  We consider an exactly tractable model of the Kramers type for the
voltage-dependent gating dynamics of single ion channels. It is assumed that
the gating dynamics is caused by the thermally activated transitions in a
bistable potential. Moreover, the closed state of the channel is highly
degenerate and embraces the whole manifold of closed substates. Opening of the
ion channel is energetically prohibited from most of the closed substates and
requires a special conformation where the voltage sensor can move along an
activation pathway and trigger the transition into the open conformation. When
the corresponding activation barrier towards the channel's opening is removed
by the applied voltage, the statistics of non-conducting time intervals become
strongly influenced by the conformational diffusion. For the corresponding
supra-threshold voltages, our model explains the origin of the power law
distribution of the closed time intervals. The exponential-linear dependence of
the opening rate on voltage, often used as an experimental fit, is also
reproduced by our model.
