Action potential

From Encyclopedia of Mathematics
Jump to: navigation, search

An electrical disturbance propagated as a wave along an axon (elongated part of a nerve cell) that is considered as the way information is transmitted in the nervous system of animals. Cardiac, muscle and some endocrine cells also display action potentials with similar properties.

An action potential is observed experimentally as a displacement of voltage from its equilibrium value that takes place in a limited part of the axon and that retains its shape while it is propagated with constant speed. It appears in response to a sufficiently large stimulus, subthreshold stimulation producing a transient departure from equilibrium that is not propagated. After the passing of an action potential the axon apparently returns to its equilibrium state but the threshold value is raised for some time, the refractory period.

A special experimental setting, called a current clamp, eliminates spatial variations and the voltage curve in this case is called a stationary action potential.

Action potentials are described mathematically as undamped travelling-wave solutions of the Hodgkin–Huxley system.


[a1] A.L. Hodgkin, A. F. Huxley, "A quantitative description of membrane current and its application to conduction and excitation in nerve" J. Physiology , 117 (1952) pp. 500–544 (Reprint: Bull. Math. Biology 52 (1990), 25–71)
[a2] J. Rinzel, "Electrical excitability of cells, theory and experiment: review of the Hodgkin–Huxley foundation and an update" Bull. Math. Biology , 52 (1990) pp. 5–23
How to Cite This Entry:
Action potential. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by I.S. Labouriau (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article