The Journal of Membrane Biology

, Volume 63, Issue 3, pp 165–190 | Cite as

Interpretation of current-voltage relationships for “active” ion transport systems: I. Steady-state reaction-kinetic analysis of class-I mechanisms

  • Ulf-Peter Hansen
  • Dietrich Gradmann
  • Dale Sanders
  • Clifford L. Slayman


This paper develops a simple reaction-kinetic model to describe electrogenic pumping and co- (or counter-) transport of ions. It uses the standard steady-state approach for cyclic enzyme- or carrier-mediated transport, but does not assume rate-limitation by any particular reaction step. Voltage-dependence is introduced, after the suggestion of Läuger and Stark (Biochim. Biophys. Acta211:458–466, 1970), via a symmetric Eyring barrier, in which the charge-transit reaction constants are written ask12=k 12 0 exp(zFΔΨ/2RT) andk21=k 21 0 exp(−zFΔΨ/2RT). For interpretation of current-voltage relationships, all voltage-independent reaction steps are lumped together, so the model in its simplest form can be described as a pseudo-2-state model. It is characterized by the two voltage-dependent reaction constants, two lumped voltage-independent reaction constants (K12,K21), and two reserve factors (ri,r0) which formally take account of carrier states that are indistinguishable in the current-voltage (I–V) analysis. The model generates a wide range ofI–V relationships, depending on the relative magnitudes of the four reaction constants, sufficient to describe essentially allI–V data now available on “active” ion-transport systems. Algebraic and numerical analysis of the reserve factors, by means of expanded pseudo-3-, 4-, and 5-state models, shows them to be bounded and not large for most combinations of reaction constants in the lumped pathway. The most important exception to this rule occurs when carrier decharging immediately follows charge transit of the membrane and is very fast relative to other constituent voltage-independent reactions. Such a circumstance generates kinetic equivalence of chemical and electrical gradients, thus providing a consistent definition of ion-motive forces (e.g., proton-motive force, PMF). With appropriate restrictions, it also yields both linear and log-linear relationships between net transport velocity and either membrane potential or PMF. The model thus accommodates many known properties of proton-transport systems, particularly as observed in “chemiosmotic” or energy-coupling membranes.

Key words

electrogenic pump reduced kinetic model Eyring barrier current-voltage curve ion-motive force chemical rectification 


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Copyright information

© Springer-Verlag New York Inc 1981

Authors and Affiliations

  • Ulf-Peter Hansen
    • 1
  • Dietrich Gradmann
    • 1
  • Dale Sanders
    • 1
  • Clifford L. Slayman
    • 1
  1. 1.Department of PhysiologyYale University School of MedicineNew Haven

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