  The opening rate of voltage-gated potassium ion channels exhibits a
characteristic, knee-like turnover where the common exponential
voltage-dependence changes suddenly into a linear one. An explanation of this
puzzling crossover is put forward in terms of a stochastic first passage time
analysis. The theory predicts that the exponential voltage-dependence
correlates with the exponential distribution of closed residence times. This
feature occurs at large negative voltages when the channel is predominantly
closed. In contrast, the linear part of voltage-dependence emerges together
with a non-exponential distribution of closed dwelling times with increasing
voltage, yielding a large opening rate. Depending on the parameter set, the
closed-time distribution displays a power law behavior which extends over
several decades.
