[Fractal properies of gating in potential-dependent K+-channels in Lymnaea stagnalis neurons]

Sets of the channel open times, [tau(o)], and closed times, [tau(c)], and the full set of the channel open and closed times, [tau(o), tau(c)], in the activity of single voltage-dependent K+-channels in mollusc L. stagnalis neurons were analyzed using the rescaled range analysis (Hurst method), fast Fourier and wavelet transforms. It was found that the Hurst dependence for each time series could be approximated by a polygonal line with at least two slopes: H1 and H2 (Hurst exponents). The averaged values of H1 and H2 for the sets [tau(o), tau(c)] were equal to 0.61 +/- 0.03 and 0.83 +/- 0.11, respectively; for the [tau(o)] sets H1 = 0.66 +/- 0.03 and H2 = 0.95 +/- 0.10; for the [tau(c)] sets, H1 = 0.62 +/- 0.05 and H2 = 0.85 +/- 0.10. In some cases, a third slope appeared on the Hurst dependences. It was very variable and ranged between 0.5 and 1. The Hurst exponents H1, H2, and H3 characterized short, intermediate, and long time ranges, respectively. The ranges greatly varied from experiment to experiment. The data obtained show that the channel openings and closings (gating process) represent a persistent process correlated in time. The randomization of the time sets resulted in a single slope, H, of 0.52 +/- 0.02 characteristic of random processes. The results were confirmed by the fast Fourier and wavelet transforms. In addition, possible voltage dependences of Hurst exponents and their correlation with tau(o) and tau(c) were investigated. As a whole, single channel activity may be characterized as a multifractal process with a slight voltage dependence of the Hurst exponents.