Abstract
Voltage perturbation methods based upon topological concepts are used to elicit responses from the Hodgkin-Huxley (HH) nonlinear differential equations. These responses present a critical check upon the validity of the HH model for electrical activity across squid axon membrane. It is shown that when a constant current is applied such that a stable equilibrium and rhythmic firing are present, the following predictions are inherent in the HH system of equations: (a) Small instantaneous voltage perturbations to the axon given at points along its firing spike result in phase resetting curves (when new phase versus old phase is plotted) with an average slope of 1. (b) A larger voltage perturbation (from certain points along the firing spike) results in the permanent cessation of periodic firing, with membrane voltage rapidly approaching the equilibrium value. (c) A still larger perturbation yields phase resetting curves with an average slope equal to 0. These predictions, coupled with Tasaki's experimental demonstration that squid axons in excellent condition do give repetitive firing under constant current, provide a critical test of the validity of the HH model.
Full text
PDF
Images in this article
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- Fitzhugh R. Impulses and Physiological States in Theoretical Models of Nerve Membrane. Biophys J. 1961 Jul;1(6):445–466. doi: 10.1016/s0006-3495(61)86902-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Gurel O. Bifurcations in nerve membrane dynamics. Int J Neurosci. 1973;5(6):281–286. doi: 10.3109/00207457309149486. [DOI] [PubMed] [Google Scholar]
- Guttman R., Barnhill R. Oscillation and repetitive firing in squid axons. Comparison of experiments with computations. J Gen Physiol. 1970 Jan;55(1):104–118. doi: 10.1085/jgp.55.1.104. [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]
- 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]
- HUXLEY A. F. Ion movements during nerve activity. Ann N Y Acad Sci. 1959 Aug 28;81:221–246. doi: 10.1111/j.1749-6632.1959.tb49311.x. [DOI] [PubMed] [Google Scholar]
- Moore J. W., Ramon F. On numerical integration of the Hodgkin and Huxley equations for a membrane action potential. J Theor Biol. 1974 May;45(1):249–273. doi: 10.1016/0022-5193(74)90054-x. [DOI] [PubMed] [Google Scholar]
- PERKEL D. H., SCHULMAN J. H., BULLOCK T. H., MOORE G. P., SEGUNDO J. P. PACEMAKER NEURONS: EFFECTS OF REGULARLY SPACED SYNAPTIC INPUT. Science. 1964 Jul 3;145(3627):61–63. doi: 10.1126/science.145.3627.61. [DOI] [PubMed] [Google Scholar]
- Sabah N. H., Spangler R. A. Repetitive response of the Hodgkin-Huxley model for the squid giant axon. J Theor Biol. 1970 Nov;29(2):155–171. doi: 10.1016/0022-5193(70)90017-2. [DOI] [PubMed] [Google Scholar]
- Winfru A. T. Oscillatory glycolysis in yeast: the pattern of phase resetting by oxygen. Arch Biochem Biophys. 1972 Apr;149(2):388–401. doi: 10.1016/0003-9861(72)90337-2. [DOI] [PubMed] [Google Scholar]