The role of the potassium inward rectifier in defining cell membrane potentials in low potassium media, analysed by computer simulation

doi:10.1016/0301-4622(93)E0104-D

Biophysical Chemistry

Volume 50, Issue 3, June 1994, Pages 345-360

https://doi.org/10.1016/0301-4622(93)E0104-D Get rights and content

Abstract

A model is presented that describes the contributions of the potassium conductance and the Na⁺/K⁺ pump to the steady state magnitude of the plasma membrane potential, V_rest, at different concentrations of potassium in the extracellular fluid: K_o. The particular properties of the potassium inward rectifier, IKR, are shown to explain that V_rest frequently depolarises on lowering K_o below a critical value, because the IKR is only conductive when V_m is near to the potassium equilibrium potential or more negative. The model aims at a generic description of the process based on compartmental analysis. It is worked out to describe V_rest in mouse muscle fibres. Sensitivity analysis demonstrates that the process of switching off the IKR depends critically on the margin between V_rest and E_K, allowed for the IKR to remain open and the power of the Na/K pump to keep this margin small during the reduction of K_o. However, cells exposed to K_o just higher than the critical value may eventually also depolarize due to excessive loss of potassium. The model also demonstrates that loss of potassium membrane selectivity after blocking the Na/K pump by ouabain requires a mechanism additional to the above mentioned properties of the inward rectifier.

References (54)

M. Mazzanti et al.
Biophys. J.
(1988)
D.G. Kennedy et al.
Biochim. Biophys. Acta.
(1990)
J.R. Balser et al.
Biophys. J.
(1991)
P. Gates et al.
Progr. Biophys. Mol. Biol.
(1989)
I.S. Cohen et al.
Biophys. J.
(1989)
S. Weidmann
(1956)
D. Noble
J. Cell. Comp. Physiol.
(1963)
N.B. Standen et al.
Pflügers Archiv
(1978)
S.M. Sims et al.
Am. J. Physiol.
(1989)
N. Uchimura et al.
J. Neurophysiol.
(1989)

T. Akiyama et al.

J. Physiol. London

(1971)

D.C. Gadsby et al.

J. Gen. Physiol.

(1977)

P.P. Nánási et al.

Pflügers Archiv

(1989)

J.Siegenbeek van Heukelom

J. Physiol. London

(1991)

H. Mølgaard et al.

Pflügers Archiv

(1980)

J.R. McCullough et al.

Circ. Res.

(1990)

J.M. Sullivan et al.

J. Neurophysiol.

(1990)

C. Miller

Science

(1991)

J.J.B. Jack et al.

(1975)

E. Carmeliet et al.

Experientia

(1987)

Hagiwara et al.

J. Membr. Biol.

(1974)

B. Katz

Arch. Sci. Physiol.

(1949)

A.L. Hodgkin et al.

J. Physiol. London

(1959)

S. Hestrin

J. Physiol. London

(1981)

H. Matsuda et al.

J. Physiol. London

(1989)

T. Brismar et al.

J. Physiol. London

(1993)

F. Lang et al.

Am. J. Physiol.

(1986)

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The role of the potassium inward rectifier in defining cell membrane potentials in low potassium media, analysed by computer simulation

Abstract

Biophys. J.

Biochim. Biophys. Acta.

Biophys. J.

Progr. Biophys. Mol. Biol.

Biophys. J.

J. Cell. Comp. Physiol.

Pflügers Archiv

Am. J. Physiol.

J. Neurophysiol.

J. Physiol. London

J. Gen. Physiol.

Pflügers Archiv

J. Physiol. London

Pflügers Archiv

Circ. Res.

J. Neurophysiol.

Science

Experientia

J. Membr. Biol.

Arch. Sci. Physiol.

J. Physiol. London

J. Physiol. London

J. Physiol. London

J. Physiol. London

Am. J. Physiol.