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diff --git a/examples/hodgkin_huxley_neron_potential/page.md b/examples/hodgkin_huxley_neron_potential/page.md new file mode 100644 index 0000000..4598c97 --- /dev/null +++ b/examples/hodgkin_huxley_neron_potential/page.md @@ -0,0 +1,86 @@ + +The Hodgkin–Huxley model, or conductance-based model, is a mathematical model +that describes how action potentials in neurons are initiated and propagated. +It is a set of nonlinear differential equations that approximates the +electrical characteristics of excitable cells such as neurons and cardiac +myocytes, and hence it is a continuous time model, unlike the Rulkov map for +example. + +Alan Lloyd Hodgkin and Andrew Fielding Huxley described the model in 1952 to +explain the ionic mechanisms underlying the initiation and propagation of +action potentials in the squid giant axon. They received the 1963 Nobel Prize +in Physiology or Medicine for this work. + +## Mathematical properties + +The Hodgkin–Huxley model can be thought of as a differential equation with four +state variables, v(t), m(t), n(t), and h(t), that change with respect to time +t. The system is difficult to study because it is a nonlinear system and cannot +be solved analytically. However, there are many numeric methods available to +analyze the system. Certain properties and general behaviors, such as limit +cycles, can be proven to exist. + +## Alternative Models + +The Hodgkin–Huxley model is regarded as one of the great achievements of 20th-century biophysics. Nevertheless, modern Hodgkin–Huxley-type models have been extended in several important ways: + +* Additional ion channel populations have been incorporated based on experimental data. + +* The Hodgkin–Huxley model has been modified to incorporate transition state + theory and produce thermodynamic Hodgkin–Huxley models. + +* Models often incorporate highly complex geometries of dendrites and axons, + often based on microscopy data. + +* Stochastic models of ion-channel behavior, leading to stochastic hybrid + systems + +Several simplified neuronal models have also been developed (such as the +FitzHugh–Nagumo model), facilitating efficient large-scale simulation of groups +of neurons, as well as mathematical insight into dynamics of action potential +generation. + + +## References + +The body of this page is from Wikipedia (see below). + +#### Papers + +"The dual effect of membrane potential on sodium conductance in the giant axon +of Loligo". *The Journal of Physiology*. **116** (4): 497–506. April 1952. +doi:10.1113/jphysiol.1952.sp004719. + +"Currents carried by sodium and potassium ions through the membrane of the +giant axon of Loligo". *The Journal of Physiology*. **116** (4): 449–72. April 1952. +doi:10.1113/jphysiol.1952.sp004717. + +"The components of membrane conductance in the giant axon of Loligo". *The +Journal of Physiology*. **116** (4): 473–96. April 1952. +doi:10.1113/jphysiol.1952.sp004718. + +"The dual effect of membrane potential on sodium conductance in the giant axon +of Loligo". *The Journal of Physiology*. **116** (4): 497–506. April 1952. +doi:10.1113/jphysiol.1952.sp004719. + +"A quantitative description of membrane current and its application to +conduction and excitation in nerve". *The Journal of Physiology*. **117** (4): +500–44. August 1952. doi:10.1113/jphysiol.1952.sp004764. + +#### Interactive Models on the Web + +* ModelDB: [Squid axon (Hodgkin, Huxley 1952)](https://senselab.med.yale.edu/ModelDB/ShowModel.cshtml?model=5426) +* Wolfram Demonstrations: + [Interactive Hodgkin-Huxley](http://demonstrations.wolfram.com/HodgkinHuxleyActionPotentialModel/) + by Shimon Marom and + [Neural Impulses: The Action Potential in Action](http://www.demonstrations.wolfram.com/NeuralImpulsesTheActionPotentialInAction/) + by Garrett Neske +* [Hodgkin-Huxley Simulation with Javascript](http://myselph.de/hodgkinHuxley.html) + by Hubert Eichner, which creates static plots in the browser. +* BioModels database: [](http://www.ebi.ac.uk/biomodels-main/BIOMD0000000020) + +#### Other Links + +* Wikipedia: [Hodgkin–Huxley model](https://en.wikipedia.org/wiki/Hodgkin%E2%80%93Huxley_model) +* [Summary of the Hodgkin-Huxley model](http://ecee.colorado.edu/~ecen4831/HHsumWWW/HHsum.html) +* [Hodgkin-Huxley model in R](http://www.magesblog.com/2012/06/hodgkin-huxley-model-in-r.html) |