Hodgkin Huxley Squid Axon Model 1952
Catherine
Lloyd
Auckland Bioengineering Institute
Model Status
This particular variant of the CellML model is based on the original model in the 1952 Hodgkin-Huxley published paper. Previous versions of the CellML model description have been modified from the original model to to be consistent with the modern convention of describing cardiac models. This particular model has been tested in both PCEnv and COR. To run the model correctly in COR you need to set the duration of the simulation to 50 ms and, to make the rendering of the results more accurate, the output to 0.1 ms.
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 CellML model itself is intended to represent the original model from the published paper. To date, all the other versions of the Hodgkin-Hulxley model have been slightly modified versions of the original published model. In particular the current descriptions were reversed to be consistent with the modern convention proposed by Prof. Denis Noble, now commonly adopted for cardiac muscle model descriptions.
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.
The complete original paper reference 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
$\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}}$
$\mathrm{E\_Na}=\mathrm{E\_R}-115\mathrm{i\_Na}=\mathrm{g\_Na}m^{3}h(V-\mathrm{E\_Na})$
$\mathrm{alpha\_m}=\frac{0.1(V+25)}{e^{\frac{V+25}{10}}-1}\mathrm{beta\_m}=4e^{\frac{V}{18}}\frac{d m}{d \mathrm{time}}=\mathrm{alpha\_m}(1-m)-\mathrm{beta\_m}m$
$\mathrm{alpha\_h}=0.07e^{\frac{V}{20}}\mathrm{beta\_h}=\frac{1}{e^{\frac{V+30}{10}}+1}\frac{d h}{d \mathrm{time}}=\mathrm{alpha\_h}(1-h)-\mathrm{beta\_h}h$
$\mathrm{E\_K}=\mathrm{E\_R}+12\mathrm{i\_K}=\mathrm{g\_K}n^{4}(V-\mathrm{E\_K})$
$\mathrm{alpha\_n}=\frac{0.01(V+10)}{e^{\frac{V+10}{10}}-1}\mathrm{beta\_n}=0.125e^{\frac{V}{80}}\frac{d n}{d \mathrm{time}}=\mathrm{alpha\_n}(1-n)-\mathrm{beta\_n}n$
$\mathrm{E\_L}=\mathrm{E\_R}-10.613\mathrm{i\_L}=\mathrm{g\_L}(V-\mathrm{E\_L})$
2002-03-26T00:00:00+00:00The Bioengineering InstituteThe University of Auckland2007-06-20T16:01:50+12:002007-06-15T12:32:55+12:00CatherineLloydMayAHodgkinL129912372002-11-20Version of model to match the original publicationWarren HedleyAlanGarny2007-06-15T12:32:55+12:002185861DavidNickerson1952-00-00 00:00AHodgkinLJamesLawsonRichardNeurongiant axonelectrophysiology2002-11-20Added more metadata.DavidNickersonThis particular variant of the CellML model is based on the original model in the 1952 Hodgkin-Huxley published paper. Previous versions of the CellML model description have been modified from the original model to to be consistent with the modern convention of describing cardiac models. This particular model has been tested in both PCEnv and COR.Correcting the equation for dv/dt.1952-01-01AHuxleyFAdded 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.CatherineLloydMayThis 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.2009-03-27T05:42:33+13:00Fixed the broken figure links.Journal of Physiologyc.lloyd@auckland.ac.nz0.1502007-06-14T07:38:16+12:000.0150000750The Journal of PhysiologyA quantitative description of membrane current and its application to conduction and excitation in nerve117500544Correcting the equation for dv/dt.keyword2002-07-19A quantitative description of membrane current and its application to conduction and excitation in nerve (Original Model)The University of Auckland, Bioengineering InstituteCatherine LloydCatherineLloydMayThe Classic Hodgkin-Huxley 1952 Model of A Squid Axon.NeuronSquid2185861AHuxleyFA quantitative description of membrane current and its application to conductance and excitation in nerve117500544