Diffusion models of ion-channel gating and the origin of power-law distributions from single-channel recording.

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Abstract
The lifetimes of the unitary currents from ion channels, as revealed from single-channel recording, are traditionally thought to follow exponential or multiexponential distributions. The interpretation of these event-time distributions is that the gating process follows Markov kinetics among a small number of states. There is recent evidence, however, that certain systems exhibit distributions that follow power laws or functions related to power laws. Likewise, it has been suggested that data sets that appear to be multiexponential may be fit to simple power laws as well. In this paper we propose a different view of ion-channel-gating kinetics that is consistent with these recent experimental observations. We retain the Markovian nature of the kinetics, but, in contrast to the traditional models, we suggest that ion-channel proteins have a very large number of states all of similar energy. Gating, therefore, resembles a diffusion process. We show that our simplest one-dimensional model exhibits single-channel distributions that follow power laws of the form t-a, where 1/2 .ltoreq. a .gtoreq. 3/2. Exponents determined from recent experiments approximately fall within this range. We believe that this model is consistent with modern views of protein dynamics and, thus, may provide a key to the molecular details of the gating process.