Model Status
This version has had a stimulus protocol component added to allow the model to simulate multiple action potentials, has been unit checked and curated and is known to run in COR and PCEnv.
Model Structure
In a series of papers published in 1952, A.L. Hodgkin and A.F. Huxley presented the results of a series of experiments in which they investigated the flow of electric current through the surface membrane of the giant nerve fibre of a squid. In the summary paper of the Hodgkin and Huxley model, the authors developed a mathematical description of the behaviour of the membrane based upon these experiments, which accounts for the conduction and excitation of the fibre. The form of this description has been used as the basis for almost all other ionic current models of excitable tissues, including Purkinje fibres and cardiac atrial and ventricular muscle.
The summary paper is cited below:
A Quantitative Description of Membrane Current and its Application to Conduction and Excitation in Nerve, A. L. Hodgkin and A. F. Huxley, 1952, The Journal of Physiology, 117, 500-544.
PubMed ID: 12991237
Electrical circuit describing the current across the cell membrane
A schematic cell diagram describing the current flows across the cell membrane that are captured in the Hodgkin Huxley model.
$\mathrm{i\_Stim}=\begin{cases}20 & \text{if $(\mathrm{time}\ge 10)\land (\mathrm{time}\le 10.5)$}\\ 0 & \text{otherwise}\end{cases}\frac{d V}{d \mathrm{time}}=\frac{-(-\mathrm{i\_Stim}+\mathrm{i\_Na}+\mathrm{i\_K}+\mathrm{i\_L})}{\mathrm{Cm}}$
$\mathrm{E\_Na}=\mathrm{E\_R}+115\mathrm{i\_Na}=\mathrm{g\_Na}m^{3}h(V-\mathrm{E\_Na})$
$\mathrm{alpha\_m}=\frac{-0.1(V+50)}{e^{\frac{-(V+50)}{10}}-1}\mathrm{beta\_m}=4e^{\frac{-(V+75)}{18}}\frac{d m}{d \mathrm{time}}=\mathrm{alpha\_m}(1-m)-\mathrm{beta\_m}m$
$\mathrm{alpha\_h}=0.07e^{\frac{-(V+75)}{20}}\mathrm{beta\_h}=\frac{1}{e^{\frac{-(V+45)}{10}}+1}\frac{d h}{d \mathrm{time}}=\mathrm{alpha\_h}(1-h)-\mathrm{beta\_h}h$
$\mathrm{E\_K}=\mathrm{E\_R}-12\mathrm{i\_K}=\mathrm{g\_K}n^{4}(V-\mathrm{E\_K})$
$\mathrm{alpha\_n}=\frac{-0.01(V+65)}{e^{\frac{-(V+65)}{10}}-1}\mathrm{beta\_n}=0.125e^{\frac{V+75}{80}}\frac{d n}{d \mathrm{time}}=\mathrm{alpha\_n}(1-n)-\mathrm{beta\_n}n$
$\mathrm{E\_L}=\mathrm{E\_R}+10.613\mathrm{i\_L}=\mathrm{g\_L}(V-\mathrm{E\_L})$
c.lloyd@auckland.ac.nzCorrecting the equation for dv/dt.Added stimulus protocol to allow simulation of trains of action potentials. The stimulus amplitude (20 microamperes per cm2) and duration (0.5 ms) were taken from the single stimulus in the previous version. Set a period of 200 ms (arbitrary) to allow visualisation of 3 action potentials together at a resonable zoom level.LawsonJamesRichardA quantitative description of membrane current and its application to conduction and excitation in nerve (Original Model + Stimulus)The University of Auckland, Bioengineering InstituteHodgkinAL129912372007-06-15T12:32:55+12:002007-06-14T07:38:16+12:00Warren HedleyJournal of PhysiologyJames LawsonHuxleyAFThis is the CellML description of Hodgkin and Huxley's inspirational work on a mathematical description of currents through the membrane of a nerve fibre (axon) in a giant squid, and their application to the modelling of excitation in the nerve. It is generally regarded as the first example of a mathematical model of biology.2002-11-20Fixed the broken figure links.2007-06-20T16:01:50+12:00This version (07) has had a stimulus protocol component added (to version 06, by James Lawson, 15/06/07) to allow the model to simulate multiple action potentials. Version 05 was created by Penny Noble of Oxford University and is known to run in COR and PCEnv. The intial voltage membrane potential was changed from 0 mV to the correct value of -75 mV. (Version 06 is the same as version 05 but has updated documentation)LloydCatherineMaykeywordNickersonDavid12991237The Classic Hodgkin-Huxley 1952 Model of A Squid Axon.SquidNeuronLloydCatherineMayLloydCatherineMay1952-01-01Correcting the equation for dv/dt.2002-07-19NickersonDavidgiant axonelectrophysiologyNeuronA quantitative description of membrane current and its application to conductance and excitation in nerve5441175000.130500002007-06-15T12:32:55+12:00Added more metadata.2002-11-20The Bioengineering InstituteThe University of Auckland2002-03-26T00:00:00+00:00