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Hodgkin and Huxley (1952), Membrane Current in the Giant Squid Axon

September 2006, model of the month by Melanie I. Stefan
Original model: BIOMD0000000020

The mechanisms and rules that govern nervous impulses have been the focus of research and speculation throughout the centuries [1]. In the 1930, Alan Hodgkin and Andrew Huxley started a series of experiments and modelling to elucidate the flow of electric current through an axonal membrane. This lead to the formulation of the Hodgkin-Huxley model in 1952 [2], which has had a lasting influence on our understanding of neuronal function. Both were awarded the Nobel Prize in Physiology or Medicine in 1963.

Hodgkin and Huxley chose the giant squid axon as a model system for their experiments, since it is unusually large (around 0.5 mm in diameter) and therefore quite suitable for electrophysiological experiments [1]. In particular, it was possible to insert a micropipette into the axon and perform voltage-clamp experiments, a technique that had been devised in the 1930s by Cole and Curtis [3]. The experiments were combined with detailed quantitative modelling, which involved a considerable amount of work: Since the university computer in Cambridge was on a six-month downtime in 1951, the calculations were performed on a hand-operated machine [4]. The outcome was a sound mathematical description of the system's behaviour, now known as the Hodgkin-Huxley equations [2].

The membrane as an electrical circuit

Figure 1: The membrane as an electrical circuit (from [2])

In the Hodgkin-Huxley model, the membrane can be represented as an electrical circuit, as shown in figure 1. Ionic current through the membrane can be divided into three components: potassium current (IK), sodium current (INa), and a small leakage current (Il) caused by other ions [2]. Each component can be expressed in terms of the cell's resting potential (E), the respective equilibrium potential for each component (EK, ENa, and El), constants reflecting the conductance of each component (GK, GNa, and Gl) and additional variables representing the activation of potassium transport (n), or the activation (m) or non-inhibition (h) of sodium transport. The equation for the total ionic current thus reads:

I = GKn4(E-EK) + GNam3h(E-ENa) + Gl(E-El)

The model thus related changes in membrane potentials to conductance changes. It proved to be very powerful in describing, amongst other things, the form and amplitude of propagated action potentials, the total inward movement of sodium ions and the total outward movement of potassium ions associated with an impulse, the threshold and response during the refractory period following an axion potential and the form of subthreshold responses [2].

An example for the fit between calculated and observed action potentials is shown in figure 2: The above graph shows the results of calculations according to the Hodgkin-Huxley model; the graph below shows the experimental tracing of an action potential. But the model did not only accurately describe experimental phenomena, but went much further. As Claude Meunier and Idal Segev put it, "equations always contain much more than it first seems" [5]. Although Hodgkin and Huxley did not draw this conclusion initially, their model eventually led to the hypothesis of ion channels [6].

Theoretical and experimental action potential

Figure 2: Theoretical and experimental action potential (from [2])

Bibliographic References

  1. L. R. Squire, F. E. Bloom, S. K. McConnell, J. L. Roberts, N. C. Spitzer, and M. J. Zigmond, editors. Fundamental Neuroscience. Academic Press, 2 edition, 2003.
  2. A. L. Hodgkin and A. F. Huxley. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol, 117(4):500-544, Aug 1952. [PubMed]
  3. K. S. Cole and H. J. Curtis. Electric impedance of the squid giant axon during activity. The Journal of General Physiology, 22:649-670, 1939.
  4. A. L. Hodgkin. Chance and design in electrophysiology: an informal account of certain experiments on nerve carried out between 1934 and 1952. J Physiol, 263(1):1-21, Dec 1976. [PubMed]
  5. C. Meunier and I. Segev. Playing the devil's advocate: is the Hodgkin-Huxley model useful? Trends Neurosci, 25(11):558-563, Nov 2002. [PubMed]
  6. A. Huxley. From overshoot to voltage clamp. Trends Neurosci, 25(11): 553-558, Nov 2002. [PubMed]