The Hodgkin-Huxley model of the action potential
In a classic series of papers from the early 1950's, A.L. Hodgkin and A.F. Huxley performed a painstaking series of experiments on the giant axon of the squid. Based on their observations, Hodgkin and Huxley constructed a mathematical model to explain the electrical excitability of neurons in terms of discrete Na+ and K+ currents. A Java version of their Nobel prize winning model (as described in J. Physiol., 1952, 117: 500-544) is presented below:
What does the model show?
What equations does the model use?
Where can I learn more?
Known bugs
What does the model show?
The model simulates an electrical signal called an action potential that passes through the axon of a neuron. Action potentials allows neurons to communicate with one another and with muscle cells. This electrical communication makes possible all of our brain's activity and all muscle movement. After you start the model and hit the stimulate button, enough current to raise the voltage +15 mV is injected into the axon. The first time you do this, you'll observe an action potential. If you hit the stimulate button again immediately after the action potential has fired, you'll notice that another action potential does not occur. If you wait a bit longer, however, and again hit the stimulate button, an action potential will again fire. This demonstrates the "refractory period". After a neuron fires, it needs to "rest" before it can fire again. If you experiment a bit with the stimulate button, you'll notice that if you hit it quickly many times in a row you can overcome the refractory period and cause the neuron to fire.
What equations does the model use?
The first 4 equations above are the differential equations which the program repeatedly steps through. You can go look up what all the symbols mean in Hodgkin and Huxley's 1952 paper (J. Physiol., 117:500-544, p. 518)!
Where can I learn more?
The classic book on this stuff is "Ionic Channels of Excitable Membranes" by Bertil Hille. The first few chapters cover the Hodgkin-Huxley model in detail. If you are looking for something a little more introductory, I am partial to "Molecular Biology of the Cell" by Alberts, Bray, Lewis, Raff, Roberts and Watson. The book covers all of cell biology (not just neurons and the like) so it is big and expensive, but it very well written and has pretty pictures. Alternatively, you could just go to graduate school!
A much more comprehensive suite of models in Java is online at http://pb010.anes.ucla.edu/