Advertisement

The Spatiotemporal Dynamics of Intracellular Ion Concentration and Potential

  • Seiichi Sakatani
  • Akira Hirose
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3316)

Abstract

It is well known that membrane potential in neuron is determined by the ion concentrations and ion permeability. However, the ion concentrations are determined by both the ion flows through ion channels and intracellular and extracellular ion flows. Therefore, it is needed to solve the ion concentrations and potential distribution simultaneously to analyze the spatiotemporal change in membrane potential. In this paper, we construct the theory for spatiotemporal dynamics of ion concentration and potential. We adopt Hodgkin–Huxley-type nonlinear conductance to express the ion permeability and use Nernst–Planck equation to denote the ion concentrations. We also assume that the electric charge is conserved at intra- and extra-cellular space and at the boundary. By using the theory, we numerically analyze the distribution of intracellular ion concentrations and potential. As a result, the following phenomena are revealed. When the cell depolarized, firstly ions flow into (or out to) only to the thin space very adjacent to the membrane by rapid ion flows through ion channels. Secondly, ions slowly diffuse far away by ion concentration gradients. The movement speeds are determined only by their diffusion coefficients and almost independent of membrane potential. This theory has a high degree of availability since it is extendable to cells with various types of ion channels.

Keywords

Planck Equation Intracellular Space Migration Speed Spatiotemporal Change Intracellular Potential 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hodgkin, A.L., Huxley, A.F.: J. Physiol. 117, 500–544 (1952)Google Scholar
  2. 2.
    Nernst, W.: Z. Phys. Chem.  3, 613–637 (1888)Google Scholar
  3. 3.
    Nernst, W.: Z. Phys. Chem.  4, 129–181 (1889)Google Scholar
  4. 4.
    Planck, M.: Ann. Phys. Chem. Neue Folge 39, 161–186 (1890)Google Scholar
  5. 5.
    Planck, M.: Ann. Phys. Chem. Neue Folge 40, 561–576 (1890)Google Scholar
  6. 6.
    Rall, W.: Neural theory and modeling. In: Reiss, R.F. (ed.), pp. 73–94. Standord University Press, Stanford (1964)Google Scholar
  7. 7.
    Perkel, D.H., et al.: Neurosci.  6, 823–837 (1981)Google Scholar
  8. 8.
    Holmes, W.R., Rall, W.: J. Neurophysiol.  68, 1421–1437 (1992)Google Scholar
  9. 9.
    Hirose, A., Murakami, S.: Neurocomp.  43, 185–196 (2002)Google Scholar
  10. 10.
    Goldman, D.E.: J. Gen. Physiol.  27, 37–60 (1943)Google Scholar
  11. 11.
    Hodgkin, A.L., Katz, B.: J. Physiol.  108, 37–77 (1949)Google Scholar
  12. 12.
    Rall, W.: Science.  126, 454 (1957)Google Scholar
  13. 13.
    Sakatani, S.: PhD thesis, Univ. of Tokyo (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Seiichi Sakatani
    • 1
    • 2
  • Akira Hirose
    • 1
  1. 1.Department of Frontier InformaticsGraduate School of Frontier Sciences, The University of TokyoTokyoJapan
  2. 2.Japan Society for the Promotion of Science 

Personalised recommendations