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Searching for self-similarity in switching time and turbulent cascades in ion transport through a biochannel. A time delay asymmetry

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  • Ausloos, Marcel
  • Ivanova, Kristinka
  • Siwy, Zuzanna

Abstract

The process of ion transport through a locust potassium channel is described by means of the Fokker–Planck equation (FPE). The deterministic and stochastic components of the process of switching between various conducting states of the channel are expressed by two coefficients, D(1) and D(2), a drift and a diffusion coefficient, respectively. The FPE leads to a Langevin equation. This analysis reveals beside the well-known deterministic aspects a turbulent, cascade type of action. The (noisy-like) switching between different conducting states prevents the channel from staying in one, closed or open state. The similarity between the hydrodynamic flow in the turbulent regime and hierarchical switching between conducting states of this biochannel is discussed. A non-trivial character of D(1) and D(2) coefficients is shown, which points to different processes governing the channel's action, asymetrically depending on the history of the previously conducting states. Moreover, the Fokker–Planck and Langevin equations provide information on whether and how the statistics of the channel action change over various time scales.

Suggested Citation

  • Ausloos, Marcel & Ivanova, Kristinka & Siwy, Zuzanna, 2004. "Searching for self-similarity in switching time and turbulent cascades in ion transport through a biochannel. A time delay asymmetry," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 319-333.
  • Handle: RePEc:eee:phsmap:v:336:y:2004:i:3:p:319-333
    DOI: 10.1016/j.physa.2003.12.055
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    References listed on IDEAS

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    1. C. Renner & J. Peinke & R. Friedrich, 2001. "Markov properties of high frequency exchange rate data," Papers cond-mat/0102494, arXiv.org, revised Apr 2001.
    2. Renner, Ch. & Peinke, J. & Friedrich, R., 2001. "Evidence of Markov properties of high frequency exchange rate data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 298(3), pages 499-520.
    3. de Oliveira, César R. & Arizmendi, C.Miguel & Sanchez, Juan, 2003. "Multifractal analysis and randomness of almost periodic forced two-level systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(3), pages 400-408.
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    Cited by:

    1. Miśkiewicz, Janusz, 2012. "Economy with the time delay of information flow—The stock market case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1388-1394.

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