS  Google Scholar 

  • Fellin, T., Gomez-Gonzalo, M., Gobbo, S., Carmignoto, G., & Haydon, P. G. (2006). Astrocytic glutamate is not necessary for the generation of epileptiform neuronal activity in hippocampal slices. Journal of Neuroscience, 26(36), 9312–9322.

    Article  PubMed  CAS  Google Scholar 

  • Fisher, R. S., Pedley, T. A., & Prince, D. A. (1976). Kinetics of potassium movement in norman cortex. Brain Research, 101(2), 223–237.

    Article  PubMed  CAS  Google Scholar 

  • Forster, D. (1990). Hydrodynamic fluctuations, broken symmetry, and correlation. Boulder: Westview.

    Google Scholar 

  • Frohlich, F., Timofeev, I., Sejnowski, T. J., & Bazhenov, M. (2008). Extracellular potassium dynamics and epileptogenesis. In I. Soltesz, & K. Staley (Eds.), Computational neuroscience in epilepsy. Amsterdam: Academic.

    Google Scholar 

  • Fujiwara-Tsukamoto, Y., Isomura, Y., Kaneda, K., & Takada, M. (2004). Synaptic interactions between pyramidal cells and interneuron subtypes during seizure-like activity in the rat hippocampus. Journal of Physiology, 557(3), 961–979.

    Article  PubMed  Google Scholar 

  • Funahashi, S., Bruce, C. J., & Goldman-Rakic, P. S. (1989). Mnemonic coding of visual space in the monkey’s dorsolateral prefrontal cortex. Journal of Neurophysiology, 61(2), 331–349.

    PubMed  CAS  Google Scholar 

  • Fuster, J. M. (1995). Memory in the cerebral cortex. Cambridge: MIT.

    Google Scholar 

  • Goldman-Rakic, P. S. (1995). Cellular basis of working memory. Neuron, 14(3), 477–485.

    Article  PubMed  CAS  Google Scholar 

  • Gutkin, B. S., Laing, C. R., Colby, C. L., Chow, C. C., & Ermentrout, G. B. (2001). Turning on and off with excitation: the role of spike-timing asynchrony and synchrony in sustained neural activity. Journal of Computational Neuroscience, 11(2), 121–134.

    Article  PubMed  CAS  Google Scholar 

  • Heinemann, U., Gabriel, S., Jauch, R., Schulze, K., Kivi, A., Eilers, A., et al. (2000). Alterations of glial cell function in temporal lobe epilepsy. Epilepsia, 41(Suppl. 6), S185–S189.

    Article  PubMed  Google Scholar 

  • Hinterkeuser, S., Schroder, W., Hager, G., Seifert, G., Blumcke, I., Elger, C. E., et al. (2000). Astrocytes in the hippocampus of patients with temporal lobe epilepsy display changes in potassium conductances. European Journal of Neuroscience, 12(6), 2087–2096.

    Article  PubMed  CAS  Google Scholar 

  • Huang, X., Troy, W. C., Yang, Q., Ma, H., Laing, C. R., Schiff, S. J., et al. (2004). Spiral waves in disinhibited mammalian neocortex. Journal of Neuroscience, 24, 9897–9902.

    Article  PubMed  CAS  Google Scholar 

  • Kager, H., Wadman, J. W., & 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.

    PubMed  CAS  Google Scholar 

  • Kager, H., Wadman, J. W., & Somjen, G. G. (2007). Seizure-like afterdischarges simulated in a model neuron. Journal of Computational Neuroscience, 22, 105–128.

    Article  PubMed  CAS  Google Scholar 

  • Kang, N., Xu, J., Xu, Q., Nedergaard, M., & Kang, J. (2005). Astrocytic glutamate release-induced transient depolarization and epileptiform discharges in hippocampal CA1 pyramidal neurons. Journal of Neurophysiology, 94(6), 4121–4130.

    Article  PubMed  CAS  Google Scholar 

  • Konnerth, A., Heinemann, U., & Yaari, Y. (1984). Slow transmission of neural activity in hippocampal area CA1 in absence of active chemical synapses. Nature, 307, 69–71.

    Article  PubMed  CAS  Google Scholar 

  • Leinekugel, X., Khazipov, R., Cannon, R., Hirase, H., Ben-Ari, Y., & Buzsaki, G. (2002). Correlated bursts of activity in the neonatal hippocampus in vivo. Science, 298(5575), 2049–2052.

    Article  Google Scholar 

  • Marder, E., & Prinz, A. A. (2002). Modulating stability in neuron and network function: The role of activity in homeostasis. BioEssays, 24, 1145–1154.

    Article  PubMed  CAS  Google Scholar 

  • Mason, A., & Larkman, A. (1990). Correlations between morphology and electrophysiology of pyramidal neurons in slices of rat visual cortex. II. Electrophysiology. Journal of Neuroscience, 10(5), 1415–1428.

    PubMed  CAS  Google Scholar 

  • Mazel, T., Simonova, Z., & Sykova, E. (1998). Diffusion heterogeneity and anisotropy in rat hippocampus. Neuroreport, 9(7), 1299–1304.

    Article  PubMed  CAS  Google Scholar 

  • McBain, C. J., Traynelis, S. F., & Dingledine, R. (1990). Regional variation of extracellular space in the hippocampus. Science, 249(4969), 674–677.

    Article  PubMed  CAS  Google Scholar 

  • McCormick, D. A., Shu, Y., Hasenstaub, A., Sanchez-Vives, M., Badoual, M., & Bal, T. (2003). Persistent cortical activity: Mechanisms of generation and effects on neuronal excitability. Cerebral Cortex, 13, 1219–1231.

    Article  PubMed  Google Scholar 

  • Miller, E. K., Erickson, C. A., & Desimone, R. (1996). Neural mechanisms of visual working memory in prefrontal cortex of the macaque. Journal of Neuroscience, 16(16), 5154–5167.

    PubMed  CAS  Google Scholar 

  • Miller, P., Brody, C. D., Romo, R., & Wang, X. J. (2003). A recurrent network model of somatosensory parametric working memory in the prefrontal cortex. Cerebral Cortex, 13, 1208–1218.

    Article  PubMed  Google Scholar 

  • Murray, J. D. (2003). Mathematical Biology II: Spatial models and biomedical applications. New York: Springer.

    Google Scholar 

  • Nadkarni, S., & Jung, P. (2003). Spontaneous oscillations of dressed neurons: A new mechanism for epilepsy? Physical Review Letters, 91(268101), 1–4.

    Google Scholar 

  • Netoff, T. I., & Schiff, S. J. (2002). Decreased neuronal synchronization during experimental seizures. Journal of Neuroscience, 22, 7297–7307.

    PubMed  CAS  Google Scholar 

  • Oberheim, N. A., Tian, G. F., Han, X., Peng, W., Takano, T., Ransom, B., et al. (2008). Loss of astrocytic domain organization in the epileptic brain. Journal of Neuroscience, 28(13), 3264–3276.

    Article  PubMed  CAS  Google Scholar 

  • Parpura, V., & Haydon, P. G. (2000). Physiological astrocytic calcium levels stimulate glutamate release to modulate adjacent neurons. Proceedings of the National Academy of Sciences of the United States of America, 97, 8629–8634.

    Article  PubMed  CAS  Google Scholar 

  • Parpura, V., Basarsky, T. A., Liu, F., Jeftinija, K., Jeftinija, S., & Haydon, P. G. (1994). Glutamate-mediated astrocyte–neuron signalling. Nature, 369(6483), 744–747.

    Article  PubMed  CAS  Google Scholar 

  • Perez-Velazquez, J. L., & Carlen, P. L. (1999). Synchronization of GABAergic interneuronal networks during seizure-like activity in the rat horizontal hippocampal slice. European Journal of Neuroscience, 11, 4110–4118.

    Article  Google Scholar 

  • Pinto, D. J., Patrick, S. L., Huang, W. C., & Connors, B. W. (2005). Initiation, propagation, and termination of epileptiform activity in rodent neocortex in vitro involve distinct mechanisms. Journal of Neuroscience, 25(36), 8131–8140.

    Article  PubMed  CAS  Google Scholar 

  • Rainer, G., Asaad, W. F., & Miller, E. K. (1998). Memory fields of neurons in the primate prefrontal cortex. Proceedings of the National Academy of Sciences of the United States of America, 95, 15008–15013.

    Article  PubMed  CAS  Google Scholar 

  • Romo, R., Brody, C. D., Hernandez, A., & Lemus, L. (1999). Neuronal correlates of parametric working memory in the prefrontal cortex. Nature, 399(6735), 470–473.

    Article  PubMed  CAS  Google Scholar 

  • Sanchez-Vives, M. V., & McCormick, D. A. (2000). Cellular and network mechanisms of rhythmic recurrent activity in neocortex. Nature Neuroscience, 3, 1027–1034.

    Article  PubMed  CAS  Google Scholar 

  • Schiff, S. J., Sauer, T., Kumar, R., & Weinstein, S. L. (2005). Neuronal spatiotemporal pattern discrimination: The dynamical evolution of seizures. NeuroImage, 28, 1043–1055.

    Article  PubMed  Google Scholar 

  • Shu, Y., Hasenstaub, A., & McCormick, D. A. (2003). Turning on and off recurrent balanced cortical activity. Nature, 423(6937), 288–293.

    Article  PubMed  CAS  Google Scholar 

  • Soltesz, I., & Staley, K. (2008). Computational neuroscience in epilepsy. Amsterdam: Academic.

    Google Scholar 

  • Somjen, G. G. (2004). Ions in the brain: normal function, seizures, and stoke. Oxford: Oxford University Press.

    Google Scholar 

  • Tian, G. F., Azmi, H., Takano, T., Xu, Q., Peng, W., Lin, J., et al. (2005). An astrocytic basis of epilepsy. Nature Medicine, 11(9), 973–981.

    PubMed  CAS  Google Scholar 

  • Trevelyan, A. J., Sussillo, D., Watson, B. O., & Yuste, R. (2006). Modular propagation of epileptiform activity: Evidence for an inhibitory veto in neocortex. Journal of Neuroscience, 26(48), 12447–12455.

    Article  PubMed  CAS  Google Scholar 

  • Turrigiano, G. G. (2008). The self-tuning neuron: Synaptic scaling of excitatory synapses. Cell, 135, 422–435.

    Article  PubMed  CAS  Google Scholar 

  • Van Vreeswijk, C., & Sompolinsky, H. (1996). Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science, 274(5293), 1724–1726.

    Article  PubMed  Google Scholar 

  • Vogels, T. P., Rajan, K., & Abbott, L. F. (2005). Neural network dynamics. Annual Review of Neuroscience, 28, 357–376.

    Article  PubMed  CAS  Google Scholar 

  • Wang, X. J. (1998). Calcium coding and adaptive temporal computation in cortical pyramidal neurons. Journal of Neurophysiology, 79(3), 1549–1566.

    PubMed  CAS  Google Scholar 

  • Wang, X. J. (1999). Synaptic basis of cortical persistent activity: the importance of NMDA receptors to working memory. Journal of Neuroscience, 19(21), 9587–9603.

    PubMed  CAS  Google Scholar 

  • Wang, X. J. (2003). Persistent neuronal activity: Experiments and theory. Cerebral Cortex, 13, 1123.

    Article  PubMed  Google Scholar 

  • Ziburkus, J., Cressman, J. R., Barreto, E., & Schiff, S. J. (2006). Interneuron and pyramidal cell interplay during in vitro seizure-like events. Journal of Neurophysiology, 95, 3948–3954.

    Article  PubMed  Google Scholar 

Download references

Acknowledgements

We thank Jokubas Ziburkus, Andrew J Trevelyan, Maxim Bazhenov, and Partha Mitra, for their valuable discussions. This work was funded by NIH Grants K02MH01493 (SJS), R01MH50006 (SJS, GU), F32NS051072 (JRC), and CRCNS-R01MH079502 (EB).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ghanim Ullah.

Additional information

Action Editor: Alain Destexhe

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ullah, G., Cressman Jr., J.R., Barreto, E. et al. The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: II. Network and glial dynamics. J Comput Neurosci 26, 171–183 (2009). https://doi.org/10.1007/s10827-008-0130-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10827-008-0130-6

Keywords

Navigation