Abstract
Phase space methods and an analog computer are used to analyze the Hodgkin-Huxley non-linear differential equations for the squid giant axon membrane. V is the membrane potential, m the Na+ activation, h the Na+ inactivation, and n the K+ activation. V and m change rapidly, relative to h and n. The (V, m) phase plane of a reduced system of equations, with h and n held constant at their resting values, has three singular points: a stable resting point, a threshold saddle point, and a stable excited point. When h and n are allowed to vary, recovery and refractoriness result from the movement with subsequent disappearance of the threshold and excited points. Multiplying the time constant of n by 100 or more, and that of h by one-third, reproduces the experimental plateau action potentials obtained with tetraethylammonium by Tasaki and Hagiwara, including the phenomena of abolition and of refractoriness of the plateau duration. The equations have, transiently, two stable states, as found in the real axon by these authors. Since the theoretical membrane conductance curves differ significantly from the experimental ones, further experimental analysis of ionic currents with tetraethylammonium is needed to decide whether the Hodgkin-Huxley model can be generalized to explain these experiments completely.
Full Text
The Full Text of this article is available as a PDF (1.7 MB).
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- COLE K. S. Membrane excitation of the Hodgkin-Huxley axon; preliminary corrections. J Appl Physiol. 1958 Jan;12(1):129–130. doi: 10.1152/jappl.1958.12.1.129. [DOI] [PubMed] [Google Scholar]
- FATT P., GINSBORG B. L. The ionic requirements for the production of action potentials in crustacean muscle fibres. J Physiol. 1958 Aug 6;142(3):516–543. doi: 10.1113/jphysiol.1958.sp006034. [DOI] [PMC free article] [PubMed] [Google Scholar]
- FRANCK U. F. Models for biological excitation processes. Prog Biophys Biophys Chem. 1956;6:171–206. [PubMed] [Google Scholar]
- HODGKIN A. L., HUXLEY A. F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol. 1952 Aug;117(4):500–544. doi: 10.1113/jphysiol.1952.sp004764. [DOI] [PMC free article] [PubMed] [Google Scholar]
- HODGKIN A. L., HUXLEY A. F., KATZ B. Measurement of current-voltage relations in the membrane of the giant axon of Loligo. J Physiol. 1952 Apr;116(4):424–448. doi: 10.1113/jphysiol.1952.sp004716. [DOI] [PMC free article] [PubMed] [Google Scholar]
- SHANES A. M. Electrochemical aspects of physiological and pharmacological action in excitable cells. II. The action potential and excitation. Pharmacol Rev. 1958 Jun;10(2):165–273. [PubMed] [Google Scholar]
- SPYROPOULOS C. S. Changes in the duration of the electric response of single nerve fibers following repetitive stimulation. J Gen Physiol. 1956 Sep 20;40(1):19–25. doi: 10.1085/jgp.40.1.19. [DOI] [PMC free article] [PubMed] [Google Scholar]
- TASAKI I., HAGIWAR A. S. Demonstration of two stable potential states in the squid giant axon under tetraethylammonium chloride. J Gen Physiol. 1957 Jul 20;40(6):859–885. doi: 10.1085/jgp.40.6.859. [DOI] [PMC free article] [PubMed] [Google Scholar]