Abstract
In this paper we explore the properties of a mathematical model for the passive sodium permeability system of excitable membranes. This model is distinguished by the explicit inclusion of a rate constant which depends not on instantaneous voltage, but on rate of voltage change. Actually, the model is a rather modest modification of the Hodgkin-Huxley model, but displays some behaviors which the H-H model does not. Among these behaviors are a pronounced inactivation shift (for certain parameter values), a difference between inactivation time constant as measured by turning off a sodium current under sustained depolarization and as measured by double pulse experiments, skip runs under sustained current stimulation, and accommodation to slowing rising currents.
Full text
PDF













Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- Armstrong C. M., Bezanilla F., Rojas E. Destruction of sodium conductance inactivation in squid axons perfused with pronase. J Gen Physiol. 1973 Oct;62(4):375–391. doi: 10.1085/jgp.62.4.375. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Armstrong C. M. Inactivation of the potassium conductance and related phenomena caused by quaternary ammonium ion injection in squid axons. J Gen Physiol. 1969 Nov;54(5):553–575. doi: 10.1085/jgp.54.5.553. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Chandler W. K., Meves H. Evidence for two types of sodium conductance in axons perfused with sodium fluoride solution. J Physiol. 1970 Dec;211(3):653–678. doi: 10.1113/jphysiol.1970.sp009298. [DOI] [PMC free article] [PubMed] [Google Scholar]
- FRANKENHAEUSER B., HODGKIN A. L. The after-effects of impulses in the giant nerve fibres of Loligo. J Physiol. 1956 Feb 28;131(2):341–376. doi: 10.1113/jphysiol.1956.sp005467. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Goldman L., Schauf C. L. Inactivation of the sodium current in Myxicola giant axons. Evidence for coupling to the activation process. J Gen Physiol. 1972 Jun;59(6):659–675. doi: 10.1085/jgp.59.6.659. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Goldman L., Schauf C. L. Quantitative description of sodium and potassium currents and computed action potentials in Myxicola giant axons. J Gen Physiol. 1973 Mar;61(3):361–384. doi: 10.1085/jgp.61.3.361. [DOI] [PMC free article] [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]
- HAGIWARA S., OOMURA Y. The critical depolarization for the spike in the squid giant axon. Jpn J Physiol. 1958 Sep 15;8(3):234–245. doi: 10.2170/jjphysiol.8.234. [DOI] [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]
- Hoyt R. C., Adelman W. J., Jr Sodium inactivation. Experimental test of two models. Biophys J. 1970 Jul;10(7):610–617. doi: 10.1016/S0006-3495(70)86323-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Hoyt R. C. Sodium inactivation in nerve fibers. Biophys J. 1968 Oct;8(10):1074–1097. doi: 10.1016/S0006-3495(68)86540-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Jain M. K., Marks R. H., Cordes E. H. Kinetic model of conduction changes across excitable membranes. Proc Natl Acad Sci U S A. 1970 Oct;67(2):799–806. doi: 10.1073/pnas.67.2.799. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Jakobsson E., Moore L. E. On making models of the sodium inactivation of axonal membranes. Biophys J. 1971 Apr;11(4):385–386. doi: 10.1016/S0006-3495(71)86222-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Jakobsson E. The physical interpretation of mathematical models for sodium permeability changes in excitable membranes. Biophys J. 1973 Nov;13(11):1200–1211. doi: 10.1016/S0006-3495(73)86055-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Takashima S., Schwan H. P. Passive electrical properties of squid axon membrane. J Membr Biol. 1974;17(1):51–68. doi: 10.1007/BF01870172. [DOI] [PubMed] [Google Scholar]
- Ulbricht W. The effect of veratridine on excitable membranes of nerve and muscle. Ergeb Physiol. 1969;61:18–71. doi: 10.1007/BFb0111446. [DOI] [PubMed] [Google Scholar]
- Wei L. Y. Quantum theory of nerve excitation. Bull Math Biophys. 1971 Jun;33(2):187–194. doi: 10.1007/BF02579471. [DOI] [PubMed] [Google Scholar]
