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Low-Dimensional Chaos in Large Conductance Ca-Activated K-Channel Gating Kinetics

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Fractals in Biology and Medicine

Part of the book series: Mathematics and Biosciences in Interaction ((MBI))

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Abstract

The dynamics of single channel gating kinetics is conventionally attributed to stochastic processes generating the open and close states of the channel. However, recent evidence has accumulated for low-dimensional deterministic dynamics in the geometric or temporal evolution of various biological systems. Representative open and close time series of a large conductance Ca-activated K-channel (BK channel), obtained from a cell-attached patch-clamp of a human pituitary cell, were studied by dynamical analysis. Dynamical analysis by nonlinear deterministic measures of the nonstationary open and close time series included geometrical reconstruction by recurrence diagrams, point correlation dimension (PD2i), “chaoticity” of time series by dynamic Lyapunov exponents, and long-range scaling properties. Statistical significance of the dynamical measures was obtained from phase-randomized data sets constructed from the original data addressing the null hypothesis that the original time series was indistinguishable from a stochastic process (linearly correlated noise). The recurrence diagrams revealed nonstationarities in the open and close data series but showed geometrically low-dimensional deterministic structure that was absent in the surrogate series. The correlation dimensions (PD2i) were 5.5 and 2.9 for open and close time series, statistically different from their surrogate counterparts (7.6 and 6.0, respectively), the small noninteger numbers suggesting low-dimensional chaos. The dynamic largest Lyapunov exponents, for most of the time series, revealed positive numbers indicative of chaotic dynamics. The asymptotic scaling exponents were > 0.5 < 1.0 for both open and close time series, suggesting the presence of scale-invariant long-range power-law correlations (“memory”). The results suggest that single ion channel gating kinetics exhibit low-dimensional chaotic dynamics and call for deterministic descriptors of channel gating, reinvestigation of other channel types and deterministic or fractal modeling.

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Author information

Authors and Affiliations

  1. Département de Physiologie, CMU, CH-1211, Genève, Switzerland

    Michael Meyer MD, PhD

  2. Department of Physiology, Max Planck Institute for experimental Medicine, Hermann-Rein-Straße 3, D-37075, Göttingen, Germany

    Michael Meyer MD, PhD

  3. Totts Gap Laboratories, Bangor, PA, 18013, USA

    J. E. Skinner

Authors
  1. Michael Meyer MD, PhD
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  2. J. E. Skinner
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Correspondence to Michael Meyer MD, PhD .

Editor information

Editors and Affiliations

  1. Laboratorio di Patologia Cellulare, Istituto Cantonale di Patologia, CH-6604, Locarno, Switzerland

    Gabriele A. Losa

  2. Centro Ricerche in Fisica e Matematica, via F. Rusco, CH-6600, Locarno, Switzerland

    Danilo Merlini

  3. Abteilung für Mathematische Physik, Universität Ulm, Albert-Einstein-Allee 11, D-89069, Ulm, Germany

    Theo F. Nonnenmacher

  4. Anatomisches Institut, Universität Bern, Bühlstrasse 26, CH-3012, Bern, Switzerland

    Ewald R. Weibel

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© 1998 Springer Basel AG

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Meyer, M., Skinner, J.E. (1998). Low-Dimensional Chaos in Large Conductance Ca-Activated K-Channel Gating Kinetics. In: Losa, G.A., Merlini, D., Nonnenmacher, T.F., Weibel, E.R. (eds) Fractals in Biology and Medicine. Mathematics and Biosciences in Interaction. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8936-0_11

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  • DOI: https://doi.org/10.1007/978-3-0348-8936-0_11

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9834-8

  • Online ISBN: 978-3-0348-8936-0

  • eBook Packages: Springer Book Archive

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