Abstract
Experiments on hippocampal slices have recorded that a novel pattern of epileptic seizures with alternating excitatory and inhibitory activities in the CA1 region can be induced by an elevated potassium ion (K+) concentration in the extracellular space between neurons and astrocytes (ECS-NA). To explore the intrinsic effects of the factors (such as glial K+ uptake, Na+–K+-ATPase, the K+ concentration of the bath solution, and K+ lateral diffusion) influencing K+ concentration in the ECS-NA on the epileptic seizures recorded in previous experiments, we present a coupled model composed of excitatory and inhibitory neurons and glia in the CA1 region. Bifurcation diagrams showing the glial K+ uptake strength with either the Na+–K+-ATPase pump strength or the bath solution K+ concentration are obtained for neural epileptic seizures. The K+ lateral diffusion leads to epileptic seizure in neurons only when the synaptic conductance values of the excitatory and inhibitory neurons are within an appropriate range. Finally, we propose an energy factor to measure the metabolic demand during neuron firing, and the results show that different energy demands for the normal discharges and the pathological epileptic seizures of the coupled neurons.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bahar S, Suh M, Zhao M et al (2006) Intrinsic optical signal imaging of neocortical seizures: the ‘epileptic dip’. NeuroReport 17(5):499–503
Bazhenov M et al (2004) Potassium model for slow (2–3 Hz) in vivo neocortical paroxysmal oscillations. J Neurophysiol 92(2):1116–1132
Cornog JL, Gonatas NK, Feierman JR (1967) Effects of intracerebral injection of ouabain on the fine structure of rat cerebral cortex. Am J Pathol 51(4):573–590
Cressman JR, Ullah G, Ziburkus J et al (2009) The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. Single neuron dynamics. J Comput Neurosci 26(2):159–170
Durand DM, Jensen AL (2010) Potassium diffusive coupling in neural networks. Philos Trans R Soc Lond 365(1551):2347–2362
Ermentrout BG, Terman D (2010) Foundations of mathematical neuroscience. Springer, New York, pp 157–167
Fröhlich F, Timofeev I, Sejnowski TJ, Bazhenov M (2008) 26—Extracellular potassium dynamics and epileptogenesis. In: Soltesz I, Staley K (eds) Computational Neuroscience in Epilepsy, Academic press, New York, pp 419–439
Gluckman BJ, Nguyen H, Schiff SJ (2001) Adaptive electric field control of epileptic seizures. J Neurosci 21(2): 590–600
Graham BP, Saudargiene A, Cobb S (2012) A computational study of the influence of synaptic cooperativity on synaptic plasticity in a hippocampal CA1 pyramidal cell. BMC Neurosci 13(Suppl 1):P164
Ingram JM, Zhang C, Xu J et al (2013) FRET excited ratiometric oxygen sensing in living tissue. J Neurosci Methods 214(1):45–51
Jensen MS, Yaari Y (1997) Role of intrinsic burst firing, potassium accumulation, and electrical coupling in the elevated potassium model of hippocampal epilepsy. J Neurophysiol 77(3):1224–1233
Kager H, Wadman WJ, Somjen GG (2000) Simulated seizures and spreading depression in a neuron model incorporating interstitial space and ion concentrations. J Neurophysiol 84(1):495–512
Kager H, Wadman WJ, Somjen G (2007) Seizure-like after discharges simulated in a model neuron. J Comput Neurosci 22(2):105–128 (24)
Larsen BR, Assentoft M, Cotrina ML et al (2014) Contributions of the Na+/K+-ATPase, NKCC1, and Kir4.1 to hippocampal K? Clearance and volume responses. Glia 62(4):608–622
Marom M et al (2003) Depolarization block of neurons during maintenance of electrographic seizures. J Neurophysiol 90(4):2402–2408
Moujahid A, D’Anjou A, Torrealdea FJ et al (2012) Energy and information in Hodgkin–Huxley neurons. Phys Rev E 83(3):681–689
Ohno Y, Tokudome K, Kunisawa N et al (2015) Role of astroglial Kir4.1 channels in the pathogenesis and treatment of epilepsy. Ther Targets Neurol Dis 2:1–10
Østby I, Øyehaug L, Einevoll GT, Nagelhus EA, Plahte E, Zeuthen T, Lloyd CM, Ottersen OP, Omholt SW (2009) Astrocytic mechanisms explaining neural-activity-induced shrinkage of extraneuronal space. PLoS Comput Biol 5(1):291–298
Øyehaug L, Østby I, Lloyd CM et al (2012) Dependence of spontaneous neuronal firing and depolarisation block on astroglial membrane transport mechanisms. J Comput Neurosci 32(1):147–165
Park EH, Durand DM (2006) Role of potassium lateral diffusion in non-synaptic epilepsy: a computational study. J Theor Biol 238(3):666–682
Pinsky PF, Rinzel J, Pinsky PF et al (1994) Intrinsic and network rhythmogenesis in a reduced Traub model for CA3 hippocampal neurons. J Comput Neurosci 1(1–2):39–60
Prinz AA (2008) Understanding epilepsy through network modeling. Proc Natl Acad Sci USA 105(16):5953–5954
Traynelis SF, Dingledine R (1988a) Potassium-induced spontaneous electrographic seizures in the rat hippocampal slice. J Neurophysiol 59(1):259–276
Ullah G, Schiff SJ (2010) Assimilating seizure dynamics. PLoS Comput Biol 6(5):e1000776–e1000776
Ullah G, Cressman JR Jr, Barreto E et al (2009) 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(2):171–183
Wendling F, Bartolomei F, Mina F et al (2012) Interictal spikes, fast ripples and seizures in partial epilepsies—combining multi-level computational models with experimental data. Eur J Neurosci 36(2):2164–2177
Yaari Y, Konnerth A, Heinemann U (1986) Nonsynaptic epileptogenesis in the mammalian hippocampus in vitro. II. Role of extracellular potassium. J Neurophysiol 56(2):424–438
Yina W, Ghanim U, Justin I et al (2014a) Oxygen and seizure dynamics: II. Computational modeling. J Neurophysiol 112(2):213–223
Yina W, Ghanim U, Schiff SJ (2014b) Unification of neuronal spikes, seizures, and spreading depression. J Neurosci 34(35):11733–11743
Ziburkus J et al (2006) Interneuron and pyramidal cell interplay during in vitro seizure-like events. J Neurophysiol 95(6):3948–3954
Žiburkus J, Cressman JR, Schiff SJ (2013) Seizures as imbalanced up states: excitatory and inhibitory conductances during seizure-like events. J Neurophysiol 109(5):1296–1306
Acknowledgments
This work is supported by National Natural Science Foundation of China under Grant Nos. 11272242 and 11472202 and Natural Science Foundation of Shaanxi Province of China (No. S2014JC12575).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Du, M., Li, J., Wang, R. et al. The influence of potassium concentration on epileptic seizures in a coupled neuronal model in the hippocampus. Cogn Neurodyn 10, 405–414 (2016). https://doi.org/10.1007/s11571-016-9390-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11571-016-9390-4