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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Hodgkin, A.L., Huxley, A.F.: J. Physiol. 117, 500–544 (1952)
Nernst, W.: Z. Phys. Chem. 3, 613–637 (1888)
Nernst, W.: Z. Phys. Chem. 4, 129–181 (1889)
Planck, M.: Ann. Phys. Chem. Neue Folge 39, 161–186 (1890)
Planck, M.: Ann. Phys. Chem. Neue Folge 40, 561–576 (1890)
Rall, W.: Neural theory and modeling. In: Reiss, R.F. (ed.), pp. 73–94. Standord University Press, Stanford (1964)
Perkel, D.H., et al.: Neurosci. 6, 823–837 (1981)
Holmes, W.R., Rall, W.: J. Neurophysiol. 68, 1421–1437 (1992)
Hirose, A., Murakami, S.: Neurocomp. 43, 185–196 (2002)
Goldman, D.E.: J. Gen. Physiol. 27, 37–60 (1943)
Hodgkin, A.L., Katz, B.: J. Physiol. 108, 37–77 (1949)
Rall, W.: Science. 126, 454 (1957)
Sakatani, S.: PhD thesis, Univ. of Tokyo (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sakatani, S., Hirose, A. (2004). The Spatiotemporal Dynamics of Intracellular Ion Concentration and Potential. In: Pal, N.R., Kasabov, N., Mudi, R.K., Pal, S., Parui, S.K. (eds) Neural Information Processing. ICONIP 2004. Lecture Notes in Computer Science, vol 3316. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30499-9_7
Download citation
DOI: https://doi.org/10.1007/978-3-540-30499-9_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23931-4
Online ISBN: 978-3-540-30499-9
eBook Packages: Springer Book Archive