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.
$\mathrm{i_Stim}=\begin{cases}20 & \text{if (\mathrm{time}\ge 10)\land (\mathrm{time}\le 10.5)}\\ 0 & \text{otherwise}\end{cases}\frac{d V}{d \mathrm{time}}}=\frac{-(-\mathrm{i_Stim}+\mathrm{i_Na}+\mathrm{i_K}+\mathrm{i_L})}{\mathrm{Cm}}$ $\mathrm{alpha_h}=0.07e^{\frac{-(V+75)}{20}}\mathrm{beta_h}=\frac{1}{e^{\frac{-(V+45)}{10}}+1}\frac{d h}{d \mathrm{time}}}=\mathrm{alpha_h}(1-h)-\mathrm{beta_h}h$ $\mathrm{alpha_n}=\frac{-0.01(V+65)}{e^{\frac{-(V+65)}{10}}-1}\mathrm{beta_n}=0.125e^{\frac{V+75}{80}}\frac{d n}{d \mathrm{time}}}=\mathrm{alpha_n}(1-n)-\mathrm{beta_n}n$ $\mathrm{E_L}=\mathrm{E_R}+10.613\mathrm{i_L}=\mathrm{g_L}(V-\mathrm{E_L})$ $\mathrm{alpha_m}=\frac{-0.1(V+50)}{e^{\frac{-(V+50)}{10}}-1}\mathrm{beta_m}=4e^{\frac{-(V+75)}{18}}\frac{d m}{d \mathrm{time}}}=\mathrm{alpha_m}(1-m)-\mathrm{beta_m}m$ $\mathrm{E_Na}=\mathrm{E_R}+115\mathrm{i_Na}=\mathrm{g_Na}m^{3}h(V-\mathrm{E_Na})$ $\mathrm{E_K}=\mathrm{E_R}-12\mathrm{i_K}=\mathrm{g_K}n^{4}(V-\mathrm{E_K})$ Maximum plasma membrane rest potential 12991237 The Classic Hodgkin-Huxley 1952 Model of A Squid Axon. Warren Hedley This 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. 0.1 30 50000 Squid Neuron 12991237 Hodgkin A L Huxley A F A quantitative description of membrane current and its application to conductance and excitation in nerve 544 117 1952-01-01 500 Journal of Physiology Neuron giant axon electrophysiology keyword Proportion of activating molecules inside of cell Displacement of the membrane potential from its resting value Proportion of activating molecules inside cell H gate sodium ion transfer constant (in to out) Proportion of activating molecules inside cell Ionic leakage equilibrium potential Time Domain H gate sodium ion transfer constant (out to in) Time Domain Time Domain Time Domain Time Domain Displacement of the membrane potential from its resting value /08032015155118835m0500#Cell culture medium Sodium current across plasma membrane Sodium current across the plasma membrane Displacement of the membrane potential from its resting value Maximum plasma membrane rest potential Time Domain Potassium conductance of the cell membrane Proportion of activating molecules inside of cell Displacement of the membrane potential from its resting value Displacement of the membrane potential from its resting value Sodium conductance of the plasma membrane Sodium ion equilibrium potential Experimental charge stimulus. Proportion of inactivating molecules inside of cell Time Domain Time Domain M gate sodium ion transfer constant (in to out) Correcting the equation for dv/dt. 2002-11-20 Nickerson David 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. 2007-06-15T12:32:55+12:00 Lawson James Richard Correcting the equation for dv/dt. 2002-11-20 Nickerson David James Lawson This 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) Added more metadata. 2002-07-19 Lloyd Catherine May The University of Auckland, Bioengineering Institute 2002-03-26T00:00:00+00:00 2007-06-20T16:01:50+12:00 Fixed the broken figure links. 2007-06-14T07:38:16+12:00 Lloyd Catherine May A quantitative description of membrane current and its application to conduction and excitation in nerve (Original Model + Stimulus) Lloyd Catherine May c.lloyd@auckland.ac.nz The Bioengineering Institute The University of Auckland 2007-06-15T12:32:55+12:00 Ionic leak conductance of the plasma membrane Proportion of inactivating molecules inside of cell Sodium current across the plasma membrane Displacement of the membrane potential from its resting value Plasma membrane charge capacity Maximum plasma membrane rest potential N gate potassium ion transfer constant (in to out) /08032015155118835m0500#Cell culture medium Potassium current across plasma membrane Potassium current across plasma membrane Potassium current across the plasma membrane Charge flow across the plasma membrane Leak current across plasma membrane Leakage current across the plasma membrane Christopher Thompson Potassium current across the plasma membrane M gate sodium ion transfer constant (out to in) Maximum plasma membrane rest potential Potassium ion equilibrium potential N gate potassium ion transfer constant (out to in) Displacement of the membrane potential from its resting value Leakage current across the plasma membrane