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}}$
$\mathrm{E\_Na}=\mathrm{E\_R}-115\mathrm{i\_Na}=\mathrm{g\_Na}m^{3}h(V-\mathrm{E\_Na})$
$\mathrm{alpha\_m}=\frac{0.1(V+25)}{e^{\frac{V+25}{10}}-1}\mathrm{beta\_m}=4e^{\frac{V}{18}}\frac{d m}{d \mathrm{time}}=\mathrm{alpha\_m}(1-m)-\mathrm{beta\_m}m$
$\mathrm{alpha\_h}=0.07e^{\frac{V}{20}}\mathrm{beta\_h}=\frac{1}{e^{\frac{V+30}{10}}+1}\frac{d h}{d \mathrm{time}}=\mathrm{alpha\_h}(1-h)-\mathrm{beta\_h}h$
$\mathrm{E\_K}=\mathrm{E\_R}+12\mathrm{i\_K}=\mathrm{g\_K}n^{4}(V-\mathrm{E\_K})$
$\mathrm{alpha\_n}=\frac{0.01(V+10)}{e^{\frac{V+10}{10}}-1}\mathrm{beta\_n}=0.125e^{\frac{V}{80}}\frac{d n}{d \mathrm{time}}=\mathrm{alpha\_n}(1-n)-\mathrm{beta\_n}n$
$\mathrm{E\_L}=\mathrm{E\_R}-10.613\mathrm{i\_L}=\mathrm{g\_L}(V-\mathrm{E\_L})$
AHodgkinL12991237A quantitative description of membrane current and its application to conduction and excitation in nerve117500544The Journal of Physiology1952-00-00 00:00AHuxleyFWarren Hedley2185861A quantitative description of membrane current and its application to conductance and excitation in nerve117500544Journal of Physiology1952-01-01AHodgkinLNeurongiant axonelectrophysiologykeyword0.0175050000This 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.AHuxleyF2185861The Classic Hodgkin-Huxley 1952 Model of A Squid Axon.NeuronSquid