A resonance model gives the response to membrane potential for an ion channel: II. Simplification of the calculation, and prediction of stochastic resonance.

In a previous communication (Green, 1998), the initial step in ion channel gating for voltage-gated channels was attributed to the tunneling of a proton between groups with similar p K values, under the influence of an electric field. This is in contrast to the standard thermally activated model, which leads to a "Boltzmann equation" for the gating current. In the paper that introduced the present model, the current-voltage curve was determined from a resonance effect, in which gating began when the local voltage crossed a threshold, causing a proton to tunnel to a new location. We have therefore investigated further the consequences of tunneling as the first step in gating; we find a method of improving the previous calculation. We also calculate a consequence of our model that has yet to be experimentally looked for, stochastic resonance. With gating a threshold process, one expects that such an effect should exist. Only a small effect is predicted by our calculation, but it may be detectable. If it is it would make possible the determination of important characteristics of the initiation of gating. For this reason it is worth determining the nature of the stochastic resonance to be expected. In addition, we have investigated further the possible ways of understanding our resonance model itself. The model assumes that not all channels have the same threshold, as local perturbations in the potential interfere. We therefore assume a Gaussian distribution of the thresholds, which is simpler than in the previous paper, in which a Gaussian gave inadequate results with the method used there. In this paper, we have reduced the number of parameters to two, and obtained the current-voltage curve, gating current, the response to a large sine wave (in the previous paper, the model was more complex), and stochastic resonance.