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Goldman-Hodgkin-Katz Equations

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Encyclopedia of Computational Neuroscience

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Synonyms

GHK current equation; GHK voltage equation

Definition

There are two Goldman-Hodgkin-Katz (GHK) equations: the GHK voltage equation and the GHK current equation. The GHK voltage equation gives the membrane potential expected to result from multiple ion species at differing concentrations on either side of the membrane. The GHK current equation gives the transmembrane current of an ion species expected at a given membrane potential for a given concentration of the ion on either side of the membrane. Both equations are derived from the Nernst-Planck equation with a constant field assumption in the membrane. This assumption is not generally true in ion channels, but the equations are a useful approximation for neuronal modelling.

Detailed Description

Physical Basis

The GHK equations apply when one or more ion species exist on both sides of a membrane permeable to them. The electrical and diffusive influences on each ion are not necessarily at equilibrium, and thus there can be a...

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References

  • Goldman DE (1943) Potential, impedance, and rectification in membranes. J Gen Physiol 27:37–60

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  • Hille B (2001) Ion channels of excitable membranes, 3rd edn. Sinauer Associates, Sunderland, MA

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  • Hodgkin AL, Katz B (1949) The effect of sodium ions on the electrical activity of the giant axon of the squid. J Physiol 108:37–77

    CAS  PubMed Central  PubMed  Google Scholar 

  • Johnston D, Wu SM-S (1995) Foundations of cellular neurophysiology. MIT Press, Cambridge, MA

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Author information

Authors and Affiliations

  1. School of Informatics, University of Edinburgh, Edinburgh, UK

    David C Sterratt

Authors
  1. David C Sterratt
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Corresponding author

Correspondence to David C Sterratt .

Editor information

Editors and Affiliations

  1. Atlanta, Georgia, USA

    Dieter Jaeger

  2. Department of Biomedical Engineering, Florida International University, Miami, Florida, USA

    Ranu Jung

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© 2014 Springer Science+Business Media New York

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Sterratt, D.C. (2014). Goldman-Hodgkin-Katz Equations. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_229-1

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  • DOI: https://doi.org/10.1007/978-1-4614-7320-6_229-1

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  • Publisher Name: Springer, New York, NY

  • Online ISBN: 978-1-4614-7320-6

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