Abstract
The kinetics of the alamethicine channel incorporated into BLM was studied using detrended fluctuation analysis and multifractal detrended fluctuation analysis. Detrended fluctuation analysis has shown that both the event series formed with dwell times on fixed channel conductivity levels and the event series formed with opened states on all channel conductivity levels are random processes. However, multifractal detrended fluctuation analysis indicated that only dwell times series on fixed channel conductivity levels are random, but the event series formed with opened states on all channel conductivity levels are the correlated multifractal processes.
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McManus, O.B. and Magleby, K.L., Inverse Relationship of the Durations of Adjacent Open and Shut Intervals For C1 and K Channels, Nature, 1985, vol. 317, pp. 625–627.
Rothberg, B.S., Bello, R.A., and Magleby, O.B., Two-Dimensional Components and Hidden Dependencies Provide Insight into Ion Channel Gating Mechanisms, Biophys. J., 1997, vol. 72, pp. 2524–2544.
Mcmanus, O.B. and Magleby, K.L., Kinetic Time Constants Independent of Previous Single-Channel Activity Suggest Markov Gating for a Large Conductance Ca-Activated K Channel, J. Gen. Physiol., 1989, vol. 64, pp. 1037–1070.
Mcmanus, O.B., Weiss, D.S., Spivak, C.E., Blatz, A.L., and Magleby, K.L., Fractal Models Are Inadequate for the Kinetics of Four Different Ion Channels, Biophys. J., 1988, vol. 54, pp. 859–870.
Liebovitch, L.S., Fichberg, J., and Koniarek, J.P., Fractal Model of Ion Channel Kinetics, J. Gen. Physiol., 1986, vol. 88, pp. 34a–35a.
Liebovitch, L.S., Fichberg, J., Koniarek, J.P., Todorova, I., and Wang, M., Fractal Model of Ion-Channel Kinetics, Biochim. Biophys. Acta, 1987, vol. 896, pp. 173–180.
Liebovitch, L.S. and Sullivan, J.M., Fractal Analysis of a Voltage-Dependent Potassium Channel from Cultured Mouse Hippocampal Neurons, Biophys. J., 1987, vol. 52, pp. 979–988.
Liebovitch, L.S. and Toth, T.I., A Model of Ion Channel Kinetics Using Deterministic Chaotic Rather Than Stochastic Processes, J. Theor. Biol., 1991, vol. 148, pp. 243–267.
Nogueira, R.A., Varanda, W.A., and Liebovitch, L.S., Hurst Analysis in the Study of Ion Channel Kinetics, Brasil. J. Med. Biol. Res., 1995, vol. 28, pp. 491–496.
Varanda, W.A., Liebovitch, L.S., Figueiroa, J.N., and Nogueira, R.A., Hurst Analysis Applied to the Study of Single Calcium-Activated Potassium Channel Kinetics, J. Theor. Biol., 2000, vol. 206, pp. 343–353.
Kochetkov, K.V., Kazachenko, V.N. Aslanidi, O.V., Chemeris, N.K., and Gapeev, A.B., Non-Markovian Gating of Ca2+-Activated K+ Channels in Cultured Kidney Cells Vero. Rescaled Range Analysis, J. Biol. Phys., 1999, vol. 25, pp. 211–222.
Kochetkov, K.V., Kazachenko, V.N., and Aslanidi, O.V., Time Correlation of Events in the Ion Channel Gating. Rescaled Range Method, Biologicheskie Membrany (Rus.), 2001, vol. 18(1), pp. 51–66.
Kazachenko, V.N., Kochetkov, K.V., Aslanidi, O.V., and Grinevich, A.A., Study of the Ion Channel Gating Fractal Properties with Fat Fourier Transfom, Biofizika, 2001, vol. 46, pp. 1062–1070.
Kochetkov, K.V., Kazachenko, V.N., and Aslanidi, O.V., Using Wavelet Transform to Analyse Single Ion Channels Activity, Biologicheskie Membrany (Rus.), 2003, vol. 20, pp. 359–368.
Kazachenko, V.N., Kochetkov, K.V., Astashev, M.E., and Grinevich, A.A., Fractal Properties of the Gating of Potential-Dependent K+-Channel in Lymnaea stagnalis Neurons, Biofizika (Rus.), 2004, vol. 49(5), pp. 852–865.
Brazhe, A.R., Astashev, M.E., Maksimov, G.V., Kazachenko, V.N., and Rubin, A.B., The Local Hurst Exponents Calculating for Dwell-Times Series of Ca2+-Activated K+-Channels, Biofizika (Rus.), 2004, vol. 49, pp. 1075–1083.
Vergara, C., Latorre, R., Marrion, N.V., and Adelman, J.P., Calcium-Activated Potassium Channel, Curr. Opin. Neurobiol., 1998, vol. 8, pp. 321–329.
Ovchinnikov, Yu.A., Ivanov, V.T., and Shkro, A.M., Membrannye kompleksy (Membrane Complexes), Moscow: Nauka, 1974.
Gordon, L.G.M. and Haydon, D.A., The Unit Conductance Channel of Alamethicin, Biochim. Biophys. Acta, 1972, vol. 255, pp. 1014–1018.
Boheim, G., Statistical Analysis of Alamethicin Channels in Black Lipid Membranes, J. Membrane Biol., 1974, vol. 19, pp. 277–303.
Bezrukov, S.M. and Vodyanoy, I., Probing Alamethicin Channels with Water-Soluble Polymers. Effect on Conductance of Channel States, Biophys. J., 1993, vol. 64, pp. 16–25.
Ermshkin, L.N., Grigoriev, P.A., and Iljasov, F.E., Short-Living Substates of Alamethicin Channel, Biofizika (Rus.), 1988, vol. 5(5), pp. 544–550.
Peng, C.-K., Buldyrev, S.V., Havlin, S., Simons, M., Stanley, H.E., and Golberger, A.L., Scaling Features of Noncoding DNA, Phys. Rev. E, 1994, vol. 49, no. 2, pp. 1685–1689.
Kantelhardt, J.W., Zschiegner, S.A., Koscielny-Bunde, E., Bunde, A., Havlin, S., and Stanley, H.E., Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series, Physica A, 2002, vol. 316, p. 87.
Whitcher, B. and Jensen, M.J., Wavelet Estimation of a Local Long Memory Parameter, Exploration Geophys., 2002, vol. 31, pp. 094–103.
Hurst, H.E., Methods of Using Long-Term Storage in Reservoirs, Trans. Amer. Soc. Civ. Engs., 1951, vol. 116, pp. 770–808.
Nogueira, R.A., Varanda, W.A., and Liebovitch, L.S., Hurst Analysis in the Study of Ion Channel Kinetics, Brasil. J. Med. Biol. Res., 1995, vol. 28, pp. 491–496.
Varanda, W.A., Liebovitch, L.S., Figueiroa, J.N., and Nogueira, R.A., Hurst Analysis Applied to the Study of Calcium-Activated Potassium Channel Kinetics, J. Theor. Biol., 2000, vol. 206, pp. 343–353.
Brazhe, A.R., Multifractal Analysis of the Dwell-Times Series of Potassium Channels, Graduation Thesis (Moscow, 2003).
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Original Russian Text © M.E. Astashev, V.N. Kazachenko, P.A. Grigoriev, 2007, published in Biologicheskie Membrany, 2007, Vol. 24, No. 3, pp. 251–258.
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Astashev, M.E., Kazachenko, V.N. & Grigoriev, P.A. Alamethicin channel kinetics: Studies using fluctuation analysis and multifractal fluctuation analysis. Biochem. Moscow Suppl. Ser. A 1, 246–252 (2007). https://doi.org/10.1134/S1990747807030087
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DOI: https://doi.org/10.1134/S1990747807030087