Stochastic resonance in two-state model of membrane channel with comparable opening and closing rates

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Abstract
Voltage-gated ion channels in biological membranes can be modeled as two-state stochastic systems with inter-state transition probabilities that depend on external stimulus. We study analytically the passage of a signal through such a system in the presence of external noise in the case when the above dependence is arbitrary, and illustrate our approach using the two models of ion channels known in the literature. The explicit expressions for the spectral density of the output signal and noise, the signal-to-noise ratio, and the coherence function are obtained for rectangular periodic signal and dichotomous noise in a wide range of parameters. The dependence of the above quantities on the bias and on the noise amplitude demonstrates strong resonant behavior in the regions where the probabilities of channel closing and opening become equal. This resonance results from additional symmetry between channel states and differs from conventional stochastic resonance studied earlier.