Book contents
- Frontmatter
- Contents
- Preface
- PART ONE FOUNDATIONS OF NEURONAL DYNAMICS
- 1 Introduction: neurons and mathematics
- 2 Ion channels and the Hodgkin–Huxley model
- 3 Dendrites and synapses
- 4 Dimensionality reduction and phase plane analysis
- PART TWO GENERALIZED INTEGRATE-AND-FIRE NEURONS
- PART THREE NETWORKS OF NEURONS AND POPULATION ACTIVITY
- PART FOUR DYNAMICS OF COGNITION
- References
- Index
2 - Ion channels and the Hodgkin–Huxley model
Published online by Cambridge University Press: 05 August 2014
- Frontmatter
- Contents
- Preface
- PART ONE FOUNDATIONS OF NEURONAL DYNAMICS
- 1 Introduction: neurons and mathematics
- 2 Ion channels and the Hodgkin–Huxley model
- 3 Dendrites and synapses
- 4 Dimensionality reduction and phase plane analysis
- PART TWO GENERALIZED INTEGRATE-AND-FIRE NEURONS
- PART THREE NETWORKS OF NEURONS AND POPULATION ACTIVITY
- PART FOUR DYNAMICS OF COGNITION
- References
- Index
Summary
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 described their dynamics in terms of differential equations. Their paper published in 1952, which presents beautiful experiments combined with an elegant mathematical theory (Hodgkin and Huxley, 1952), 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 shall 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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- Neuronal DynamicsFrom Single Neurons to Networks and Models of Cognition, pp. 28 - 57Publisher: Cambridge University PressPrint publication year: 2014
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