Journal of Computational Neuroscience

, Volume 26, Issue 2, pp 159–170 | Cite as

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

  • John R. CressmanJr.Email author
  • Ghanim Ullah
  • Jokubas Ziburkus
  • Steven J. Schiff
  • Ernest Barreto


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.


Potassium dynamics Bifurcation Glia Seizures Instabilities 



This work was funded by NIH Grants K02MH01493 (SJS), R01MH50006 (SJS, GU), F32NS051072 (JRC), and CRCNS-R01MH079502 (EB).


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • John R. CressmanJr.
    • 1
    Email author
  • Ghanim Ullah
    • 2
  • Jokubas Ziburkus
    • 3
  • Steven J. Schiff
    • 2
    • 4
  • Ernest Barreto
    • 1
  1. 1.Department of Physics and Astronomy, The Center for Neural Dynamics, and The Krasnow Institute for Advanced StudyGeorge Mason UniversityFairfaxUSA
  2. 2.Center for Neural Engineering, Department of Engineering Science and MechanicsThe Pennsylvania State UniversityUniversity ParkUSA
  3. 3.Department of Biology and BiochemistryThe University of HoustonHoustonUSA
  4. 4.Departments of Neurosurgery and PhysicsThe Pennsylvania State UniversityUniversity ParkUSA

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