Multifractal Analysis of Ion-Channel Currents: A Comparative Study of the WTMM and MFDFA Approaches

The multifractal properties of ion-channel currents recorded from Beta vulgaris L. vacuoles were analyzed using multifractal detrended fluctuation analysis (MFDFA) and the Wavelet Transform Modulus Maxima (WTMM) method. The study covered a range of membrane potentials, different incubation times with indole-3-acetic acid (IAA), and regimes with single and multiple active channels. Clear multifractal behavior was observed, with the spectrum width, Δα, varying with voltage, biochemical modulation, and channel occupancy. A comparative analysis shows that WTMM provides a more reliable and detailed characterization of the scaling properties. In particular, WTMM yields stronger nonlinearity in the scaling exponents τ(q), clearer scaling regimes, and higher sensitivity to variations in Δα, whereas MFDFA results are affected by deviations from ideal scaling. The presence of multiple channels introduces a structured, non-monotonic dependence of Δα on voltage, indicating collective dynamics. These results demonstrate that WTMM is better suited for analyzing nonstationary, dichotomous ion-channel signals.