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Electrostatic calculations for an ion channel part 2 kinetic behavior of the gramicidin a channel

, : Electrostatic calculations for an ion channel part 2 kinetic behavior of the gramicidin a channel. Biophysical Journal 22(2): 221-248

A theoretical model of the gramicidin A channel is presented, and the kinetic behavior of the model is derived and compared with previous experimental results. The major assumption of the model is that the only interaction between ions in a multiply-occupied channel is electrostatic. The electrostatic calculations indicate that there will be potential wells at each end of the channel and, at high concentrations, that both wells can be occupied. The kinetics are based on 2 reaction steps: movement of the ion from the bulk solution to the well and movement between the 2 wells. The kinetics for this reaction rate approach are identical to those based on the Nernst-Planck equation in the limit where the movement between the 2 wells is rate limiting. The experimental results for Na and K are consistent with a maximum of 2 ions/channel. To explain the Tl results, it is necessary to allow 3 ions/channel. This case is compatible with the electrostatic calculations if the presence of an anion is included. The theoretical kinetics are in reasonable quantitative agreement with the following experimental measurements: single channel conductance of Na, K and Tl, bi-ionic potential and permeability ratio between Na-K and K-Tl; the limiting conductance of K and Tl at high applied voltages; current-voltage curves for Na and K at low (but not high) concentrations; and the inhibition of Na conductance by Tl. The potential well is probably located close to the channel mouth, and the conductance is partially limited by the rate of going from the bulk solution to the well. For Tl this entrance rate is probably diffusion limited.

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