Hurst analysis in the study of ion channel kinetics

Ion channels are protein molecules which can assume distinct open and closed conformational states. The transitions between these states can be controlled by the electrical field, ions and/or drugs. Records of unitary current events show that short open-time intervals are frequently adjacent to much longer closed-time intervals, and vice-versa, suggesting that the kinetic process has memory, i.e., the intervals are correlated in time. Here the rescaled range analysis (R/S Hurst analysis) is proposed as a method to test for correlation. Simulations were performed with a two-state Markovian model, which has no memory. The calculated Hurst coefficients (H) presented a mean +/- SD value of 0.493 +/- 0.025 (N = 100). For the Ca(2+)-activated K+ channels of Leydig cells, H was equal to 0.75, statistically different (1% level) from that calculated for the memoryless process. Randomly shuffling the experimental data resulted in an H = 0.55, not significantly different (1% level) from that found for the two-state Markovian model. For a linear three-state Markovian model, H was equal to 0.548 +/- 0.017 (N = 15), again not significantly different (1% level) from that of the memoryless process. Although the three-state Markovian model adequately describes the open- and closed-time distributions, it does not account for the correlation found in this Ca(2+)-activated K+ channel. Our results illustrate the efficacy of the R/S analysis in determining whether successive opening and closing events are correlated in time and can be of help in deciding which model should be used to describe the kinetics of ion channels.