Application of dwell-time series in studies of long-range correlation in single channel ion transport: analysis of ion current through a big conductance locust potassium channel

The time series of successive closed- and open-states durations determined for a voltage-dependent big conductance locust potassium channel (BK channel) have been analyzed. The problem of correlation between the states have been discussed by means of the autocorrelation function, Hurst and detrended fluctuation analysis (DFA) as well as surrogate data tools. We showed that the existence of correlation between closed and open times can be detected only by simultaneous application of several different tools. All techniques pointed at a stronger correlation, therefore longer memory, in the series of closed states. Persistent character of both examined dwell-time series has been shown by the Hurst and DFA analyses, whose exponents were found significantly larger than 0.5—a value typical for random walk. It may originate from the externally applied electric field, which directs ion movement and influences channel kinetics. DFA detected two ranges of different correlations in the series of closed states durations. This result points to the existence of two processes with different correlation characteristics which govern the channel functioning. The DFA exponent equal to 0.86±0.07 for long-range scaling of closed times suggests that the long memory of the BK channel action arising from the dichotomous nature of the signal and the long-tail properties of the closed-times distribution can be also governed by the correlation between closed states. The possible biological implications of the findings have been also discussed.