Gating Models of the Anomalous Mole-Fraction Effect of Single-Channel Current in Chara

Abstract

The dependence of single-channel current on the Tl⁺/K⁺ mole fraction exhibiting a minimum at [Tl⁺]/[K⁺] of about 1:15 is proportional to open probability in bursts. Five models are suggested to explain modulation of gating by the Tl⁺/K⁺ ratio. Three models start from a channel with 4 identical subunits, each with an allosteric binding site for K⁺ or Tl⁺. In the first model, ion binding is directly observable as a transition from one Markov state to another. This model can explain the dependence of the apparent single-channel current on Tl⁺ concentrations. However, the predicted linear dependence on ion concentrations of the apparent rate constants was not observed in measurements in 25 or 250 mM KNO₃ and 250 mM Tl NO₃. The second model can overcome this problem by introducing saturation kinetics for ion binding. In the third model, gating is caused by inherent vibrations of the protein, and the rate constants of the related transitions depend on the occupation of the allosteric sites. The fourth model is based on the foot-in-the-door approach with the essential feature that two K⁺ ions in the selectivity filter are necessary to keep the pore radius suitable for K⁺ ions. The fifth model is also a foot-in-the-door model, but non-Markovian because, similar to model 3, it is assumed that the conformation of the protein (and thus the rate constants of the Markov model of the time series) depends on the force exerted by the temporal average over the states of a Markov model of ion occupation. These ions may reside in the pore itself or outside.