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

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

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

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

Bikson M, Hahn PJ, Fox JE, Jefferys JG. (2003). Depolarization block of neurons during maintenance of electrographic seizures. Journal of neurophysiology. 90 [PubMed]

Connors BW, Telfeian AE. (2000). Dynamic properties of cells, synapses, circuits, and seizures in neocortex. Advances in neurology. 84 [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. Journal of computational neuroscience. 26 [PubMed]

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

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

FRANKENHAEUSER B, HODGKIN AL. (1956). The after-effects of impulses in the giant nerve fibres of Loligo. The Journal of physiology. 131 [PubMed]

Fertziger AP, Ranck JB. (1970). Potassium accumulation in interstitial space during epileptiform seizures. Experimental neurology. 26 [PubMed]

Fröhlich F, Bazhenov M. (2006). Coexistence of tonic firing and bursting in cortical neurons. Physical review. E, Statistical, nonlinear, and soft matter physics. 74 [PubMed]

Fröhlich F, Bazhenov M, Iragui-Madoz V, Sejnowski TJ. (2008). Potassium dynamics in the epileptic cortex: new insights on an old topic. The Neuroscientist : a review journal bringing neurobiology, neurology and psychiatry. 14 [PubMed]

Fröhlich F, Bazhenov M, Timofeev I, Steriade M, Sejnowski TJ. (2006). Slow state transitions of sustained neural oscillations by activity-dependent modulation of intrinsic excitability. The Journal of neuroscience : the official journal of the Society for Neuroscience. 26 [PubMed]

Fröhlich F, Sejnowski TJ, Bazhenov M. (2010). Network bistability mediates spontaneous transitions between normal and pathological brain states. The Journal of neuroscience : the official journal of the Society for Neuroscience. 30 [PubMed]

GRAFSTEIN B. (1956). Mechanism of spreading cortical depression. Journal of neurophysiology. 19 [PubMed]

GREEN JD. (1964). THE HIPPOCAMPUS. Physiological reviews. 44 [PubMed]

Guckenheimer J. (1986). Multiple bifurcation problems for chemical reactors Physica D. 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. The Journal of physiology. 117 [PubMed]

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

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

• 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. Journal of neurophysiology. 77 [PubMed]

Kager H, Wadman WJ, Somjen GG. (2000). Simulated seizures and spreading depression in a neuron model incorporating interstitial space and ion concentrations. Journal of neurophysiology. 84 [PubMed]

Kager H, Wadman WJ, Somjen GG. (2002). Conditions for the triggering of spreading depression studied with computer simulations. Journal of neurophysiology. 88 [PubMed]

Kager H, Wadman WJ, Somjen GG. (2007). Seizure-like afterdischarges simulated in a model neuron. Journal of computational neuroscience. 22 [PubMed]

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. The Journal of neuroscience : the official journal of the Society for Neuroscience. 25 [PubMed]

Martens EA et al. (2009). Exact results for the Kuramoto model with a bimodal frequency distribution. Physical review. E, Statistical, nonlinear, and soft matter physics. 79 [PubMed]

Park EH, Durand DM. (2006). Role of potassium lateral diffusion in non-synaptic epilepsy: a computational study. Journal of theoretical biology. 238 [PubMed]

Pinsky PF, Rinzel J. (1994). Intrinsic and network rhythmogenesis in a reduced Traub model for CA3 neurons. Journal of computational neuroscience. 1 [PubMed]

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

Postnov DE, Müller F, Schuppner RB, Schimansky-Geier L. (2009). Dynamical structures in binary media of potassium-driven neurons. Physical review. E, Statistical, nonlinear, and soft matter physics. 80 [PubMed]

Shilnikov A, Calabrese RL, Cymbalyuk G. (2005). Mechanism of bistability: tonic spiking and bursting in a neuron model. Physical review. E, Statistical, nonlinear, and soft matter physics. 71 [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. Journal of computational neuroscience. 25 [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. Journal of computational neuroscience. 26 [PubMed]

Ziburkus J, Cressman JR, Barreto E, Schiff SJ. (2006). Interneuron and pyramidal cell interplay during in vitro seizure-like events. Journal of neurophysiology. 95 [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. The Journal of neuroscience : the official journal of the Society for Neuroscience. 36 [PubMed]

• Subiculum network model with dynamic chloride/potassium homeostasis (Buchin et al 2016) [Model]

Conte C, Lee R, Sarkar M, Terman D. (2018). A mathematical model of recurrent spreading depolarizations. Journal of computational neuroscience. 44 [PubMed]

• A model for recurrent spreading depolarizations (Conte et al. 2017) [Model]

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

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

Huguet G et al. (2016). Neuroprotective Role of Gap Junctions in a Neuron Astrocyte Network Model. Biophysical journal. 111 [PubMed]

• Neuroprotective Role of Gap Junctions in a Neuron Astrocyte Network Model (Huguet et al 2016) [Model]

Hübel N, Andrew RD, Ullah G. (2016). Large extracellular space leads to neuronal susceptibility to ischemic injury in a Na+/K+ pumps-dependent manner. Journal of computational neuroscience. 40 [PubMed]

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

Hübel N, Dahlem MA. (2014). Dynamics from seconds to hours in Hodgkin-Huxley model with time-dependent ion concentrations and buffer reservoirs. PLoS computational biology. 10 [PubMed]

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

Hübel N, Hosseini-Zare MS, Žiburkus J, Ullah G. (2017). The role of glutamate in neuronal ion homeostasis: A case study of spreading depolarization. PLoS computational biology. 13 [PubMed]

• The role of glutamate in neuronal ion homeostasis: spreading depolarization (Hubel et al 2017) [Model]

Hübel N, Ullah G. (2016). Anions Govern Cell Volume: A Case Study of Relative Astrocytic and Neuronal Swelling in Spreading Depolarization. PloS one. 11 [PubMed]

• An ion-based model for swelling of neurons and astrocytes (Hubel & Ullah 2016) [Model]

Janjic P, Solev D, Kocarev L. (2023). Non-trivial dynamics in a model of glial membrane voltage driven by open potassium pores Biophysical journal. 122 [PubMed]

• Glial voltage dynamics driven by Kir & K2P currents (Janjic et al 2023) [Model]

Joos B, Barlow BM, Morris CE. (2018). Calculating the Consequences of Left-Shifted Nav Channel Activity in Sick Excitable Cells. Handbook of experimental pharmacology. 246 [PubMed]

• Calculating the consequences of left-shifted Nav channel activity in sick cells (Joos et al 2018) [Model]

Kim CM, Nykamp DQ. (2017). The influence of depolarization block on seizure-like activity in networks of excitatory and inhibitory neurons. Journal of computational neuroscience. 43 [PubMed]

• Modeling epileptic seizure induced by depolarization block (Kim & Dykamp 2017) [Model]

Krishnan GP, Filatov G, Shilnikov A, Bazhenov M. (2015). Electrogenic properties of the Na?/K? ATPase control transitions between normal and pathological brain states. Journal of neurophysiology. 113 [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. (2016). Effects of polarization induced by non-weak electric fields on the excitability of elongated neurons with active dendrites. Journal of computational neuroscience. 40 [PubMed]

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

Solbrå A et al. (2018). A Kirchhoff-Nernst-Planck framework for modeling large scale extracellular electrodiffusion surrounding morphologically detailed neurons. PLoS computational biology. 14 [PubMed]

• Modelling large scale electrodiffusion near morphologically detailed neurons (Solbra et al 2018) [Model]

Stein W, Harris AL. (2022). Interneuronal dynamics facilitate the initiation of spike block in cortical microcircuits Journal of computational neuroscience. 50 [PubMed]

• Cortical Interneuron & Pyramidal Cell Model of Cortical Spreading Depression (Stein & Harris 2022) [Model]

Sætra MJ, Einevoll GT, Halnes G. (2021). An electrodiffusive neuron-extracellular-glia model for exploring the genesis of slow potentials in the brain PLoS computational biology. 17 [PubMed]

• The electrodiffusive neuron-extracellular-glia (edNEG) model (Sætra et al. 2021) [Model]

Wei Y, Ullah G, Ingram J, Schiff SJ. (2014). Oxygen and seizure dynamics: II. Computational modeling. Journal of neurophysiology. 112 [PubMed]

Zandt BJ, ten Haken B, van Dijk JG, van Putten MJ. (2011). Neural dynamics during anoxia and the "wave of death". PloS one. 6 [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 [PubMed]

• 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. The Journal of neuroscience : the official journal of the Society for Neuroscience. 37 [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 Frontiers in computational neuroscience. 11 [PubMed]

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