Ion channel gating: a first passage time analysis of the Kramers type

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.