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Biophys J, February 1999, p. 782-803, Vol. 76, No. 2

Kramers' Diffusion Theory Applied to Gating Kinetics of Voltage-Dependent Ion Channels

Daniel Sigg,* Hong Qian,# and Francisco Bezanilla*

 *Department of Physiology and Department of Anesthesiology, School of Medicine, University of California, Los Angeles, California 90095, and  #Department of Applied Mathematics, University of Washington, Seattle, Washington 98195 USA

Kramers' diffusion theory of reaction rates in the condensed phase is considered as an alternative to the traditional discrete-state Markov (DSM) model in describing ion channel gating current kinetics. Diffusion theory can be expected to be particularly relevant in describing high-frequency (>100 kHz) events in channel activation. The generalized voltage sensor of a voltage-dependent ion channel is treated as a Brownian motion particle undergoing spatial diffusion along a one-dimensional energy landscape. Two classes of energy landscapes are considered. The first class contains large barriers, which give rise to gating currents with two distinct time scales: the usual low-frequency decay, which can modeled with a DSM scheme, and a high-frequency component arising from intrastate relaxation. Large depolarizations reduce potential barriers to such a degree that activation rates are diffusion limited, causing the two time scales to merge. Landscapes of the second class are either featureless or contain barriers that are small compared to kT; these are termed "drift landscapes." These landscapes require a larger friction coefficient to generate slow gating kinetics. The high-frequency component that appears with barrier models is not present in pure drift motion. The presence of a high-frequency component can be tested experimentally with large-bandwidth recordings of gating currents. Topics such as frequency domain analysis, spatial dependence of the friction coefficient, methods for determining the adequacy of a DSM model, and the development of physical models of gating are explored.

Biophys J, February 1999, p. 782-803, Vol. 76, No. 2
© 1999 by the Biophysical Society   0006-3495/99/02/782/22  $2.00


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Copyright © 1999 by the Biophysical Society.