The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. Single neuron dynamics

John R. Cressman, Ghanim Ullah, Jokubas Ziburkus, Steven J. Schiff, Ernest Barreto

Research output: Contribution to journalArticle

134 Citations (Scopus)

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. In this first paper, we construct a mathematical model consisting of a single conductance-based neuron together with intra- and extracellular ion concentration dynamics. We formulate a reduction of this model that permits a detailed bifurcation analysis, and show that the reduced model is a reasonable approximation of the full model. We find that competition between intrinsic neuronal currents, sodium-potassium pumps, glia, and diffusion can produce very slow and large-amplitude oscillations in ion concentrations similar to what is seen physiologically in seizures. Using the reduced model, we identify the dynamical mechanisms that give rise to these phenomena. These models reveal several experimentally testable predictions. Our work emphasizes the critical role of ion concentration homeostasis in the proper functioning of neurons, and points to important fundamental processes that may underlie pathological states such as epilepsy.

Original languageEnglish (US)
Pages (from-to)159-170
Number of pages12
JournalJournal of Computational Neuroscience
Volume26
Issue number2
DOIs
StatePublished - Jan 1 2009

Fingerprint

Potassium
Seizures
Sodium
Ions
Neurons
Sodium-Potassium-Exchanging ATPase
Neuroglia
Epilepsy
Homeostasis
Theoretical Models

All Science Journal Classification (ASJC) codes

  • Sensory Systems
  • Cognitive Neuroscience
  • Cellular and Molecular Neuroscience

Cite this

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The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states : I. Single neuron dynamics. / Cressman, John R.; Ullah, Ghanim; Ziburkus, Jokubas; Schiff, Steven J.; Barreto, Ernest.

In: Journal of Computational Neuroscience, Vol. 26, No. 2, 01.01.2009, p. 159-170.

Research output: Contribution to journalArticle

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