The current-voltage curve for ion channels is perhaps the best known characteristic of these channels. One of the first properties measured, it is accurately known for a variety of channels. The curve is usually described by a single thermal activation energy, which is assumed to show the number of channels opening in response to a voltage step. Activation allows movement of charges as the membrane depolarizes; the putative number of charges moving to open the channel is a parameter estimated from the curve. As the activation energy, E, creates a probability dependent on exp(-E/kBT) (kBT=Boltzmann's constantxtemperature) for a given channel to reach the open state, the opening probability distribution is referred to as a Boltzmann curve. The Boltzmann calculation of the complete curve is consistent with the experimental results on the i-V curve. However, other experimental data are not so easily explained by a Boltzmann curve, and there exists an alternative. A calculation based on the assumption of a threshold potential, which, if passed, allows a channel to open, leads to an open probability vs. potential curve which is also consistent with the measured current vs. voltage curve over its entire voltage range. The calculation assumes fluctuations in the local environment, leading to a distribution of the potential at which channels cross the threshold. There is a physical mechanism which would account for such a threshold, tunneling of a proton as the mechanism of charge movement. Actually, two or more almost independent tunneling transitions are required to obtain agreement with experiment, but this changes no essential feature of the model. Because tunneling requires matching of energy levels in two wells, it is appropriately referred to as a resonance. This model also makes it possible to explain an additional experiment: Fohlmeister & Adelman (1985a, b, 1986) have shown that a sinusoidal potential added to the membrane potential produces second harmonics of the sinusoidal frequency in the output current. Similar response to a sinusoidal input is found from the model, and compared qualitatively to the published experimental results of Fohlmeister & Adelman. A time delay can also be introduced between reaching the threshold and channel opening, which is both physically necessary and necessary for agreement with experiment. Unlike the Boltzmann model, out model agrees (qualitatively) with their experiment. We have tested two distributions of state as a function of potential: Gaussian, and skewed Gaussian ( reverse similarV2 exp(-aV2), V=potential). The latter comes closer to representing both the open probability-potential curve and the Fohlmeister & Adelman results, although the pure Gaussian is still better than the Boltzmann model.Copyright 1998 Academic Press