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Natural Fluctuations of an Electropore Show Fractional Lévy Stable Motion

Department of Biomedical Engineering and Instrumentation, Wroclaw University of Technology, 50-370 Wroclaw, Poland

Correspondence: Address reprint requests to Malgorzata Kotulska, Dept. of Biomedical Engineering and Instrumentation, Wroclaw University of Technology, 50-370 Wroclaw, Poland. E-mail: kotulska{at}pwr.wroc.pl.

Until now a stable long-lived electronanopore could be generated in a lipid membrane only under current-clamp conditions, and stochastic properties of a single nanopore have been studied by the chronopotentiometry. The current-clamp experiment introduces negative feedback, which could be responsible for the electropore fluctuations and observed 1/f ^B power spectrum. A new electroporation method, chronoamperometry after current clamp (CACC), prevents irreversible rupture of the membrane and eliminates the feedback by clamping the voltage after previous electroporation. The experiments show that the electropore size can also be stabilized under constant potential. The electropore fluctuations do not need feedback to appear. The fluctuations are self-similar with a short memory. CACC provides an effective tool for studying the natural dynamics of an electropore in various environments, which was tested with Na⁺ and Al³⁺ ions. Comparison between chronopotentiometry and CACC reveals that the feedback mainly shortens the memory of the stochastic fluctuations. Statistical analysis shows that the conductance fluctuations can be approximately modeled as a fractional Lévy stable motion for a small hydrophilic electropore, which tends to fractional Brownian motion when the electropore increases its size. A hypothesis is presented that this transition reflects a more regular shape of big nanopores.