Abstract
Two stable steady states were found in the numerical solution of the Hodgkin-Huxley equations for the intact squid axon bathed in potassium-rich sea water with an externally applied inward current. Under the conditions the two stable steady-states exist, the Hodgkin-Huxley equations have a complex bifurcation structure including, in addition to the two stable steady-states, a stable limit cycle, two unstable equilibrium points, and one asymptotically stable equilibrium point. It was also concluded that two stable steady states can appear in the Hodgkin-Huxley axons when the leak current is comparable to the currents through the Na and K channels.
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Selected References
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- Aihara K., Matsumoto G. Temporally coherent organization and instabilities in squid giant axons. J Theor Biol. 1982 Apr 21;95(4):697–720. doi: 10.1016/0022-5193(82)90349-6. [DOI] [PubMed] [Google Scholar]
- FRANKENHAEUSER B., HODGKIN A. L. The action of calcium on the electrical properties of squid axons. J Physiol. 1957 Jul 11;137(2):218–244. doi: 10.1113/jphysiol.1957.sp005808. [DOI] [PMC free article] [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]
- Hassard B. Bifurcation of periodic solutions of Hodgkin-Huxley model for the squid giant axon. J Theor Biol. 1978 Apr 6;71(3):401–420. doi: 10.1016/0022-5193(78)90168-6. [DOI] [PubMed] [Google Scholar]
- Inoue I. Separation of the action potential into a Na-channel spike and a K-channel spike by tetrodotoxin and by tetraethylammonium ion in squid giant axons internally perfused with dilute Na-salt solutions. J Gen Physiol. 1980 Sep;76(3):337–354. doi: 10.1085/jgp.76.3.337. [DOI] [PMC free article] [PubMed] [Google Scholar]
- MOORE J. W. Excitation of the squid axon membrane in isosmotic potassium chloride. Nature. 1959 Jan 24;183(4656):265–266. doi: 10.1038/183265b0. [DOI] [PubMed] [Google Scholar]
- Meves H., Vogel W. Calcium inward currents in internally perfused giant axons. J Physiol. 1973 Nov;235(1):225–265. doi: 10.1113/jphysiol.1973.sp010386. [DOI] [PMC free article] [PubMed] [Google Scholar]
- SEGAL J. R. An anodal threshold phenomenon in the squid giant axon. Nature. 1958 Nov 15;182(4646):1370–1370. doi: 10.1038/1821370a0. [DOI] [PubMed] [Google Scholar]
- TASAKI I. Demonstration of two stable states of the nerve membrane in potassium-rich media. J Physiol. 1959 Oct;148:306–331. doi: 10.1113/jphysiol.1959.sp006290. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Tasaki I., Lerman L., Watanabe A. Analysis of excitation process in squid giant axons under bi-ionic conditions. Am J Physiol. 1969 Jan;216(1):130–138. doi: 10.1152/ajplegacy.1969.216.1.130. [DOI] [PubMed] [Google Scholar]