2. Detailed Neuron Models

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. 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.

- 2.1 Equilibrium potential

- 2.2 Hodgkin-Huxley Model

- 2.3 The Zoo of Ion Channels
- 2.3.1 Sodium Channels
- 2.3.2 Potassium Channels
- 2.3.3 Low-Threshold Calcium Current
- 2.3.4 High-threshold calcium current and Ca
^{2+}-Activated Potassium Channels - 2.3.5 Calcium Dynamics

- 2.4 Synapses

- 2.5 Spatial Structure: The Dendritic Tree
- 2.5.1 Derivation of the Cable Equation
- 2.5.2 Green's Function (*)
- 2.5.3 Non-linear Extensions to the Cable Equation

- 2.6 Compartmental Models
- 2.7 Summary

Cambridge University Press, 2002

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