A Fully Coupled Transient Excited State Model for the Sodium Channel. I. Conductance in the Voltage Clamped Case

Overview

Journal J Math Biol

Date 1978 Mar 3

PMID 731134

Citations 7

Authors

E Jakobsson

Affiliations

Soon will be listed here.

Abstract

The behavior under voltage clamp conditions of a coupled kinetic scheme for the sodium channel is examined. The scheme is given diagrammatically by: Numerical simulations are presented which show that this model fits the voltage clamp data which are well described by the Hodgkin-Huxley equations, but also gives the sorts of behavior anomalous to the Hodgkin-Huxley model which have been seen experimentally. Further, straightforward changes in parameter values are shown to be capable of mimicking the ways in which some axonal preparations differ from others. Detailed, but admittedly heuristic, arguments are presented for the propositions that: 1) the model is minimal; i.e. no simpler kinetic model will fit the array of data simulated, and: 2) the transient excited state is necessary; i.e. no model of comparable simplicity with pure voltage dependent kinetics will fit the array of data simulated.

Citing Articles

Frequency entrainment of squid axon membrane.

Guttman R, Feldman L, Jakobsson E J Membr Biol. 1980; 56(1):9-18.

PMID: 7441721 DOI: 10.1007/BF01869347.

The standard Hodgkin-Huxley model and squid axons in reduced external Ca++ fail to accommodate to slowly rising currents.

Jakobsson E, Guttman R Biophys J. 1980; 31(2):293-7.

PMID: 7260290 PMC: 1328786. DOI: 10.1016/S0006-3495(80)85059-4.

Kinetic models suggest bimolecular reaction steps in axonal Na+-channel gating.

Dorogi P, Neumann E Proc Natl Acad Sci U S A. 1980; 77(11):6582-6.

PMID: 6256748 PMC: 350330. DOI: 10.1073/pnas.77.11.6582.

Voltage and temperature dependence of normal and chemically modified inactivation of sodium channels. Quantitative description by a cyclic three-state model.

Schmidtmayer J Pflugers Arch. 1989; 414(3):273-81.

PMID: 2550880 DOI: 10.1007/BF00584626.

Gating current harmonics. I. Sodium channel activation gating in dynamic steady states.

Fohlmeister J, Adelman Jr W Biophys J. 1985; 48(3):375-90.

PMID: 2412603 PMC: 1329352. DOI: 10.1016/S0006-3495(85)83794-2.

References

Goldman L . Quantitative description of the sodium conductance of the giant axon of Myxicola in terms of a generalized second-order variable. Biophys J. 1975; 15(2 Pt 1):119-36. PMC: 1334599. DOI: 10.1016/s0006-3495(75)85796-1. View

Goldman L, Schauf C . Quantitative description of sodium and potassium currents and computed action potentials in Myxicola giant axons. J Gen Physiol. 1973; 61(3):361-84. PMC: 2203452. DOI: 10.1085/jgp.61.3.361. View

Eigen M . New looks and outlooks on physical enzymology. Q Rev Biophys. 1968; 1(1):3-33. DOI: 10.1017/s0033583500000445. View

HOYT R, Adelman Jr W . Sodium inactivation. Experimental test of two models. Biophys J. 1970; 10(7):610-7. PMC: 1367785. DOI: 10.1016/S0006-3495(70)86323-8. View

Moore J, Cox E . A kinetic model for the sodium conductance system in squid axon. Biophys J. 1976; 16(2 Pt 1):171-92. PMC: 1334827. DOI: 10.1016/s0006-3495(76)85673-1. View

McQuarrie D, Mulas P . Asymmetric charge distributions in planar bilayer systems. Biophys J. 1977; 17(2):103-9. PMC: 1473464. DOI: 10.1016/S0006-3495(77)85629-4. View

Rothman J, Lenard J . Membrane asymmetry. Science. 1977; 195(4280):743-53. DOI: 10.1126/science.402030. View

Schauf C . Comparison of two-pulse sodium inactivation with reactivation in Myxicola giant axons. Biophys J. 1976; 16(3):245-8. PMC: 1334835. DOI: 10.1016/S0006-3495(76)85684-6. View

HODGKIN A, HUXLEY A . A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol. 1952; 117(4):500-44. PMC: 1392413. DOI: 10.1113/jphysiol.1952.sp004764. View

10.

Jakobsson E, Scudiero C . A transient excited state model for sodium permeability changes in excitable membranes. Biophys J. 1975; 15(6):577-90. PMC: 1334740. DOI: 10.1016/S0006-3495(75)85840-1. View

11.

HOYT R . Sodium inactivation in nerve fibers. Biophys J. 1968; 8(10):1074-97. PMC: 1367656. DOI: 10.1016/S0006-3495(68)86540-3. View

12.

Rawlings P, Neumann E . Physical-chemical approach to the transient change in Na ion conductivity of excitable membranes. Proc Natl Acad Sci U S A. 1976; 73(12):4492-6. PMC: 431513. DOI: 10.1073/pnas.73.12.4492. View

13.

Oxford G, Pooler J . Selective modification of sodium channel gating in lobster axons by 2, 4, 6-trinitrophenol: Evidence for two inactivation mechanisms. J Gen Physiol. 1975; 66(6):765-79. PMC: 2226227. DOI: 10.1085/jgp.66.6.765. View

14.

Jakobsson E . The physical interpretation of mathematical models for sodium permeability changes in excitable membranes. Biophys J. 1973; 13(11):1200-11. PMC: 1484384. DOI: 10.1016/S0006-3495(73)86055-2. View

15.

Jakobsson E . An assessment of a coupled three-state kinetic model for sodium conductance changes. Biophys J. 1976; 16(4):291-301. PMC: 1334843. DOI: 10.1016/S0006-3495(76)85689-5. View

16.

Schauf C . Sodium currents in Myxicola axons. Nonexponential recovery from the inactive state. Biophys J. 1974; 14(2):151-4. PMC: 1334538. DOI: 10.1016/S0006-3495(74)70006-6. View

17.

Chandler W, HODGKIN A, MEVES H . The effect of changing the internal solution on sodium inactivation and related phenomena in giant axons. J Physiol. 1965; 180(4):821-36. PMC: 1357424. DOI: 10.1113/jphysiol.1965.sp007733. View