Stochastic origins of the long-range correlations of ionic current fluctuations in membrane channels

An explicit stochastic representation of a stationary ionic current signal recorded from a single channel of a biological membrane is presented. In the framework of the proposed approach we show how the dichotomous time structure of the signal leads to the non-Markovian character of the channel current. The rescaled range Hurst and detrended fluctuation analyses confirm the theoretical result. To investigate the ionic current fluctuations we introduce the Orey index as a statistical method providing additional information on the properties of stochastic processes. In order to reveal any differences between the experimental and reconstructed signals, we apply also the statistical tests to the model-based simulations of the channel action.