Study on the Hippocampal Neuron's Minimal Models' Discharge Patterns

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Yueping Peng 1,* Haiying Wu 1 Nan Zou 1

1. Engineering College of Armed Police Force, 710086, Xi’an, China

* Corresponding author.


Received: 25 Feb. 2011 / Revised: 7 Apr. 2011 / Accepted: 12 May 2011 / Published: 8 Jun. 2011

Index Terms

Neuron, the minimal model, discharge pattern


The hippocampal CA1 pyramid neuron has plenty of discharge actions. The one-compartment model of CA1 pyramid neuron developed by David is a nine-dimension complex dynamic model. In the thesis, the currents related to the nine-dimension complex model are analyzed and classified by the model’s reduction theory and methods based on neurodynamics, and four minimal models are gotten: (INa+IKdr)-minimal model, (INa+IM)-minimal model, (INa+ICa+Iy)-minimal model, and (INa+ICa+IsAHP)-minimal model. These minimal models have plenty of dynamic actions, and under the current’s stimulation, they can all generate regular discharge and have period discharge pattern, bursting pattern, the chaos discharge pattern, and so on. Compared with the initial nine-dimension complex model, these minimal models’ dimension are much reduced, and are more convenient to numerical simulation, calculating, and analyzing. In addition, these minimal models provide a simpler and flexible method to discuss the specific currents’ dynamic characteristics and functions of the initial nine-dimension complex model by the theory of neurodynamics.

Cite This Paper

Yueping Peng,Haiying Wu,Nan Zou,"Study on the Hippocampal Neuron's Minimal Models' Discharge Patterns", IJIGSP, vol.3, no.4, pp.32-38, 2011. DOI: 10.5815/ijigsp.2011.04.05


[1]Urbani A and Belluzzi O, “Riluzole inhibits the persistent sodium current in mammalian CNS neurons,” Eur J Neurosci, vol. 12, pp. 3567–3574, January 2000. 

[2]Vasilyev DV and Barish ME, “Postnatal development of the hyperpolarization-activated excitatory current Ih in mouse hippocampal pyramidal neurons,” J Neurosci, vol. 22, pp. 8992–9004, April 2002. 

[3]Vervaeke K, Hu H, Graham LJ, and Storm JF, “Contrasting effects of the persistent Na_current on neuronal excitability and spike timing,” Neuron, vol. 49, pp. 257–270, May 2006.

[4]Shuai J, Bikson M, Hahn PJ, Lian J, and Durand DM, “Ionic mechanisms underlying spontaneous CA1 neuronal firing in Ca2+-free solution,” Biophys J, vol. 84, pp. 2009–2011, April 2003.

[5]Gu N, Vervaeke K, Hu H, and Storm JF, “Kv7/KCNQ/M and HCN/h, but not KCa2/SK channels, contribute to the somatic medium after-hyperpolarization and excitability control in CA1 hippocampal pyramidal cells,” J Physiol, vol. 566, pp. 689–715, June 2005.

[6]Chen S, Yue C, and Yaari Y, “A transitional period of calcium-dependent bursting triggered by spike backpropagation into apical dendrites in developing hippocampal neurons,” J Physiol, vol. 567, pp. 79–93, March 2005.

[7]Metz AE, Jarsky T, Martina M, and Spruston N, “R-type calcium channels contribute to afterdepolarization and bursting in hippocampal CA1 pyramidal neurons,” J Neurosci, vol. 25, pp. 5763–5773, April 2005.

[8]Traub RD, Wong RK, Miles R, and Michelson H, “A model of a CA3 hippocampal pyramidal neuron incorporating voltage-clamp data on intrinsic conductances,” J Neurophysiol, vol. 66, pp. 635–649, 1991.

[9]Traub RD and Miles R, “Neuronal networks of the hippocampus,” New York: Cambridge, 1991.

[10]Traub RD, Jefferys JGR, Miles R, Whittington MA, and To´th K , “A branching dendritic model of a rodent CA3 pyramidal neurone,” J Physiol, vol. 481, pp. 79–95, February 1994.

[11]Warman EN, Durand DM, and Yuen GL, “Reconstruction of hippocampal CA1 pyramidal cell electrophysiology by computer simulations,” J Neurophysiol, vol. 71, pp. 2033–2045, April 1994.

[12]Yue C, Remy S, Su H, Beck H, and Yaari Y, “Proximal persistent Na+ channels drive spike afterdepolarizations and associated bursting in adult CA1 pyramidal cells,” J Neurosci, vol. 25, pp. 9704–9720, 2005.

[13]Yue C and Yaari Y, “KCNQ/M channels control spike afterdepolarization and burst generation in hippocampal neurons,” J Neurosci, vol. 24, pp. 4614–4624, 2004.

[14]Yue C and Yaari Y, “Axo-somatic and apical dendritic Kv7/M channels differentially regulate the intrinsic 

[15]excitability of adult rat CA1 pyramidal cells,” J Neurophysiol, vol. 95, pp. 3480–3495, April 2006.

[16]David Golomb, Cuiyong Yue, and Yoel Yaari, “Contribution of Persistent Na+ Current and M-Type K+ Current to Somatic Bursting in CA1 Pyramidal Cells: Combined Experimental and Modeling Study,” J Neurophysiol, vol. 96, pp. 1912–1926, 2006.

[17]Berger TW, “Long-term potentiation of hippocampal synaptic transmission affects rate of behavioral learning,” Science, vol. 224, pp. 627-630, 1984.

[18]Xiao MY, Zhuo Q and Nicoll RA, “Metabotropic glutamate receptor activation causes a rapid redistribution of AMPA receptors,” Neuropharmacology, vol.41, pp. 664-671, June 2001.

[19]Mellentin C and Abraham WC, “Priming stimulation of group II metabotropic glutamate receptors inhibits the subsequeng induction of rat hippocampal long-term depression in vitro,” Neurosci Lett, vol.307, pp.13-16, January 2001.

[20]Hammarstrom AK, Gage PW, “Hypoxia and persistent sodium current,” Eur Biophys J, Vol.31, pp. 323-330, 2002.

[21]Horn EM, waldrop TG, “Hypoxic augmentation of fast2inactivating and persistent sodium currents in rat caudalhypothalamic neurons,” J Neurophysiol, vol. 84, pp. 2572-2581, 2000.

[22]R. M. Ghigliazza and P. Holmes, “Minimal models of bursting neurons: How multiple current, conductances and timescales affect bifurcation diagrams,” SIAM Journal on Applied Dynamical Systems, 2004.

[23]Miaoxing Yao and Fangqi Chen, “Mathematical Foundation of Nonlinear Theory,” Tianjin: Tianjin University Press, 2005.

[24]Eugene M.Izhikevich, “Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting,” The MIT Press, 2005.

[25]Izhikevich E. M. and Hoppensteadt F.C., “Polychronous Wavefront Computations,” International Journal of Bifurcation and Chaos, vol.19, pp. 1733-1739, 2009.

[26]Szatmary B. and Izhikevich E. M., “Spike-Timing Theory of Working Memory,” PLoS Computational Biology, vol.6, pp. e1000879, Auguest 2010.

[27]Wu Ying, Xu Jianxue, He Daihai, Jin Wuyin., “Study on nonlinear characteristic of two synchronizing uncoupled Hindmarsh-Rose neurons,” Acta Physica Sinica, vol.54, pp. 3457-3464, June 2005.