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 in measuring these currents and describing their dynamics in terms of differential equations. In Section 2.2, the Hodgkin–Huxley model is reviewed and its behavior illustrated by several examples.

The Hodgkin–Huxley equations are the starting point for detailed neuron models which account for numerous ion channels, different types of synapse, and the specific spatial geometry of an individual neuron. Ion channels, synaptic dynamics, and the spatial structure of dendrites are the topics of Sections 2.3–2.5. The Hodgkin–Huxley model is also an important reference model for the derivation of simplified neuron models in Chapters 3 and 4. Before we can turn to the Hodgkin–Huxley equations, we need to give some additional information on the equilibrium potential of ion channels.

Equilibrium potential

Neurons are, just as other cells, enclosed by a membrane which separates the interior of the cell from the extracellular space. Inside the cell the concentration of ions is different from that in the surrounding liquid. The difference in concentration generates an electrical potential which plays an important role in neuronal dynamics. In this section, we want to provide some background information and give an intuitive explanation of the equilibrium potential.