Hodgkin-Huxley Action Potential Model

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The voltage across membranes of excitable cells (e.g. nervous system, muscles, heart, endocrine system) transiently changes, creating a pulse-like wave called an "action potential". The action potential serves as a major signal for the initiation of many cellular and intercellular processes. The canonical mathematical-physical model of the phenomenon was presented by Alan Hodgkin and Andrew Huxley in 1952 in a series of seminal papers [2], where membrane potential dynamics is described in terms of voltage-dependent ionic conductance, dominated by four coupled ordinary differential equations. In the Demonstration presented here, the action potential is triggered by a short current stimulus. Shown are time evolutions of membrane voltage (blue trace) and conductance gates (, , and ).

Contributed by: Shimon Marom (April 2012)
Open content licensed under CC BY-NC-SA


Units: , , , and .

Rate functions:

αm=0.1 (v+40)/(1-exp(-0.1(v+40))); βm=4 exp(-0.05(v+65)); αn=-0.01(v+55)/((exp(-0.1(v+55))-1); βn =0.25 exp(-0.0125(v+65)); αh=0.07 exp(-0.05(v+65)); βh =1/((exp(-0.1(v+55))+1)


Maximal conductances are , , and for sodium, potassium, and leak, respectively. Nernst equilibrium potentials are , , and for sodium, potassium, and leak, respectively. Membrane capacitance is set to 1.


[1] B. Hille, Ion Channels of Excitable Membranes, Sunderland, MA: Sinauer, 2001.

[2] A. L. Hodgkin and A. F. Huxley, "A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve," Journal of Physiology, 117, 1952 pp. 500–544.


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