From a biophysical point of view, action potentials are the result of currents that pass through ion channels in the cell membrane. In an extensive series of experiments on the giant axon of the squid, Hodgkin and Huxley succeeded to measure these currents and to describe their dynamics in terms of differential equations. The paper published in 1952 which presents beautiful experiments combined with an elegant mathematical theory (222), was rapidly recognized as groundbreaking work and eventually led to the Nobel Prize for Hodgkin and Huxley in 1963. In this Chapter, the Hodgkin-Huxley model is reviewed and its behavior illustrated by several examples.

The Hodgkin-Huxley model in its original form describes only three types of ion channel. However, as we will see in Section 2.3 it can be extended to include many other ion channel types. The Hodgkin-Huxley equations are the basis for detailed neuron models which account for different types of synapse, and the spatial geometry of an individual neuron. Synaptic dynamics and the spatial structure of dendrites are the topics of Chapter 3. The Hodgkin-Huxley model is also the starting point for the derivation of simplified neuron models in Chapter 4 and will serve as a reference throughout the discussion of Generalized Integrate-and-Fire models in Part II of the book.

Before we can turn to the Hodgkin-Huxley equations, we need to give some additional information on the equilibrium potential of ion channels.

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