Stochastic resonance with applied and induced fields: the case of voltage-gated ion channels

We consider a charged Brownian particle in an asymmetric bistable electrostatic potential biased by an externally applied or induced time periodic electric field. While the amplitude of the applied field is independent of frequency, that of the one induced by a magnetic field is. Borrowing from protein channel terminology, we define the open probability as the relative time the Brownian particle spends on a prescribed side of the potential barrier. We show that while there is no peak in the open probability as the frequency of the applied field and the bias (depolarization) of the potential are varied, there is a narrow range of low frequencies of the induced field and a narrow range of the low bias of the potential where the open probability peaks. This manifestation of stochastic resonance is consistent with experimental results on the voltage gated IKs and KCNQ1 potassium channels of biological membranes and on cardiac myocytes.