The model of Hodgkin-Huxley is one of the most (the most?) brilliant examples of computational model explaining quantitatively a living process. In addition, the work involving mathematical modelling, numerical simulation and data-based parametrization, it marks IMHO the starting point of Systems Biology (despite the fact that the name was coined by Bertalanffy in 1928, and the domain really exploded in 1998).
The model provides a mechanistic explanation of the propagation of action potentials in axons, based on the combined behaviours of a system of ionic channels. The model itself is described in a highly cited paper (12635 times according to Google Scholar on Feb 19th 2013; However we know that GS largely underestimate citations of papers published before the “web”):
Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol. 1952 Aug;117(4):500-544. http://identifiers.org/pmc/PMC1392413/
However, this paper is the culmination of a fantastic series of articles published back to back in Journal of Physiology.
- Hodgkin AL, Huxley AF, Katz B. Measurement of current-voltage relations in the membrane of the giant axon of Loligo. J Physiol. 1952 116(4):424-448
- Hodgkin AL, Huxley AF. Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo. J Physiol. 1952 116(4):449-472
- Hodgkin AL, Huxley AF. The components of membrane conductance in the giant axon of Loligo. J Physiol. 1952 116(4):473-496
- Hodgkin AL, Huxley AF. The dual effect of membrane potential on sodium conductance in the giant axon of Loligo. J Physiol. 1952 116(4):497-506
In total, we have 126 pages that changed the way we understand how nervous systems, and ultimately our brain, function. The last article is by far the most extraordinary piece of science I personally read.
Part I analyze their experimental results and should be given to every student as a model of scientific reasoning. Their conclusions predict the existence of voltage-sensing ionic channels, different for sodium and potassium, and even the existence of their segment S4, a charged domain sensing the difference of potential and moving accordingly. Note that in 1952, they had absolutely no clues about transmembrane channels, or the nature of the excitable membrane!
In Part II, Hodgkin and Huxley start from the description of an electrical circuit, a natural starting point for them since they recorded electrical properties of the giant squid axon, and progressively derive a model that mechanistically account for each biochemical event, each structural transition of the ionic channels. They even predict the existence of four gates for the channels. Using extremely accurate experimental measurements, they fit the model and determine the values of the different parameters regulating the opening and closing of sodium and potassium channels.
Part III puts Humpty Dumpty together again. Hodgkin and Huxley gathered a system of 4 differential equations, 1 for the voltage and 1 for each type of gate, and 6 assignment rule determining the propensity of each gate type to open or close in function of the voltage. Since the unique electrical computer of Cambridge University was out of order, they then simulated the model using a hand-operated machine! The rest is history, and Hodgkin and Huxley won the 1963 Nobel Prize in Physiology or Medicine. Hodgkin-Huxley models are still used in modern multi-compartment models of neuronal systems, for instance used in the Blue Brain Project. More information can be found in the BioModels Database model of the month writen by Melanie Stefan, and on the relevant Wikipedia page.