Resolving linear and non-linear interactive kinetic mechanisms for ions in membrane channels.

Thallous ion in gramicidin channels displays the anomalous molefraction effect and other behavior that suggests its permeationmechanism might be more complicated than the mechanisms for sodiumor potassium ion permeation. The permeation is modeled by eithermultistate first order kinetics where the number of states and therate constants are modified to fit the data or an ion displacementmechanism that requires higher order rate terms. Although the twoclasses of mechanism are difficult to distinguish usingcurrent-voltage data, the two classes give different responses toa modulated transmembrane potential with frequency comparable tothe rate constants for intrachannel ion transitions. Themultistate first order kinetics give currents only at themodulation frequency. Information is transmitted in the phase andamplitude of the observed current. The non-linear iondisplacement mechanism produces harmonic frequencies. A detailedspectral analysis then distinguishes the two classes of mechanismand provides a range of frequency and phase data that permitsdetermination of the appropriate rate constants.