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.
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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.
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.
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.
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.
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.
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.
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.
Fisher, R. S., Pedley, T. A., & Prince, D. A. (1976). Kinetics of potassium movement in norman cortex. Brain Research, 101(2), 223–237.
Forster, D. (1990). Hydrodynamic fluctuations, broken symmetry, and correlation. Boulder: Westview.
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.
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.
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.
Fuster, J. M. (1995). Memory in the cerebral cortex. Cambridge: MIT.
Goldman-Rakic, P. S. (1995). Cellular basis of working memory. Neuron, 14(3), 477–485.
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.
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.
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.
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.
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.
Kager, H., Wadman, J. W., & Somjen, G. G. (2007). Seizure-like afterdischarges simulated in a model neuron. Journal of Computational Neuroscience, 22, 105–128.
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.
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.
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.
Marder, E., & Prinz, A. A. (2002). Modulating stability in neuron and network function: The role of activity in homeostasis. BioEssays, 24, 1145–1154.
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.
Mazel, T., Simonova, Z., & Sykova, E. (1998). Diffusion heterogeneity and anisotropy in rat hippocampus. Neuroreport, 9(7), 1299–1304.
McBain, C. J., Traynelis, S. F., & Dingledine, R. (1990). Regional variation of extracellular space in the hippocampus. Science, 249(4969), 674–677.
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.
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.
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.
Murray, J. D. (2003). Mathematical Biology II: Spatial models and biomedical applications. New York: Springer.
Nadkarni, S., & Jung, P. (2003). Spontaneous oscillations of dressed neurons: A new mechanism for epilepsy? Physical Review Letters, 91(268101), 1–4.
Netoff, T. I., & Schiff, S. J. (2002). Decreased neuronal synchronization during experimental seizures. Journal of Neuroscience, 22, 7297–7307.
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.
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.
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.
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.
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.
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.
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.
Sanchez-Vives, M. V., & McCormick, D. A. (2000). Cellular and network mechanisms of rhythmic recurrent activity in neocortex. Nature Neuroscience, 3, 1027–1034.
Schiff, S. J., Sauer, T., Kumar, R., & Weinstein, S. L. (2005). Neuronal spatiotemporal pattern discrimination: The dynamical evolution of seizures. NeuroImage, 28, 1043–1055.
Shu, Y., Hasenstaub, A., & McCormick, D. A. (2003). Turning on and off recurrent balanced cortical activity. Nature, 423(6937), 288–293.
Soltesz, I., & Staley, K. (2008). Computational neuroscience in epilepsy. Amsterdam: Academic.
Somjen, G. G. (2004). Ions in the brain: normal function, seizures, and stoke. Oxford: Oxford University Press.
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.
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.
Turrigiano, G. G. (2008). The self-tuning neuron: Synaptic scaling of excitatory synapses. Cell, 135, 422–435.
Van Vreeswijk, C., & Sompolinsky, H. (1996). Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science, 274(5293), 1724–1726.
Vogels, T. P., Rajan, K., & Abbott, L. F. (2005). Neural network dynamics. Annual Review of Neuroscience, 28, 357–376.
Wang, X. J. (1998). Calcium coding and adaptive temporal computation in cortical pyramidal neurons. Journal of Neurophysiology, 79(3), 1549–1566.
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.
Wang, X. J. (2003). Persistent neuronal activity: Experiments and theory. Cerebral Cortex, 13, 1123.
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.
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).
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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
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DOI: https://doi.org/10.1007/s10827-008-0130-6