Abstract
In the 1940s, Alan Hodgkin and Andrew Huxley clarified the fundamental physical mechanism by which electrical impulses are generated by nerve cells, and travel along axons, in animals and humans. They experimented with isolated pieces of the giant axon of the squid. They summarized their conclusions in a series of publications in 1952; the last of these papers [76] is arguably the single most influential paper ever written in neuroscience, and forms the foundation of the field of mathematical and computational neuroscience. This chapter is an introduction to the Hodgkin-Huxley model.
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Notes
- 1.
An “ordinary differential equation” (ODE) involves derivatives of functions of one variable only. By contrast, a “partial differential equation” (PDE) involves partial derivatives of functions of several variables.
- 2.
However, when a potassium channel was imaged in detail for the first time [39], decades after the work of Hodgkin and Huxley, the channel turned out to have four identical subunits.
- 3.
Denoting by v HH the “v” of Hodgkin and Huxley, our “v” is − v HH − 70 mV, in line with the notation that is now common.
Bibliography
D. A. Doyle, J. M. Cabral, R. A. Pfuetzner, A. Kuo, J. M. Gulbis, S. L. Cohen, B. T. Chait, and R. MacKinnon, The structure of the potassium channel: molecular basis of K+ conduction and selectivity, Science, 280 (1998), pp. 69–77.
A. L. Hodgkin and A. F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. (London), 117 (1952), pp. 500–544.
G. Marmont, Studies on the axon membrane. 1. A new method, J. Cell Physiol., 34 (1949), pp. 351–382.
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Börgers, C. (2017). The Classical Hodgkin-Huxley ODEs. In: An Introduction to Modeling Neuronal Dynamics. Texts in Applied Mathematics, vol 66. Springer, Cham. https://doi.org/10.1007/978-3-319-51171-9_3
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DOI: https://doi.org/10.1007/978-3-319-51171-9_3
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