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Barreto E, Cressman JR (2011) Ion concentration dynamics as a mechanism for neuronal bursting Journal of Biological Physics 37:361-373[PubMed]

   Ion concentration dynamics as a mechanism for neuronal bursting (Barreto & Cressman 2011)

References and models cited by this paper

References and models that cite this paper

Bazhenov M, Timofeev I, Steriade M, Sejnowski TJ (2004) Potassium model for slow (2-3 Hz) in vivo neocortical paroxysmal oscillations. J Neurophysiol 92:1116-32 [Journal] [PubMed]

Bikson M, Hahn PJ, Fox JE, Jefferys JG (2003) Depolarization block of neurons during maintenance of electrographic seizures. J Neurophysiol 90:2402-8 [PubMed]

Connors BW, Telfeian AE (2000) Dynamic properties of cells, synapses, circuits, and seizures in neocortex. Adv Neurol 84:141-52 [PubMed]

Cressman JR, Ullah G, Ziburkus J, Schiff SJ, Barreto E (2009) The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. Single neuron dynamics. J Comput Neurosci 26:159-70 [Journal] [PubMed]

   Single neuron with dynamic ion concentrations (Cressman et al. 2009) [Model]

Cymbalyuk GS, Calabrese R, Shilnikov AL (2005) How a neuron model can demonstrate co-existence of tonic spiking and bursting? Neurocomputing 65-66:869-875

Dayan P, Abbott LF (2001) Theoretical Neuroscience. Computational and Mathematical Modeling of Neural Systems

Fertziger AP, Ranck JB (1970) Potassium accumulation in interstitial space during epileptiform seizures. Exp Neurol 26:571-85 [PubMed]

FRANKENHAEUSER B, HODGKIN AL (1956) The after-effects of impulses in the giant nerve fibres of Loligo. J Physiol 131:341-76 [PubMed]

Frohlich F, Bazhenov M (2006) Coexistence of tonic firing and bursting in cortical neurons. Phys Rev E Stat Nonlin Soft Matter Phys 74:031922

Frohlich F, Bazhenov M, Iragui-Madoz V, Sejnowski TJ (2008) Potassium dynamics in the epileptic cortex: new insights on an old topic. Neuroscientist 14:422-33

Frohlich F, Bazhenov M, Timofeev I, Steriade M, Sejnowski TJ (2006) Slow state transitions of sustained neural oscillations by activity-dependent modulation of intrinsic excitability. J Neurosci 26(23):6153-62 [PubMed]

Frohlich F, Sejnowski TJ, Bazhenov M (2010) Network bistability mediates spontaneous transitions between normal and pathological brain states. J Neurosci 30:10734-43 [PubMed]

GRAFSTEIN B (1956) Mechanism of spreading cortical depression. J Neurophysiol 19:154-71 [PubMed]

GREEN JD (1964) THE HIPPOCAMPUS. Physiol Rev 44:561-608

Guckenheimer J (1986) Multiple bifurcation problems for chemical reactors Physica D 20:1-20

Guckenheimer J, Holmes P (1983) Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, 2nd edition.

Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500-44 [Journal] [PubMed]

   Squid axon (Hodgkin, Huxley 1952) (LabAXON) [Model]
   Squid axon (Hodgkin, Huxley 1952) (NEURON) [Model]
   Squid axon (Hodgkin, Huxley 1952) (SNNAP) [Model]
   Squid axon (Hodgkin, Huxley 1952) used in (Chen et al 2010) (R language) [Model]
   Squid axon (Hodgkin, Huxley 1952) (SBML, XPP, other) [Model]

Izhikevich EM (2007) Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting [Journal]

   Artificial neuron model (Izhikevich 2003, 2004, 2007) [Model]

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 77:1224-33 [Journal] [PubMed]

Kager H, Wadman WJ, Somjen GG (2000) Simulated seizures and spreading depression in a neuron model incorporating interstitial space and ion concentrations. J Neurophysiol 84:495-512 [Journal] [PubMed]

Kager H, Wadman WJ, Somjen GG (2002) Conditions for the triggering of spreading depression studied with computer simulations. J Neurophysiol 88:2700-12 [Journal] [PubMed]

Kager H, Wadman WJ, Somjen GG (2007) Seizure-like afterdischarges simulated in a model neuron. J Comput Neurosci 22:105-128 [Journal] [PubMed]

Komendantov A, Cressman JR, Barreto E (2010) Ion concentration homeostasis and the regulation of neuronal firing activity: the role of cation-chloride cotransporters. Bmc Neurosci 1:27

Marchetti C, Tabak J, Chub N, O'Donovan MJ, Rinzel J (2005) Modeling spontaneous activity in the developing spinal cord using activity-dependent variations of intracellular chloride. J Neurosci 25:3601-12 [PubMed]

Martens EA, Barreto E, Strogatz SH, Ott E, So P, Antonsen TM (2009) Exact results for the Kuramoto model with a bimodal frequency distribution. Phys Rev E Stat Nonlin Soft Matter Phys 79:026204

Park EH, Durand DM (2006) Role of potassium lateral diffusion in non-synaptic epilepsy: a computational study. J Theor Biol 238:666-82 [PubMed]

Pinsky PF, Rinzel J (1994) Intrinsic and network rhythmogenesis in a reduced Traub model for CA3 neurons. J Comput Neurosci 1:39-60 [Journal] [PubMed]

   CA3 pyramidal cell: rhythmogenesis in a reduced Traub model (Pinsky, Rinzel 1994) [Model]

Postnov DE, Muller F, Schuppner RB, Schimansky-Geier L (2009) Dynamical structures in binary media of potassium-driven neurons. Phys Rev E Stat Nonlin Soft Matter Phys 80:031921-33

Shilnikov A, Calabrese RL, Cymbalyuk G (2005) Mechanism of bistability: tonic spiking and bursting in a neuron model. Phys Rev E Stat Nonlin Soft Matter Phys 71:056214 [PubMed]

Somjen GG (2004) Ions in the brain: Normal function, seizures and stroke

Somjen GG, Kager H, Wadman WJ (2008) Computer simulations of neuron-glia interactions mediated by ion flux. J Comp Neurosci 25(2):349-65 [Journal] [PubMed]

   Computer simulations of neuron-glia interactions mediated by ion flux (Somjen et al. 2008) [Model]

Somjen GG, Kager H, Wadman WJ (2009) Calcium sensitive non-selective cation current promotes seizure-like discharges and spreading depression in a model neuron. J Comput Neurosci 26:139-47 [Journal] [PubMed]

Ziburkus J, Cressman JR, Barreto E, Schiff SJ (2006) Interneuron and pyramidal cell interplay during in vitro seizure-like events. J Neurophysiol 95:3948-54 [PubMed]

Buchin A, Chizhov A, Huberfeld G, Miles R, Gutkin BS (2016) Reduced Efficacy of the KCC2 Cotransporter Promotes Epileptic Oscillations in a Subiculum Network Model. J Neurosci 36:11619-11633 [Journal] [PubMed]

Dahlem MA, Schumacher J, Hubel N (2014) Linking a genetic defect in migraine to spreading depression in a computational model. PeerJ 2:e379 [Journal] [PubMed]

   Spreading depression model for FHM3 with Nav1.1 mutation (Dahlem et al. 2014) [Model]

Hubel N, Andrew RD, Ullah G (2016) Large extracellular space leads to neuronal susceptibility to ischemic injury in a Na(+)/K (+) pumps-dependent manner. J Comput Neurosci 40:177-92 [Journal] [PubMed]

   Anoxic depolarization, recovery: effect of brain regions and extracellular space (Hubel et al. 2016) [Model]

Hubel N, Dahlem MA (2014) Dynamics from seconds to hours in Hodgkin-Huxley model with time-dependent ion concentrations and buffer reservoirs PLoS Comp Biol 10:e1003941 [Journal] [PubMed]

   Hodgkin-Huxley with dynamic ion concentrations (Hubel and Dahlem, 2014) [Model]

Kim CM, Nykamp DQ (2017) The influence of depolarization block on seizure-like activity in networks of excitatory and inhibitory neurons. J Comput Neurosci 43:65-79 [Journal] [PubMed]

Krishnan GP, Filatov G, Shilnikov A, Bazhenov M (2015) Electrogenic properties of the Na+/K+ ATPase controls transitions between normal and pathological brain states J Neurophysiol (113(9):3356-3374 [Journal] [PubMed]

   Single cell model with variable ion concentrations and Na+/K+ ATPase (Krishnan et al. 2015) [Model]

Reznik RI, Barreto E, Sander E, So P (2015) Effects of polarization induced by non-weak electric fields on the excitability of elongated neurons with active dendrites. J Comput Neurosci [Journal] [PubMed]

   Non-Weak E-Fields Pyramidal Neurons (Reznik et. al.,2015) [Model]

Wei Y, Ullah G, Ingram J, Schiff SJ (2014) Oxygen and Seizure Dynamics: II. Computational Modeling. J Neurophysiol [Journal] [PubMed]

Zandt BJ, ten Haken B, van Dijk JG, van Putten MJAM (2011) Neural Dynamics during Anoxia and the "Wave of Death" PLoS ONE 6(7):e22127 [Journal] [PubMed]

   Single neuron with ion concentrations to model anoxic depolarization (Zandt et al. 2011) [Model]

Zylbertal A, Kahan A, Ben-Shaul Y, Yarom Y, Wagner S (2015) Prolonged Intracellular Na+ Dynamics Govern Electrical Activity in Accessory Olfactory Bulb Mitral Cells PLOS Biology 13(12):e1002319 [Journal]

   AOB mitral cell: persistent activity without feedback (Zylbertal et al., 2015) [Model]

Zylbertal A, Yarom Y, Wagner S (2017) Synchronous infra-slow bursting in the mouse accessory olfactory bulb emerge from interplay between intrinsic neuronal dynamics and network connectivity. J Neurosci [Journal] [PubMed]

   A network of AOB mitral cells that produces infra-slow bursting (Zylbertal et al. 2017) [Model]

Zylbertal A, Yarom Y, Wagner S (2017) The Slow Dynamics of Intracellular Sodium Concentration Increase the Time Window of Neuronal Integration: A Simulation Study Front. Comput. Neurosci. 11(85):1-16 [Journal]

   Cortical Layer 5b pyr. cell with [Na+]i mechanisms, from Hay et al 2011 (Zylbertal et al 2017) [Model]

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